02186nam a22003735a 45000010009000000030012000090050017000210060019000380070015000570080041000720200018001130240021001310400014001520720017001660840036001831000031002192450068002502600082003183000034004003360026004343370026004603380036004863470024005224900061005465060066006075200866006736500032015396500048015716500040016196500029016596500024016888560032017128560068017444-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20040131sz fot ||| 0|eng d a978303719504870a10.4171/0042doi ach0018173 7aPBKG2bicssc a58-xxa35-xxa46-xxa81-xx2msc1 aWehrheim, Katrin,eauthor.10aUhlenbeck Compactnessh[electronic resource] /cKatrin Wehrheim3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2004 a1 online resource (219 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book gives a detailed account of the analytic foundations of gauge theory – Uhlenbeck’s compactness theorems for general connections and for Yang–Mills connections. It intends to guide graduate students into the analysis of Yang–Mills theory as well as to serve as a reference for researchers in the field.
The book is largely self-contained. It contains a number of appendices (e.g. on Sobolev spaces of maps between manifolds) and an introductory part covering the Lp-regularity theory for the inhomogenous Neumann problem. The two main parts contain the full proofs of Uhlenbeck’s weak and strong compactness theorems on closed manifolds as well as their generalizations to manifolds with boundary and noncompact manifolds. These parts include a number of useful analytic tools such as general patching constructions and local slice theorems.07aFunctional analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc07aFunctional analysis2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/004423cover imageuhttps://www.ems-ph.org/img/books/wehrheim_mini.jpg02008nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400290018410000270021324500900024026000820033030000340041233600260044633700260047233800360049834700240053449000510055850600660060952007000067565000470137565000310142265000400145365000550149385600320154885600660158012-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080626sz fot ||| 0|eng d a978303719563570a10.4171/0632doi ach0018173 7aPBMP2bicssc a53-xxa16-xxa32-xx2msc1 aSeidel, Paul,eauthor.10aFukaya Categories and Picard–Lefschetz Theoryh[electronic resource] /cPaul Seidel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (334 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe central objects in the book are Lagrangian submanifolds and their
invariants, such as Floer homology and its multiplicative structures,
which together constitute the Fukaya category. The relevant aspects
of pseudo-holomorphic curve theory are covered in some detail, and
there is also a self-contained account of the necessary homological
algebra.
Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations, and contains many previously unpublished results. The book will be of
interest to graduate students and researchers in symplectic geometry
and mirror symmetry.
Winner 2010 AMS Veblen Prize in Geometry.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aAssociative rings and algebras2msc07aSeveral complex variables and analytic spaces2msc40uhttps://doi.org/10.4171/063423cover imageuhttps://www.ems-ph.org/img/books/seidel_mini.jpg02690nam a22004335a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200160018307200160019908400290021510000310024424501390027526000820041430000340049633600260053033700260055633800360058234700240061849000530064250600660069552011410076165000370190265000200193965000260195965000530198565000230203865000380206170000290209970000290212885600320215785600670218915-210304CH-001817-320210304234502.0a fot ||| 0|cr nn mmmmamaa210304e20031215sz fot ||| 0|eng d a978303719500070a10.4171/0002doi ach0018173 7aPBT2bicssc 7aPBF2bicssc 7aPBR2bicssc a60-xxa11-xxa12-xx2msc1 aArratia, Richard,eauthor.10aLogarithmic combinatorial structures: a probabilistic approachh[electronic resource] /cRichard Arratia, A. D. Barbour, Simon Tavaré3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2003 a1 online resource (374 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of `typical' elements of large size. For instance, the total number of components grows logarithmically with the size of the element, and the size of the largest component is an appreciable fraction of the whole.
This book explains the similarities in asymptotic behaviour as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient. The book is thus of particular interest to graduate students and researchers in both combinatorics and probability theory.07aProbability & statistics2bicssc07aAlgebra2bicssc07aNumber theory2bicssc07aProbability theory and stochastic processes2msc07aNumber theory2msc07aField theory and polynomials2msc1 aBarbour, A. D.,eauthor.1 aTavaré, Simon,eauthor.40uhttps://doi.org/10.4171/000423cover imageuhttps://www.ems-ph.org/img/books/arratia_mini.jpg01708nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000300019924501010022926000820033030000340041233600260044633700260047233800360049834700240053449000510055850600660060952005170067565000350119265000460122785600320127385600650130516-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20040531sz fot ||| 0|eng d a978303719503170a10.4171/0032doi ach0018173 7aPBKJ2bicssc a37-xx2msc1 aPesin, Yakov B.,eauthor.10aLectures on partial hyperbolicity and stable ergodicityh[electronic resource] /cYakov B. Pesin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2004 a1 online resource (128 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is an introduction to the modern theory of partial hyperbolicity with applications to stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of the theory and describes all the basic concepts and major results that have been obtained in the area since its creation around the early 1970s. It can be used as a textbook for a graduate student course and is also of interest to professional mathematicians working in the field of dynamical systems and their applications.07aDifferential equations2bicssc07aDynamical systems and ergodic theory2msc40uhttps://doi.org/10.4171/003423cover imageuhttps://www.ems-ph.org/img/books/pesin_mini.jpg03259nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400220018310000350020524501170024026000820035730000330043933600260047233700260049833800360052434700240056049000500058450600660063452020050070065000200270565000430272565000400276885600320280885600690284018-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20040228sz fot ||| 0|eng d a978303719502470a10.4171/0022doi ach0018173 7aPBF2bicssc a17-xxa22-xx2msc1 aOnishchik, Arkady L.,eauthor.10aLectures on Real Semisimple Lie Algebras and Their Representationsh[electronic resource] /cArkady L. Onishchik3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2004 a1 online resource (95 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn 1914, E. Cartan posed the problem to find all irreducible real
linear Lie algebras. An updated exposition of his work was given by
Iwahori (1959). This theory reduces the classification of irreducible
real representations of a real Lie algebra to a description of the
so-called self-conjugate irreducible complex representations of this
algebra and to the calculation of an invariant of such a representation
(with values +1 or -1) which is called the index. Moreover, these two
problems were reduced to the case when the Lie algebra is simple and
the highest weight of its irreducible complex representation is
fundamental. A complete case-by-case classification for all simple real
Lie
algebras was given (without proof) in the tables of Tits (1967). But
actually a general solution of these problems is contained in a paper
of Karpelevich (1955) (written in Russian and not widely known), where
inclusions between real forms induced by a complex representation were
studied.
We begin with a simplified (and somewhat extended and corrected)
exposition of the main part of this paper and relate it to the theory
of Cartan-Iwahori. We conclude with some tables, where an involution of
the Dynkin diagram which allows us to find self-conjugate
representations is described and explicit formulas for the index are
given. In a short addendum, written by J. v. Silhan, this involution is
interpreted in terms of the Satake diagram.
The book is aimed at students in Lie groups, Lie algebras and their
representations, as well as researchers in any field where these
theories are used. The reader is supposed to know the classical theory
of complex semisimple Lie algebras and their finite dimensional
representation; the main facts are presented without proofs in Section
1. In the remaining sections the exposition is made with detailed
proofs, including the correspondence between real forms and involutive
automorphisms, the Cartan decompositions and the con...07aAlgebra2bicssc07aNonassociative rings and algebras2msc07aTopological groups, Lie groups2msc40uhttps://doi.org/10.4171/002423cover imageuhttps://www.ems-ph.org/img/books/onishchik_mini.jpg02535nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000390019924501000023826000820033830000340042033600260045433700260048033800360050634700240054249000510056650600660061752013330068365000310201665000450204785600320209285600730212419-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080205sz fot ||| 0|eng d a978303719505570a10.4171/0052doi ach0018173 7aPHRD2bicssc a83-xx2msc1 aChristodoulou, Demetrios,eauthor.10aMathematical Problems of General Relativity Ih[electronic resource] /cDemetrios Christodoulou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (157 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aGeneral Relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton’s theory of gravitation as well as Newton’s equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of
Gauss’ intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems.
One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether’s fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler–Lagrange system of partial differential equations. Another method is the study and systematic use of foliations by characteristic (null) hypersurfaces, and is in the spirit of the approach of Roger Penrose in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media.
The book is intended for advanced students and researchers seeking an introduction into the methods and applications of general relativity.07aGeneral relativity2bicssc07aRelativity and gravitational theory2msc40uhttps://doi.org/10.4171/005423cover imageuhttps://www.ems-ph.org/img/books/christodoulou_mini.jpg02497nam a22003975a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400360020110000360023724501030027326000820037630000340045833600260049233700260051833800360054434700240058049000510060450600660065552010420072165000470176365000350181065000310184565000400187665000380191665000480195485600320200285600650203421-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20041025sz fot ||| 0|eng d a978303719506270a10.4171/0062doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc a53-xxa35-xxa57-xxa58-xx2msc1 aChang, Sun-Yung Alice,eauthor.10aNon-linear Elliptic Equations in Conformal Geometryh[electronic resource] /cSun-Yung Alice Chang3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2004 a1 online resource (100 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aNon-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian.
In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g. higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aDifferential geometry2msc07aPartial differential equations2msc07aManifolds and cell complexes2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/006423cover imageuhttps://www.ems-ph.org/img/books/chang_mini.jpg02110nam a22003975a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400360020110000370023724501210027426000820039530000340047733600260051133700260053733800360056334700240059949000820062350600660070552006230077165000290139465000470142365000240147065000410149465000550153565000180159085600320160885600720164022-141027CH-001817-320141027234500.0a fot ||| 0|cr nn mmmmamaa141027e20140118sz fot ||| 0|eng d a978303719632870a10.4171/1322doi ach0018173 7aPBKD2bicssc 7aPBMP2bicssc a26-xxa30-xxa32-xxa51-xx2msc1 aPapadopoulos, Athanase,eauthor.10aMetric Spaces, Convexity and Nonpositive Curvatureh[electronic resource] :bSecond edition /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (320 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v61 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. It also contains a systematic introduction to metric geometry, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature.
The concepts and the techniques are illustrated by many examples, in particular from hyperbolic geometry, Hilbert geometry and Teichmüller
theory.
For the second edition, some corrections and a few additions have been made, and the bibliography has been updated.07aComplex analysis2bicssc07aDifferential & Riemannian geometry2bicssc07aReal functions2msc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc07aGeometry2msc40uhttps://doi.org/10.4171/132423cover imageuhttps://www.ems-ph.org/img/books/papadopoulos_mini.jpg07500nam a22003135a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200150016724501100018226000820029230000340037433600260040833700260043433800360046034700240049650544360052050600660495652020160502265000240703870000260706285600320708885600660712023-091109CH-001817-320091109150325.0a fot 1|| 0|cr nn mmmmamaa091109e20050630sz fot 1|| 0|eng d a978303719509370a10.4171/0092doi ach0018173 7aPB2bicssc10aEuropean Congress of Mathematics Stockholm, June 27 – July 2, 2004h[electronic resource] /cAri Laptev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2005 a1 online resource (897 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tStructure of Null Sets in the Plane and Applications /rGiovanni Alberti, Marianna Csörnyei, David Preiss --tSome Open Questions about Symplectic 4-manifolds, Singular Plane Curves and Braid Group Factorizations /rDenis Auroux --tHarmonic Measure on Fractal Sets /rD. Beliaev, Stanislav Smirnov --tSingular Approximations to Hyperbolic Systems of Conservation Laws /rStefano Bianchini --tRepresentation Theory and Random Point Processes /rAlexei Borodin, Grigori Olshanski --tStability of Relaxation Models for Conservation Laws
/rFrançois Bouchut --tHyperbolic 3-manifolds and the Geometry of the Curve Complex /rBrian H. Bowditch --tProof of an Intersection Theorem via Fourier Analysis /rEhud Friedgut --tNonlinear Schrödinger Equations on Compact Manifolds /rPatrick Gérard --tA Probabilistic Approach to Some Problems in von Neumann Algebras /rAlice Guionnet --tSingular Elements of Affine Kac–Moody Groups /rStefan Helmke, Peter Slodowy --tOn the Camassa–Holm and Hunter–Saxton equations /rHelge Holden --tMultiple Scales Asymptotics for Atmospheric Flows /rRupert Klein, Eileen Mikusky, Antony Owinoh --tProof Complexity /rJan Krajícek --tHorizontal Configurations of Points in Link Complements /rDaan Krammer --tInvariant Measures for Multiparameter Diagonalizable Algebraic Actions - A Short Survey /rElon Lindenstrauss --tPhase Transition Phenomena in Random Discrete Structures /rTomasz Łuczak --tSystems Controlled by Rough Paths /rTerry J. Lyons --tThe Stable Mapping Class Group and Stable Homotopy Theory /rJørgen Ellegaard Andersen, Michael Weiss --tA Non-asymptotic Theory for Model Selection /rPascal Massart --tReflection, Bernoulli Numbers and the Proof of Catalan's Conjecture /rPreda Mihailescu --tF-thresholds and Bernstein–Sato Polynomials /rMircea Mustaţă, Shunsuke Takagi, Kei-ichi Watanabe --tHyperkähler Manifolds and Algebraic Geometry /rKieran G. O'Grady --tSumsets /rImre Z. Ruzsa --tMeasurable Group Theory /rYehuda Shalom --tSome Mathematical Problems of Neural Networks Theory /rM. Shcherbina --tZeroes of Gaussian Analytic Functions /rMikhail Sodin --tPainlevé's Problem, Analytic Capacity and Curvature of Measures /rXavier Tolsa --tRegularization Techniques for Singular Source Terms in Differential Equations /rAnna-Karin Tornberg --tEquilibrium Measures and Polynomials /rVilmos Totik --tSLE, Conformal Restriction, Loops /rWendelin Werner --tOn the Integral Points on Certain Algebraic Varieties /rUmberto Zannier --tSome Problems Related with Holomorphic Functions on Tube Domains over Light Cones /rAline Bonami --tHyperbolic PDEs, Kinetic Formulation, Geometric Measure Theory /rYann Brenier --tRandom Dynamics in Spatially Extended Systems /rFrank den Hollander --tAnalysis and Operators 2000-2004 - Four Years of Network Activity /rJean Esterle --tAnalysis of the Bottom of the Spectrum of Schrödinger Operators with Magnetic Potentials and Applications /rBernard Helffer --tMathematical Aspects of Quantum Chaos /rJ.P. Keating --tThe Research Training Network “Algebraic Combinatorics in Europe” /rChristian Krattenthaler --tAlgebras with Involution and Adjoint Groups /rMarina Monsurrò --tConstructing Algebraic Varieties via Commutative Algebra /rMiles Reid --tMathematical Problems of Large Quantum Systems /rRyszard Nest --tThe Grothendieck-Teichmüller Group and Galois Theory of the Rational Numbers – European Network GTEM /rJakob Stix --tHydrodynamic Limits /rFrançois Golse --tMathematical Aspects of Mean Field Spin Glass Theory /rFrancesco Guerra --tComplexity Theory, Proofs and Approximation /rJohan Håstad --tRandom Surfaces Enumerating Algebraic Curves /rElliott H. Lieb --tOn Heegaard Diagrams and Holomorphic Disks /rPeter S. Ozsváth, Zoltán Szabó --tEmergence of Symmetry: Conformal Invariance in Scaling Limits of Random Systems /rMichael H. Freedman --tRecent Progresses in Kähler and Complex Algebraic Geometry /rClaire Voisin --tIsoperimetric Inequalities, Probability Measures and Convex Geometry /rFranck Barthe --tSymplectic Topology and Algebraic Families /rPaul Biran --tVortices in the Ginzburg-Landau Model of Superconductivity /rSylvia Serfaty --tValidated Numerics for Pedestrians /rWarwick Tucker --tFrom Classical to Non-commutative Iwasawa Theory: An Introduction to the GL2 Main Conjecture /rOtmar Venjakob.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996 and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004 with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six “Science Lectures” covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prize winners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prize winners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today.
Plenary lectures
François Golse (Paris, France)
Francesco Guerra (Roma, Italy)
Johan Håstad (Stockholm, Sweden)
Andrei Okounkov (Princeton, USA)
Oded Schramm (Microsoft Research, USA)
Zoltán Szabó (Princeton, USA)
Claire Voisin (Paris, France)
Invited Lectures
Giovanni Alberti (Pisa, Italy)
Denis Auroux (MIT, USA and Palaiseau, France)
Stefano Bianchini (Rome, Italy)
François Bouchut (Paris, France)
Brian Bowditch (Southampton, UK)
Ehud Friedgut (Jerusalem, Israel)
Patrick Gérard (Orsay, France)
Alice Guionnet (Lyon, France)
Stefan Helmke (Kyoto, Japan)
Helge Holden (Trondheim, Norway)
Rupert Klein (Berlin, Germany)
Jan Krajícek (Prague, Czech Republic)
Daan Krammer (Warwick, UK)
Elon Lindenstrauss (Clay Mathematics Institute, USA)
Tomas...07aMathematics2bicssc1 aLaptev, Ari,eeditor.40uhttps://doi.org/10.4171/009423cover imageuhttps://www.ems-ph.org/img/books/laptev_mini.jpg04005nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018324501550019826000820035330000340043533600260046933700260049533800360052134700240055749000820058150517630066350600660242652008410249265000310333365000280336470000330339270000300342570000300345570000350348585600320352085600670355224-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20050531sz fot ||| 0|eng d a978303719512370a10.4171/0122doi ach0018173 7aPBS2bicssc a65-xx2msc10aNumerical Methods for Hyperbolic and Kinetic Problemsh[electronic resource] /cStéphane Cordier, Thierry Goudon, Michael Gutnic, Eric Sonnendrücker3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2005 a1 online resource (367 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v700tNumerical charge conservation in Particle-In-Cell codes /rR. Barthelmé, C. Parzani --tAn adaptive Particle-In-Cell method using multi-resolution analysis /rJ.-P. Chehab, Albert Cohen, D. Jennequin, J. J. Nieto, J. R. Roche, Ch. Roland --tAdaptive numerical resolution of the Vlasov equation /rM. Campos Pinto, M. Mehrenberger --tA conservative and entropic method for the Vlasov–Fokker–Planck–Landau equation /rN. Crouseilles, F. Filbet --tNumerical studies for nonlinear Schrödinger equations: the Schrödinger–Poisson-Xα model and Davey–Stewartson systems /rChristophe Besse, Norbert J. Mauser, Hans Peter Stimming --tIonospheric plasmas: model derivation, stability /rChristophe Besse, Jean Claudel, P. Degond, F. Deluzet, Gerard Gallice, Christian Tessieras --tA case study on the reliability of multiphase WKB approximation for the one-dimensional Schrödinger equation /rL. Gosse --tLiquid jet generation and break-up /rCéline Baranger, G. Baudin, L. Boudin, Bruno Després, Frédéric Lagoutière, E. Lapébie, Takéo Takahashi --tNumerical study of a conservative bifluid model with interpenetration /rB. Després, S. Jaouen, C. Mazeran, Takéo Takahashi --tDINMOD: A diffuse interface model for two-phase flows modelling /rF. Caro, F. Coquel, D. Jamet, S. Kokh --tSharp and diffuse interface methods for phase transition problems in liquid-vapour flows /rF. Coquel, D. Diehl, C. Merkle, Christian Rohde --tGeometric Eddington factor for radiative transfer /rJ. Cartier, A. Munnier --tArbitrary high order discontinuous Galerkin schemes /rMichael Dumbser, C.-D. Munz --tThe multiple pressure variables method for fluid dynamics and aeroacoustics at low Mach numbers /rC.-D. Munz, Michael Dumbser, M. Zucchini.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the CEMRACS summer research center held at CIRM in Luminy in 2003 was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the results are now reported in the present book.
The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative
transfer, sprays and aeroacoustics.
The text is aimed at researchers and engineers interested in modelling and numerical simulation of hyperbolic and kinetic problems arising from applications.07aNumerical analysis2bicssc07aNumerical analysis2msc1 aCordier, Stéphane,eeditor.1 aGoudon, Thierry,eeditor.1 aGutnic, Michael,eeditor.1 aSonnendrücker, Eric,eeditor.40uhttps://doi.org/10.4171/012423cover imageuhttps://www.ems-ph.org/img/books/cordier_mini.jpg02453nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000320020624501300023826000820036830000340045033600260048433700260051033800360053634700240057249000510059650600660064752011920071365000350190565000400194065000250198085600320200585600660203725-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060430sz fot ||| 0|eng d a978303719521570a10.4171/0212doi ach0018173 7aPBKJ2bicssc a35-xxa76-xx2msc1 aKuksin, Sergei B.,eauthor.10aRandomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensionsh[electronic resource] /cSergei B. Kuksin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (102 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book gives an account of recent achievements in the mathematical theory of two-dimensional turbulence, described by the 2D Navier–Stokes equation, perturbed by a random force. The main results presented here were obtained during the last five to ten years and, up to now, have been available only in papers in the primary literature. Their summary and synthesis here, beginning with some preliminaries on partial differential equations and stochastics, make the book a self-contained account that will appeal to readers with a general background in analysis.
After laying the groundwork, the author goes on to recent results on ergodicity of random dynamical systems, which the randomly forced Navier-Stokes equation defines in the function space of divergence-free vector fields, including a Central Limit Theorem. The physical meaning of these results is discussed as well as their relations with the theory of attractors. Next, the author studies the behaviour of solutions when the viscosity goes to zero. In the final section these dynamical methods are used to derive the so-called balance relations - the infinitely many algebraical relations satisfied by the solutions.07aDifferential equations2bicssc07aPartial differential equations2msc07aFluid mechanics2msc40uhttps://doi.org/10.4171/021423cover imageuhttps://www.ems-ph.org/img/books/kuksin_mini.jpg03467nam a22004335a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018407200170020108400360021824501180025426000820037230000340045433600260048833700260051433800360054034700240057649000820060050508380068250600660152052010290158665000470261565000350266265000660269765000310276365000400279465000240283465000450285870000310290385600320293485600670296632-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20050531sz fot ||| 0|eng d a978303719513070a10.4171/0132doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc 7aPHTR2bicssc a53-xxa35-xxa81-xxa83-xx2msc10aAdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundariesh[electronic resource] /cOlivier Biquard3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2005 a1 online resource (259 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v800tGeometric aspects of the AdS/CFT correspondence /rMichael T. Anderson --tSome aspects of the AdS/CFT correspondence /rJan de Boer, Liat Maoz, Asad Naqvi --tThe ambient obstruction tensor and Q-curvature /rC. Robin Graham, Kengo Hirachi --tAdS/CFT correspondence and geometry /rIoannis Papadimitriou, Kostas Skenderis --tMass formulae for asymptotically hyperbolic manifolds /rMarc Herzlich --tReconstructing Minkowski space-time /rSergey N. Solodukhin --tNon-trivial, static, geodesically complete space-times with a negative cosmological constant II. n ≥ 5 /rMichael T. Anderson, Piotr T. Chruściel, Erwann Delay --tThe conformal boundary of anti-de Sitter space-times /rCharles Frances --tSupersymmetric AdS backgrounds in string and M-theory /rJerome P. Gauntlett, Dario Martelli, James Sparks, Daniel Waldram.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSince its discovery in 1997 by Maldacena, AdS/CFT correspondence has
become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of
viewpoints between mathematics and physics.
Written by leading experts and directed at research mathematicians and
theoretical physicists as well as graduate students, this volume gives an overview
of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aRelativistic quantum mechanics & quantum field theory2bicssc07aDifferential geometry2msc07aPartial differential equations2msc07aQuantum theory2msc07aRelativity and gravitational theory2msc1 aBiquard, Olivier,eeditor.40uhttps://doi.org/10.4171/013423cover imageuhttps://www.ems-ph.org/img/books/biquard_mini.jpg03170nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018424501310019926000820033030000340041233600260044633700260047233800360049834700240053450510210055850600660157952009420164565000210258765000460260870000300265470000380268485600320272285600660275433-091109CH-001817-320091109150325.0a fot |1| 0|cr nn mmmmamaa091109e20060110sz fot |1| 0|eng d a978303719511670a10.4171/0112doi ach0018173 7aPBWP2bicssc a37-xx2msc10aDynamics on the Riemann Sphereh[electronic resource] :bA Bodil Branner Festschrift /cPoul G. Hjorth, Carsten Lunde Petersen3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (226 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tOn Lattès Maps /rJohn Milnor --tBranner–Hubbard motions and attracting dynamics /rTan Lei, Carsten Lunde Petersen --tExamples of Feigenbaum Julia sets with small Hausdorff dimension /rArtur Avila, Mikhail Lyubich --tParabolic explosion and the size of Siegel disks in the quadratic family /rArnaud Cheritat --tSierpinski Carpets and Gaskets as Julia sets of Rational Maps /rPaul Blanchard, Robert L. Devaney, Daniel M. Look, Monica Moreno Rocha, Pradipta Seal, Stefan Siegmund, David Uminsky --tOn capture zones for the family fλ(z) = z2 + λ/z2 /rP. Roesch --tSemiconjugacies between the Julia sets of geometrically finite rational maps II /rTomoki Kawahira --tHomeomorphisms of the Mandelbrot Set /rWolf Jung --tArnold Disks and the Moduli of Herman Rings of the Complex Standard Family /rNúria Fagella, Christian Henriksen --tStretching rays and their accumulations, following Pia Willumsen /rTan Lei --tConjectures about the Branner–Hubbard motion of Cantor sets in C /rAdrien Douady.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDynamics on the Riemann Sphere presents a collection of original research articles by leading experts in the area of holomorphic dynamics. These papers arose from the symposium Dynamics in the Complex Plane, held on the occasion of the 60th birthday of Bodil Branner. Topics covered range from Lattès maps to cubic polynomials over rational maps with Sierpinsky Carpets and Gaskets as Julia sets, as well as rational and entire transcendental maps with Herman rings.
Contributors include Artur Avila (Paris VI, France), Arnault Chéritat (Toulouse, France), Robert L. Devaney (Boston, USA), Adrien Douady (Orsay, France), Nuria Fagella (Barcelona, Spain), Christian Henriksen (Lyngby, Denmark), Wolf Jung (Aachen, Germany), Tomoki Kawahira (Kyoto, Japan), Tan Lei (Cergy Pontoise, France), Mikhail Lyubich (Stony Brook, USA), Carsten Lunde Petersen (Roskilde, Denmark), John Milnor (Stony Brook, USA), Pascale Roesch (Lille, France).07aFractals2bicssc07aDynamical systems and ergodic theory2msc1 aHjorth, Poul G.,eeditor.1 aLunde Petersen, Carsten,eeditor.40uhttps://doi.org/10.4171/011423cover imageuhttps://www.ems-ph.org/img/books/hjorth_mini.gif02542nam a22003015a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200150016710000300018224501050021226000820031730000330039933600260043233700260045833800360048434700240052050600660054452015060061065000240211685600320214085600680217234-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20050830sz fot ||| 0|eng d a978303719514770a10.4171/0142doi ach0018173 7aPB2bicssc1 aTrzeciak, Jerzy,eauthor.10aWriting Mathematical Papers in Englishh[electronic resource] :ba practical guide /cJerzy Trzeciak3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2005 a1 online resource (51 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis booklet is intended to provide practical help for authors of mathematical papers. It is written mainly for non-English speaking writers but should prove useful even to native speakers of English who are beginning their mathematical writing and may not yet have developed a command of the structure of mathematical discourse.
The first part provides a collection of ready-made sentences and expressions occurring in mathematical papers. The examples are divided into sections according to their use (in introductions, definitions, theorems, proofs, comments, references to the literature, acknowledgements, editorial correspondence and referee's reports). Typical errors are also pointed out.
The second part concerns selected problems of English grammar and usage, most often encountered by mathematical writers. Just as in the first part, an abundance of examples are presented, all of them taken from actual mathematical texts.
"The author has packed an awful lot in a few pages and has obviously been collecting his best (or worst) examples for a long time."
Edwin F. Beschler
About the author:
Jerzy Trzeciak, formerly of Polish Scientific Publishers, is now the senior copy editor at the Institute of Mathematics, Polish Academy of Sciences. He is responsible for journals including Studia Mathematica, Fundamenta Mathematicae, Acta Arithmetica and others.
He is also the author of "Mathematical English Usage - a Dictionary", available at www.impan.gov.pl/Dictionary.07aMathematics2bicssc40uhttps://doi.org/10.4171/014423cover imageuhttps://www.ems-ph.org/img/books/trzeciak_mini.jpg02385nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000310020624500780023726000820031530000340039733600260043133700260045733800360048334700240051949000610054350600660060452011690067065000310183965000380187065000280190885600320193685600670196835-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060214sz fot ||| 0|eng d a978303719515470a10.4171/0152doi ach0018173 7aPBMW2bicssc a52-xxa14-xx2msc1 aEkedahl, Torsten,eauthor.10aOne Semester of Elliptic Curvesh[electronic resource] /cTorsten Ekedahl3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (138 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThese lecture notes grew out of a one semester introductory course on elliptic curves given to an audience of computer science and mathematics students, and assume only minimal background knowledge. After having covered basic analytic and algebraic aspects, putting special emphasis on explaining the interplay between algebraic and analytic formulas, they go on to some more specialized topics. These include the j-function from an algebraic and analytic perspective, a discussion of elliptic curves over finite fields, derivation of recursion formulas for the division polynomials, the algebraic structure of the torsion points of an elliptic curve, complex multiplication, and modular forms.
In an effort to motivate basic problems the book starts very slowly, but considers some aspects such as modular forms of higher level which are not usually treated. It presents more than 100 exercises and a
Mathematica™ notebook that treats a number of calculations involving elliptic curves.
The book is aimed at students of mathematics with a general interest in elliptic curves but also at students of computer science interested in their cryptographic aspects.07aAlgebraic geometry2bicssc07aConvex and discrete geometry2msc07aAlgebraic geometry2msc40uhttps://doi.org/10.4171/015423cover imageuhttps://www.ems-ph.org/img/books/ekedahl_mini.gif03097nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200160018408400220020010000280022224501280025026000820037830000340046033600260049433700260052033800360054634700240058249000390060650600660064552017360071165000350244765000310248265000410251365000280255470000310258285600320261385600660264536-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060228sz fot ||| 0|eng d a978303719517870a10.4171/0172doi ach0018173 7aPBKJ2bicssc 7aPBS2bicssc a34-xxa65-xx2msc1 aKunkel, Peter,eauthor.10aDifferential-Algebraic Equationsh[electronic resource] :bAnalysis and Numerical Solution /cPeter Kunkel, Volker Mehrmann3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (385 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDifferential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others.
This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge--Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text.
The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.07aDifferential equations2bicssc07aNumerical analysis2bicssc07aOrdinary differential equations2msc07aNumerical analysis2msc1 aMehrmann, Volker,eauthor.40uhttps://doi.org/10.4171/017423cover imageuhttps://www.ems-ph.org/img/books/kunkel_mini.gif03015nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400360018410000310022024500690025126000820032030000340040233600260043633700260046233800360048834700240052449000390054850600660058752016980065365000340235165000400238565000380242565000420246365000360250585600320254185600680257337-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060228sz fot ||| 0|eng d a978303719516170a10.4171/0162doi ach0018173 7aPBFD2bicssc a22-xxa12-xxa20-xxa43-xx2msc1 aStroppel, Markus,eauthor.10aLocally Compact Groupsh[electronic resource] /cMarkus Stroppel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (312 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aLocally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory.
In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter–Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to
Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups.
The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.07aGroups & group theory2bicssc07aTopological groups, Lie groups2msc07aField theory and polynomials2msc07aGroup theory and generalizations2msc07aAbstract harmonic analysis2msc40uhttps://doi.org/10.4171/016423cover imageuhttps://www.ems-ph.org/img/books/stroppel_mini.jpg11510nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200150016708400150018224501800019726000820037730000350045933600260049433700260052033800360054634700240058250591560060650600660976252010540982865000241088265000171090670000321092370000281095570000301098370000281101385600321104185600631107339-091109CH-001817-320091109150325.0a fot 1|| 0|cr nn mmmmamaa091109e20070515sz fot 1|| 0|eng d a978303719522270a10.4171/0222doi ach0018173 7aPB2bicssc a00-xx2msc10aProceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006h[electronic resource] /cMarta Sanz-Solé, Javier Soria, Juan L. Varona, Joan Verdera3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (4392 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda20tThe work of Andrei Okounkov /rGiovanni Felder --tThe work of Grigory Perelman /rJohn Lott --tThe work of Terence Tao /rCharles Fefferman --tThe work of Wendelin Werner /rCharles M. Newman --tThe work of Jon Kleinberg /rJohn Hopcroft --tOn Kiyosi Itô's work and its impact /rHans Föllmer --tUniversality for mathematical and physical systems /rPercy Deift --tKähler manifolds and transcendental techniques in algebraic geometry /rJean-Pierre Demailly --tOptimal computation /rRonald A. DeVore --tSymplectic field theory and its applications /rYasha Eliashberg --tKnots and dynamics /rÉtienne Ghys --tPrime numbers and L-functions /rHenryk Iwaniec --tHigh dimensional statistical inference and random matrices /rIain M. Johnstone --tIwasawa theory and generalizations /rKazuya Kato --tEnergy-driven pattern formation /rRobert V. Kohn --tModuli spaces from a topological viewpoint /rJørgen Ellegaard Andersen --tAdvances in convex optimization: conic programming /rArkadi Nemirovski --tDeformation and rigidity for group actions and von Neumann algebras /rSorin Popa --tCardiovascular mathematics /rAlfio Quarteroni --tConformally invariant scaling limits: an overview and a collection of problems /rOded Schramm --tIncreasing and decreasing subsequences and their variants /rRichard P. Stanley --tThe dichotomy between structure and randomness, arithmetic progressions, and the primes /rTerence Tao --tPerspectives in nonlinear diffusion: between analysis, physics and geometry /rJuan Luis Vázquez --tApplications of equivariant cohomology /rMichèle Vergne --tP, NP and mathematics – a computational complexity perspective /rAvi Wigderson --tThe Poincaré Conjecture /rJohn W. Morgan --tPanel discussion: Should mathematicians care about communicating to broad audiences? Theory and practice --tICM 2006 Closing round table: Are pure and applied mathematics drifting apart? --tFrom the private to the public: The road from Zurich (1897) to Madrid (2006) /rJosé M. Sánchez-Ron --tAlgorithmic randomness and computability /rRodney G. Downey --tDeterminacy and large cardinals /rItay Neeman --tThe art of ordinal analysis /rMichael Rathjen --tAnalytic difference rings /rThomas Scanlon --tBorel superrigidity and the classification problem for the torsion-free abelian groups of finite rank /rSimon Thomas --tQuiver algebras, weighted projective lines, and the Deligne–Simpson problem /rWilliam Crawley-Boevey --tZeta functions of groups and rings /rMarcus J. du Sautoy, Fritz Grunewald --tOn differential graded categories /rBernhard Keller --tDerived equivalences and finite dimensional algebras /rRaphaël Rouquier --tAlgorithmic and asymptotic properties of groups /rMark V. Sapir --tA unified approach to computations with permutation and matrix groups /rÁkos Seress --tSome results in noncommutative ring theory /rAgata Smoktunowicz --tHigher composition laws and applications /rManjul Bhargava --tHigher composition laws and applications /rChing-Li Chai --tHeegner points, Stark–Heegner points, and values of L-series /rHenri Darmon --tGalois deformations and arithmetic geometry of Shimura varieties /rKazuhiro Fujiwara --tGeneralising the Hardy–Littlewood method for primes /rBen J. Green --tAspects géométriques du Lemme Fondamental de Langlands-Shelstad /rGérard Laumon --tEquidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik /rPhilippe Michel, Akshay Venkatesh --tp-adic motivic cohomology in arithmetic /rWiesława Nizioł --tVanishing of L-functions and ranks of Selmer groups /rChristopher Skinner, Eric Urban --tSpecial values of L-functions modulo p /rVinayak Vatsal --tHigher-dimensional analogues of stable curves /rValery Alexeev --tEvaluation maps, slopes, and algebraicity criteria /rJean-Benoît Bost --tDerived categories of coherent sheaves /rTom Bridgeland --tInvariants of singularities of pairs /rLawrence Ein, Mircea Mustaţă --tRational curves and rational points /rTom Graber --tRigidity of rational homogeneous spaces /rJun-Muk Hwang --tGeometry of multiple zeta values /rTomohide Terasoma --tGeometry over nonclosed fields /rYuri Tschinkel --tAlgebraic Morse theory and the weak factorization theorem /rJarosław Włodarczyk --tManifolds with positive curvature operators are space forms /rChristoph Böhm, Burkhard Wilking --tElliptic and parabolic problems in conformal geometry /rSimon Brendle --tThe topology and geometry of contact structures in dimension three /rKo Honda --tGeneralized triangle inequalities and their applications /rMichael Kapovich --tThe asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity /rBruce Kleiner --tLagrangian submanifolds: from the local model to the cluster complex /rPhilippe Charron --tGromov–Witten invariants and moduli spaces of curves /rXiaobo Liu --tExtremal metrics and stabilities on polarized manifolds /rToshiki Mabuchi --tTropical geometry and its applications /rGrigory Mikhalkin --tEmbedded minimal surfaces /rWilliam P. Minicozzi II --tFloer homology in symplectic geometry and in mirror symmetry /rYong-Geun Oh, Kenji Fukaya --tProperly embedded minimal surfaces with finite topology /rAntonio Ros --tApplications of loop group factorization to geometric soliton equations /rChuu-Lian Terng --tFiniteness of arithmetic Kleinian reflection groups /rIan Agol --tNon-positive curvature and complexity for finitely presented groups /rMartin R. Bridson --tLink homology and categorification /rAaron D. Lauda --tCurve complexes, surfaces and 3-manifolds /rYair N. Minsky --tA1-algebraic topology /rFabien Morel --tDevelopment in symplectic Floer theory /rKaoru Ono --tHeegaard diagrams and Floer homology /rPeter S. Ozsváth, Zoltán Szabó --tThe cohomology of automorphism groups of free groups /rKaren Vogtmann --tNoncommutative counterparts of the Springer resolution /rRoman Bezrukavnikov --tSpaces of quasi-maps into the flag varieties and their applications /rAlexander Braverman --tOn the local Langlands and Jacquet–Langlands correspondences /rGuy Henniart --tAn invitation to bounded cohomology /rNicolas Monod --tFibration de Hitchin et structure endoscopique de la formule des traces /rBao-Châu Ngô --tHecke algebras and harmonic analysis /rEric M. Opdam --tContinuous representation theory of p-adic Lie groups /rPeter Schneider --tThe algebraization of Kazhdan’s property (T) /rYehuda Shalom --tRankin–Selberg integrals, the descent method, and Langlands functoriality /rDavid Soudry --tRepresentation theory and the cohomology of arithmetic groups /rBirgit Speh --tSome results on compactifications of semisimple groups /rTonny A. Springer --tQuasiconformal geometry of fractals /rMario Bonk --tLocal Tb theorems and applications in PDE /rDorina Mitrea --tAlmost everywhere convergence and divergence of Fourier series /rSergey Konyagin --tIterated Segre mappings of real submanifolds in complex space and applications /rLinda Preiss Rothschild --tTowards conformal invariance of 2D lattice models /rStanislav Smirnov --tAspects of the L2-Sobolev theory of the ∂-Neumann problem /rEmil J. Straube --tGreedy approximations with regard to bases /rVladimir N. Temlyakov --tAnalytic capacity, rectifiability, and the Cauchy integral /rXavier Tolsa --tThe Brunn–Minkowski theorem and related geometric and functional inequalities /rFranck Barthe --tIsomorphic and almost-isometric problems in high-dimensional convex geometry /rBo'az Klartag --tAmenable actions and applications /rNarutaka Ozawa --tStructure and classification of C*-algebras /rMikael Rørdam --tConvexity, complexity, and high dimensions /rStanislaw J. Szarek --tHigher index theory of elliptic operators and geometry of groups /rGuoliang Yu --tOn spectral invariants in modern ergodic theory /rOleg N. Ageev --tErgodic Ramsey theory: a dynamical approach to static theorems /rVitaly Bergelson --tHyperbolic billiards and statistical physics /rNikolai Chernov, Dmitry Dolgopyat --tSome recent progress in geometric methods in the instability problem in Hamiltonian mechanics /rRafael de la Llave --tDiagonalizable flows on locally homogeneous spaces and number theory /rManfred Einsiedler, Elon Lindenstrauss --tBraids and differential equations /rRobert Ghrist --tNewton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems /rAnton Gorodetski, Brian Hunt, Vadim Kaloshin --tFrom combinatorics to ergodic theory and back again /rBryna Kra --tFrom Brouwer theory to the study of homeomorphisms of surfaces /rPatrice Le Calvez --tAll, most, some differentiable dynamical systems /rMichael Shub --tGeodesics on ﬂat surfaces /rAnton Zorich --tAsymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximation /rStefano Bianchini --tNonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem /rPatrick Gérard.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aNote: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.
The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science.
The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress.
The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.07aMathematics2bicssc07aGeneral2msc1 aSanz-Solé, Marta,eeditor.1 aSoria, Javier,eeditor.1 aVarona, Juan L.,eeditor.1 aVerdera, Joan,eeditor.40uhttps://doi.org/10.4171/022423cover imageuhttps://www.ems-ph.org/img/books/ICM_mini.jpg02322nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000330019924500790023226000820031130000340039333600260042733700260045333800360047934700240051549000610053950600660060052011600066665000310182665000280185785600320188585600670191740-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060510sz fot ||| 0|eng d a978303719523970a10.4171/0232doi ach0018173 7aPBPD2bicssc a55-xx2msc1 aMatveev, Sergey V.,eauthor.10aLectures on Algebraic Topologyh[electronic resource] /cSergey V. Matveev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (106 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAlgebraic topology is the study of the global properties of spaces
by means of algebra. It is an important branch of modern mathematics
with a wide degree of applicability to other fields, including
geometric topology, differential geometry, functional analysis,
differential equations, algebraic geometry, number theory, and
theoretical physics.
This book provides an introduction to the basic concepts and methods
of algebraic topology for the beginner. It presents elements of
both homology theory and homotopy theory, and includes various
applications.
The author's intention is to rely on the geometric approach by
appealing to the reader's own intuition to help understanding. The
numerous illustrations in the text also serve this purpose. Two
features make the text different from the standard literature:
first, special attention is given to providing explicit algorithms
for calculating the homology groups and for manipulating the
fundamental groups. Second, the book contains many exercises, all of
which are supplied with hints or solutions. This makes the book suitable
for both classroom use and for independent study.07aAlgebraic topology2bicssc07aAlgebraic topology2msc40uhttps://doi.org/10.4171/023423cover imageuhttps://www.ems-ph.org/img/books/matveev_mini.jpg02717nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000340023024500920026426000820035630000340043833600260047233700260049833800360052434700240056049000610058450600660064552013070071165000470201865000660206565000480213165000290217965000240220885600320223285600670226441-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060630sz fot ||| 0|eng d a978303719524670a10.4171/0242doi ach0018173 7aPBMP2bicssc 7aPHTR2bicssc a58-xxa46-xxa81-xx2msc1 aVárilly, Joseph C.,eauthor.10aAn Introduction to Noncommutative Geometryh[electronic resource] /cJoseph C. Várilly3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (121 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aNoncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras, and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples.
This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the condiditons on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples.
The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.07aDifferential & Riemannian geometry2bicssc07aRelativistic quantum mechanics & quantum field theory2bicssc07aGlobal analysis, analysis on manifolds2msc07aFunctional analysis2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/024423cover imageuhttps://www.ems-ph.org/img/books/varilly_mini.jpg02156nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400290018410000310021324500760024426000820032030000340040233600260043633700260046233800360048834700240052449000500054850600660059852008490066465000470151365000310156065000550159165000480164685600320169485600680172642-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060710sz fot ||| 0|eng d a978303719525370a10.4171/0252doi ach0018173 7aPBMP2bicssc a53-xxa32-xxa58-xx2msc1 aBallmann, Werner,eauthor.10aLectures on Kähler Manifoldsh[electronic resource] /cWerner Ballmann3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (182 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThese notes are based on lectures the author held at the University of Bonn and the Erwin-Schrödinger-Institute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern–Weil theory, symmetric spaces, and L2-cohomology.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aSeveral complex variables and analytic spaces2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/025423cover imageuhttps://www.ems-ph.org/img/books/ballmann_mini.jpg02557nam a22003975a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200170018308400220020010000350022224501550025726000820041230000340049433600260052833700260055433800360058034700240061649000610064050600660070152010950076765000370186265000240189965000530192365000200197670000300199670000320202685600320205885600690209044-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070110sz fot ||| 0|eng d a978303719527770a10.4171/0272doi ach0018173 7aPBT2bicssc 7aPBWL2bicssc a60-xxa62-xx2msc1 adel Barrio, Eustasio,eauthor.10aLectures on Empirical Processesh[electronic resource] :bTheory and Statistical Applications /cEustasio del Barrio, Paul Deheuvels, Sara van de Geer3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (263 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe theory of empirical processes constitutes the mathematical toolbox of asymptotic statistics. Its growth was accelerated by the 1950s work on the Functional Central Limit Theorem and the Invariance Principle. The theory has developed in parallel with statistical methodologies, and has been successfully applied to a large diversity of problems related to the asymptotic behaviour of statistical procedures.
The three sets of lecture notes in the book offer a wide panorama of contemporary empirical processes theory. Techniques are developed in the framework of probability in Banach spaces, Hungarian-style strong approximations,
using tools from general stochastic process theory. Other tools appear in this text in connection with historical as well as modern applications, such as goodness-of-fit tests, density estimation or general M-estimators.
This book gives an excellent overview of the broad scope of the theory of empirical processes. It will be an invaluable aid for students and researchers interested in an advanced and well-documented approach to the selected topics.07aProbability & statistics2bicssc07aStochastics2bicssc07aProbability theory and stochastic processes2msc07aStatistics2msc1 aDeheuvels, Paul,eauthor.1 avan de Geer, Sara,eauthor.40uhttps://doi.org/10.4171/027423cover imageuhttps://www.ems-ph.org/img/books/deheuvels_mini.jpg03271nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000280023024500960025826000820035430000330043633600260046933700260049533800360052134700240055749000610058150600660064252018770070865000470258565000350263265000480266765000400271565000310275585600320278685600670281848-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060830sz fot ||| 0|eng d a978303719530770a10.4171/0302doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc a58-xxa35-xxa53-xx2msc1 aMüller, Reto,eauthor.10aDifferential Harnack Inequalities and the Ricci Flowh[electronic resource] /cReto Müller3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (99 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe classical Harnack inequalities play an important role in the study of parabolic partial differential equations. The idea of finding a differential version of such a classical Harnack inequality goes back to Peter Li and Shing Tung Yau, who introduced a pointwise gradient estimate for a solution of the linear heat equation on a manifold which leads to a classical Harnack type inequality if being integrated along a path. Their idea has been
successfully adopted and generalized to (nonlinear) geometric heat flows such as mean curvature flow or Ricci flow; most of this work was done by Richard Hamilton. In 2002, Grisha Perelman presented a new kind of differential Harnack inequality which involves both the (adjoint) linear heat equation and the Ricci flow. This led to a completely new approach to the Ricci flow that allowed interpretation as a gradient flow which maximizes different entropy functionals. This approach forms the main analytic core of Perelman’s attempt to prove the Poincaré conjecture. It is, however, of completely independent interest and may as well prove useful in various
other areas, such as, for instance, the theory of Kähler manifolds.
The goal of this book is to explain this analytic tool in full detail for the two examples of the linear heat equation and the Ricci flow. It begins with the original Li–Yau result, presents Hamilton's Harnack inequalities for the Ricci flow, and ends with Perelman's entropy formulas and space-time geodesics.
The text is a self-contained, modern introduction to the Ricci flow and the analytic methods to study it. It is primarily addressed to students who have a basic introductory knowledge of analysis and of Riemannian geometry and who are attracted to further study in geometric analysis. No previous knowledge of differential Harnack inequalities or the Ricci flow is required.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/030423cover imageuhttps://www.ems-ph.org/img/books/mueller_mini.jpg02933nam a22004095a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200160018408400360020024500700023626000820030630000340038833600260042233700260044833800360047434700240051049000830053450506700061750600660128752008490135365000350220265000480223765000230228565000380230865000260234665000240237270000290239685600320242585600660245749-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20061012sz fot ||| 0|eng d a978303719528470a10.4171/0282doi ach0018173 7aPBRH2bicssc 7aPHT2bicssc a11-xxa52-xxa68-xxa81-xx2msc10aPhysics and Number Theoryh[electronic resource] /cLouise Nyssen3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (274 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1000tThe phase of oscillations and prime numbers: classical and quantum /rMichel Planat --tOn self-similar finitely generated uniformly discrete (SFU-)sets and sphere packings /rJean-Louis Verger-Gaugry --tNested quasicrystalline discretisations of the line /rJean-Pierre Gazeau, Zuzana Masáková, Edita Pelantová --tHopf algebras in renormalization theory: locality and Dyson–Schwinger equations from Hochschild cohomology /rChristoph Bergbauer, Dirk Kreimer --tFonction ζ et matrices aléatoires /rEmmanuel Royer --tSome recent applications of Kloostermania /rPhilippe Michel --tIntroduction à la correspondance de Langlands locale /rAriane Mézard.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThere is a rich and historical relationship between theoretical physics and number theory. This volume presents a selection of problems which are currently in full development and inspire a lot of research going on. Each of the seven contributions starts with an introductory survey which makes it possible even for non-specialists to understand the results and to gain an idea of the great variety of subjects and techniques used.
Topics covered are: phase locking in oscillating systems, crystallography, Hopf algebras and renormalisation theory, Zeta-function and random matrices, Kloosterman sums and the local Langlands correspondence.
Intended for research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of recent developments in an exciting subject crossing several disciplines.07aAnalytic number theory2bicssc07aQuantum physics (quantum mechanics)2bicssc07aNumber theory2msc07aConvex and discrete geometry2msc07aComputer science2msc07aQuantum theory2msc1 aNyssen, Louise,eeditor.40uhttps://doi.org/10.4171/028423cover imageuhttps://www.ems-ph.org/img/books/nyssen_mini.jpg03534nam a22004575a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400360020124501960023726000820043330000340051533600260054933700260057533800360060134700240063749000820066150511970074350600660194052005810200665000350258765000340262265000280265665000420268465000550272665000400278170000310282170000330285270000300288570000290291570000330294485600320297785600670300950-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20061201sz fot ||| 0|eng d a978303719520870a10.4171/0202doi ach0018173 7aPBKJ2bicssc 7aPBFD2bicssc a14-xxa20-xxa32-xxa35-xx2msc10aDifferential Equations and Quantum Groupsh[electronic resource] :bAndrey A. Bolibrukh Memorial Volume /cDaniel Bertrand, Benjamin Enriquez, Claude Mitschi, Claude Sabbah, Reinhard Schäfke3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (302 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v900tRealization of irreducible monodromy by Fuchsian systems and reduction to the Birkhoff standard form (by Andrey Bolibrukh) /rYulij Ilyashenko --tThe work of Andrey Bolibrukh on isomonodromic deformations /rClaude Sabbah --tTwo notions of integrability /rMichèle Audin --tFormal power series solutions of the heat equation in one spatial variable /rWerner Balser --tMultiplicity of critical points of master functions and Schubert calculus /rPrakash Belkale, Evgeny Mukhin, Alexander Varchenko --tSome explicit solutions to the Riemann–Hilbert problem /rPhilip Boalch --tGalois theory of parameterized differential equations and linear differential algebraic groups /rPhyllis J. Cassidy, Michael F. Singer --tOn the reductions and classical solutions of the Schlesinger equations /rBoris Dubrovin, Marta Mazzocco --tOn the Riemann–Hilbert correspondence for generalized Knizhnik–Zamolodchikov equations for different root systems /rValentina Golubeva --tMonodromy groups of regular systems on the Riemann sphere /rVladimir Petrov Kostov --tMonodromy of Cherednik–Kohno–Veselov connections /rVladimir P. Leksin --tInvitation to Galois theory /rHiroshi Umemura.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis special volume is dedicated to the memory of Andrey A. Bolibrukh. It
contains two expository articles devoted to some aspects of Bolibrukh's work,
followed by ten refereed research articles.
Topics cover complex linear and nonlinear differential equations as well as quantum
groups: monodromy, Fuchsian linear systems, Riemann–Hilbert problem,
differential Galois theory, differential algebraic groups, multisummability,
isomonodromy, Painlevé equations, Schlesinger equations, integrable systems,
KZ equations, complex reflection groups, root systems.07aDifferential equations2bicssc07aGroups & group theory2bicssc07aAlgebraic geometry2msc07aGroup theory and generalizations2msc07aSeveral complex variables and analytic spaces2msc07aPartial differential equations2msc1 aBertrand, Daniel,eeditor.1 aEnriquez, Benjamin,eeditor.1 aMitschi, Claude,eeditor.1 aSabbah, Claude,eeditor.1 aSchäfke, Reinhard,eeditor.40uhttps://doi.org/10.4171/020423cover imageuhttps://www.ems-ph.org/img/books/irma_mitschi.jpg03391nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000390023024501020026926000820037130000350045333600260048833700260051433800360054034700240057649000530060050600660065352020040071965000350272365000280275865000400278665000480282665000250287485600320289985600740293151-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070110sz fot ||| 0|eng d a978303719531470a10.4171/0312doi ach0018173 7aPBKJ2bicssc 7aPHDF2bicssc a35-xxa58-xxa76-xx2msc1 aChristodoulou, Demetrios,eauthor.10aThe Formation of Shocks in 3-Dimensional Fluidsh[electronic resource] /cDemetrios Christodoulou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (1000 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe equations describing the motion of a perfect fluid were first formulated by Euler in 1752. These equations were among the first partial differential equations to be written down, but, after a lapse of two and a half centuries, we are still far from adequately understanding the observed phenomena which are supposed to lie within their domain of validity.
These phenomena include the formation and evolution of shocks in compressible fluids, the subject of the present monograph. The first work on shock formation was done by Riemann in 1858. However, his analysis was limited to the simplified case of one space dimension. Since then, several deep physical insights have been attained and new methods of mathematical analysis invented. Nevertheless, the theory of the formation and evolution of shocks in real three-dimensional fluids has remained up to this day fundamentally incomplete.
This monograph considers the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. We consider initial data for these equations which outside a sphere coincide with the data corresponding to a constant state. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems that give a complete description of the maximal classical development. In particular, it is shown that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signalling shock formation. The theorems give a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there. A complete picture of shock formation in three-dimensional fluids is thereby obtained. The approach is geometric, the central concept being that of the acoustical spacetime manifold.
The monograph will be of interest to people working in partial differential equations in general and in fluid mechanics...07aDifferential equations2bicssc07aFluid mechanics2bicssc07aPartial differential equations2msc07aGlobal analysis, analysis on manifolds2msc07aFluid mechanics2msc40uhttps://doi.org/10.4171/031423cover imageuhttps://www.ems-ph.org/img/books/christodoulou2_mini.jpg02455nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000290023024500950025926000820035430000340043633600260047033700260049633800360052234700240055849000510058250600660063352010950069965000340179465000300182865000400185865000280189865000440192685600320197085600670200252-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070303sz fot ||| 0|eng d a978303719534570a10.4171/0342doi ach0018173 7aPBFD2bicssc 7aPBMS2bicssc a16-xxa14-xxa70-xx2msc1 aEtingof, Pavel,eauthor.10aCalogero–Moser systems and representation theoryh[electronic resource] /cPavel Etingof3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (101 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aCalogero–Moser systems, which were originally discovered
by specialists in integrable systems are currently at the crossroads
of many areas of mathematics and within the scope of interests of
many mathematicians. More specifically, these systems and their
generalizations turned out to have intrinsic connections with such fields
as algebraic geometry (Hilbert schemes of surfaces),
representation theory (double affine Hecke algebras, Lie groups, quantum
groups), deformation theory (symplectic reflection algebras),
homological algebra (Koszul algebras), Poisson geometry, etc. The goal of
the present lecture notes is to give an introduction
to the theory of Calogero–Moser systems, highlighting their
interplay with these fields. Since these lectures are designed
for non-experts, we give short introductions to each of the
subjects involved, and provide a number of exercises.
The book will be suitable for mathematics graduate students
and researchers in the areas of representation theory, noncommutative
algebra, algebraic geometry, and related areas.07aGroups & group theory2bicssc07aAnalytic geometry2bicssc07aAssociative rings and algebras2msc07aAlgebraic geometry2msc07aMechanics of particles and systems2msc40uhttps://doi.org/10.4171/034423cover imageuhttps://www.ems-ph.org/img/books/etingof_mini.jpg02635nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400220018310000300020524502230023526000820045830000350054033600260057533700260060133800360062734700240066349000560068750600660074352011950080965000260200465000230203065000380205370000380209170000320212985600320216185600680219353-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070404sz fot ||| 0|eng d a978303719538370a10.4171/0382doi ach0018173 7aPBR2bicssc a11-xxa12-xx2msc1 aIwaniec, Henryk,eauthor.10aAndrzej Schinzel, Selectah[electronic resource] :bVolume I: Diophantine Problems and Polynomials Volume II: Elementary, Analytic and Geometric Number Theory /cHenryk Iwaniec, Władysław Narkiewicz, Jerzy Urbanowicz3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (1417 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAndrzej Schinzel, born in 1937, is a leading number theorist whose
work has a lasting impact on modern mathematics. He is the author of
over 200 research articles in various branches of arithmetics,
including elementary, analytic and algebraic number theory. He has
also been, for nearly 40 years, the editor of Acta Arithmetica,
the first international journal devoted exclusively to number
theory.
These Selecta contain Schinzel's most important articles published
between 1955 and 2006. The arrangement is by topic, with each major
category introduced by an expert's comment. Many of the hundred
selected papers deal with arithmetical and algebraic properties of
polynomials in one or several variables, but there are also articles
on Euler's totient function, the favorite subject of Schinzel's early
research, on prime numbers (including the famous paper with Sierpiński
on
the Hypothesis “H”), algebraic number theory, diophantine
equations, analytical number theory and geometry of numbers. Volume
II concludes with some papers from outside number theory, as well as
a list of unsolved problems and unproved conjectures, taken from the
work of Schinzel.07aNumber theory2bicssc07aNumber theory2msc07aField theory and polynomials2msc1 aNarkiewicz, Władysław,eauthor.1 aUrbanowicz, Jerzy,eauthor.40uhttps://doi.org/10.4171/038423cover imageuhttps://www.ems-ph.org/img/books/schinzel_mini.jpg02482nam a22004095a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000300023024501330026026000820039330000340047533600260050933700260053533800360056134700240059749000500062150600660067152009780073765000470171565000350176265000480179765000400184565000310188570000300191670000300194685600320197685600640200854-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070321sz fot ||| 0|eng d a978303719537670a10.4171/0372doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc a58-xxa35-xxa53-xx2msc1 aBär, Christian,eauthor.10aWave Equations on Lorentzian Manifolds and Quantizationh[electronic resource] /cChristian Bär, Nicolas Ginoux, Frank Pfäffle3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (202 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides a detailed introduction to linear wave equations
on Lorentzian manifolds (for vector-bundle valued fields). After a
collection of preliminary material in the first chapter one finds in the second
chapter the construction of local fundamental solutions together with their
Hadamard expansion. The third chapter establishes the existence and uniqueness
of global fundamental solutions on globally hyperbolic spacetimes and discusses
Green's operators and well-posedness of the Cauchy problem. The last chapter is
devoted to field quantization in the sense of algebraic quantum field theory.
The necessary basics on C*-algebras and CCR-representations are developed
in full detail.
The text provides a self-contained introduction to these topics
addressed to graduate students in mathematics and physics. At the
same time it is intended as a reference for researchers in global
analysis, general relativity, and quantum field theory.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc07aDifferential geometry2msc1 aGinoux, Nicolas,eauthor.1 aPfäffle, Frank,eauthor.40uhttps://doi.org/10.4171/037423cover imageuhttps://www.ems-ph.org/img/books/baer_mini.jpg04492nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018424500940020626000820030030000340038233600260041633700260044233800360046834700240050449000830052850515670061150600660217852016260224465000290387065000410389965000550394070000370399585600320403285600660406455-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070525sz fot ||| 0|eng d a978303719529170a10.4171/0292doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc10aHandbook of Teichmüller Theory, Volume Ih[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (802 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1100tIntroduction to Teichmüller theory, old and new /rAthanase Papadopoulos --tHarmonic maps and Teichmüller theory /rGeorgios D. Daskalopoulos, Richard A. Wentworth --tOn Teichmüller’s metric and Thurston’s asymmetric metric on Teichmüller space /rAthanase Papadopoulos, Guillaume Théret --tSurfaces, circles, and solenoids /rRobert C. Penner --tAbout the embedding of Teichmüller space in the space of geodesic Hölder distributions /rJean-Pierre Otal --tTeichmüller spaces, triangle groups and Grothendieck dessins /rWilliam J. Harvey --tOn the boundary of Teichmüller disks in Teichmüller and in Schottky space /rFrank Herrlich, Gabriela Schmithüsen --tIntroduction to mapping class groups of surfaces and related groups /rShigeyuki Morita --tGeometric survey of subgroups of mapping class groups /rJohn Loftin --tDeformations of Kleinian groups /rAlbert Marden --tGeometry of the complex of curves and of Teichmüller space /rUrsula Hamenstädt --tParameters for generalized Teichmüller spaces /rCharalampos Charitos, Ioannis Papadoperakis --tOn the moduli space of singular euclidean surfaces /rMarc Troyanov --tDiscrete Riemann surfaces /rChristian Mercat --tOn quantizing Teichmüller and Thurston theories /rLeonid Chekhov, Robert C. Penner --tDual Teichmüller and lamination spaces /rVladimir V. Fock, Alexander Goncharov --tAn analog of a modular functor from quantized Teichmüller theory /rJörg Teschner --tOn quantum moduli space of flat PSL2(ℝ)-connections on a punctured surface /rRinat Kashaev.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Teichmüller space of a surface was introduced by O. Teichmüller
in the 1930s. It is a basic tool in the study of Riemann's moduli
space and of the mapping class group. These objects are fundamental
in several fields of mathematics including algebraic geometry,
number theory, topology, geometry, and dynamics.
The original setting of Teichmüller theory is complex analysis.
The work of Thurston in the 1970s brought techniques of hyperbolic
geometry in the study of Teichmüller space and of its asymptotic
geometry. Teichmüller spaces are also studied from the point of view
of the representation theory of the fundamental group of the surface
in a Lie group G, most notably G = PSL(2,ℝ) and G = PSL(2,ℂ).
In the 1980s, there evolved an essentially combinatorial treatment of
the Teichmüller and moduli spaces involving techniques and ideas
from high-energy physics, namely from string theory. The current
research interests include the quantization of Teichmüller space, the
Weil–Petersson symplectic and Poisson geometry of this space as well
as gauge-theoretic extensions of these structures. The quantization
theories can lead to new invariants of hyperbolic 3-manifolds.
The purpose of this handbook is to give a panorama of some of
the most important aspects of Teichmüller theory. The handbook
should be useful to specialists in the field, to graduate students,
and more generally to mathematicians who want to learn about the
subject. All the chapters are self-contained and have a pedagogical
character. They are written by leading experts in the subject.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/029423cover imageuhttps://www.ems-ph.org/img/books/irma11_mini.jpg02336nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000390019924501470023826000820038530000340046733600260050133700260052733800360055334700240058949000390061350600660065252010570071865000350177565000400181070000310185085600320188185600730191356-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070531sz fot ||| 0|eng d a978303719533870a10.4171/0332doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aDaskalopoulos, Panagiota,eauthor.10aDegenerate Diffusionsh[electronic resource] :bInitial Value Problems and Local Regularity Theory /cPanagiota Daskalopoulos, Carlos E. Kenig3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (207 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v11 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book deals with existence, uniqueness, regularity and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation ut = Δum, m ≥ 0, u ≥ 0. Such models arise in plasma physics, diffusions through porous media, thin liquid film dynamics as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems is through the use of local regularity estimates and Harnack type inequalities, which yield compactness for families of solutions. The theory is quite complete in the slow diffusion case (m > 1) and in the supercritical fast diffusion case (mc < m < 1, mc = (n – 2)+/n) while many problems remain in the range m ≤ mc. All of these aspects of the theory are discussed in the book.
The book is addressed to both researchers and to graduate students with a good background in analysis and some previous exposure to partial differential equations.07aDifferential equations2bicssc07aPartial differential equations2msc1 aKenig, Carlos E.,eauthor.40uhttps://doi.org/10.4171/033423cover imageuhttps://www.ems-ph.org/img/books/daskalopoulos_mini.jpg03273nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018310000310019824502040022926000820043330000340051533600260054933700260057533800360060134700240063749000390066150600660070052019650076665000210273165000400275270000320279285600320282485600670285657-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070531sz fot ||| 0|eng d a978303719532170a10.4171/0322doi ach0018173 7aPBP2bicssc a22-xx2msc1 aHofmann, Karl H.,eauthor.10aThe Lie Theory of Connected Pro-Lie Groupsh[electronic resource] :bA Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups /cKarl H. Hofmann, Sidney A. Morris3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (693 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v21 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aLie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them.
If a complete topological group G can be approximated by Lie groups in
the sense that every identity neighborhood U of G
contains a
normal subgroup N such that G/N is a Lie group,
then it is called a pro-Lie group.
Every locally compact connected topological group and every
compact group is a pro-Lie group.
While the class of locally compact groups is not closed under the
formation
of arbitrary products, the class of pro-Lie groups is.
For half a century, locally compact pro-Lie groups have drifted
through the literature, yet this is the first book which
systematically treats the Lie and structure theory of pro-Lie groups
irrespective of local compactness. This study fits very well into
that current trend which addresses infinite dimensional Lie groups.
The results of this text are based on a theory of pro-Lie algebras
which parallels the structure theory of finite dimensional real Lie
algebras to an astonishing degree even though it has to overcome
greater technical obstacles.
This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006), and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.07aTopology2bicssc07aTopological groups, Lie groups2msc1 aMorris, Sidney A.,eauthor.40uhttps://doi.org/10.4171/032423cover imageuhttps://www.ems-ph.org/img/books/hofmann_mini.jpg02824nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000290020624500940023526000820032930000340041133600260044533700260047133800360049734700240053349000530055750600660061052015570067665000470223365000180228065000310229870000320232985600320236185600690239358-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070524sz fot ||| 0|eng d a978303719536970a10.4171/0362doi ach0018173 7aPBMP2bicssc a51-xxa53-xx2msc1 aBuyalo, Sergei,eauthor.10aElements of Asymptotic Geometryh[electronic resource] /cSergei Buyalo, Viktor Schroeder3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (212 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAsymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity.
In the first part of this book, in analogy with the
concepts of classical hyperbolic geometry, the authors provide a systematic
account of the basic theory
of Gromov hyperbolic spaces. These spaces have been studied extensively
in the last twenty years, and have found applications in group theory,
geometric topology, Kleinian groups, as well as dynamics and rigidity theory.
In the second part of the book, various
aspects of the asymptotic geometry of arbitrary metric spaces are considered.
It turns out that the boundary at infinity approach is not appropriate in the general case,
but dimension theory proves useful for finding interesting results and applications.
The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory.
The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich. It addressed to graduate students and researchers working in geometry, topology, and geometric group theory.07aDifferential & Riemannian geometry2bicssc07aGeometry2msc07aDifferential geometry2msc1 aSchroeder, Viktor,eauthor.40uhttps://doi.org/10.4171/036423cover imageuhttps://www.ems-ph.org/img/books/schroeder_mini.jpg02632nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400220020110000260022324500760024926000820032530000340040733600260044133700260046733800360049334700240052949000390055350600660059252013910065865000310204965000320208065000200211265000290213285600320216185600650219359-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070806sz fot ||| 0|eng d a978303719539070a10.4171/0392doi ach0018173 7aPBMW2bicssc 7aPBKG2bicssc a19-xxa46-xx2msc1 aMeyer, Ralf,eauthor.10aLocal and Analytic Cyclic Homologyh[electronic resource] /cRalf Meyer3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (368 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v31 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aPeriodic cyclic homology is a homology theory for non-commutative algebras
that plays a similar role in non-commutative geometry as de Rham
cohomology for smooth manifolds. While it produces good results for
algebras of smooth or polynomial functions, it fails for bigger
algebras such as most Banach algebras or C*-algebras. Analytic
and local cyclic homology are variants of periodic cyclic homology
that work better for such algebras. In this book the author
develops and compares these theories, emphasising their homological
properties. This includes the excision theorem, invariance under
passage to certain dense subalgebras, a Universal Coefficient
Theorem that relates them to K-theory, and the Chern–Connes
character for K-theory and K-homology.
The cyclic homology theories studied in this text require a good
deal of functional analysis in bornological vector spaces, which is
supplied in the first chapters. The focal points here are the
relationship with inductive systems and the functional calculus in
non-commutative bornological algebras.
The book is mainly intended for researchers and advanced graduate
students interested in non-commutative geometry. Some chapters are
more elementary and independent of the rest of the book, and will
be of interest to researchers and students working in functional
analysis and its applications.07aAlgebraic geometry2bicssc07aFunctional analysis2bicssc07a$K$-theory2msc07aFunctional analysis2msc40uhttps://doi.org/10.4171/039423cover imageuhttps://www.ems-ph.org/img/books/meyer_mini.jpg03153nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400220018310000280020524501160023326000820034930000340043133600260046533700260049133800360051734700240055349000510057750600660062852018140069465000370250865000530254565000640259870000300266285600320269285600670272462-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070906sz fot ||| 0|eng d a978303719535270a10.4171/0352doi ach0018173 7aPBT2bicssc a60-xxa91-xx2msc1 aBalkema, Guus,eauthor.10aHigh Risk Scenarios and Extremesh[electronic resource] :bA geometric approach /cGuus Balkema, Paul Embrechts3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (389 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aQuantitative Risk Management (QRM) has become a field of research of considerable
importance to numerous areas of application, including insurance,
banking, energy, medicine, reliability. Mainly motivated by examples
from insurance and finance, the authors develop a theory for
handling multivariate extremes. The approach borrows ideas from
portfolio theory and aims at an intuitive approach in the spirit of
the Peaks over Thresholds method. The point of view is geometric. It
leads to a probabilistic description of what in QRM language may be
referred to as a high risk scenario: the conditional behaviour of
risk factors given that a large move on a linear combination
(portfolio, say) has been observed. The theoretical models which
describe such conditional extremal behaviour are characterized and
their relation to the limit theory for coordinatewise maxima is
explained.
The first part is an elegant exposition of coordinatewise extreme
value theory; the second half develops the more basic geometric
theory. Besides a precise mathematical deduction of the main
results, the text yields numerous discussions of a more applied
nature. A twenty page preview introduces the key concepts; the
extensive introduction provides links to financial mathematics and
insurance theory.
The book is based on a graduate course on point processes and
extremes. It could form the basis for an advanced course on
multivariate extreme value theory or a course on mathematical issues
underlying risk. Students in statistics and finance with a
mathematical, quantitative background are the prime audience.
Actuaries and risk managers involved in data based risk analysis
will find the models discussed in the book stimulating. The text
contains many indications for further research.07aProbability & statistics2bicssc07aProbability theory and stochastic processes2msc07aGame theory, economics, social and behavioral sciences2msc1 aEmbrechts, Paul,eauthor.40uhttps://doi.org/10.4171/035423cover imageuhttps://www.ems-ph.org/img/books/balkema_mini.jpg02891nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000330019924501260023226000820035830000340044033600260047433700260050033800360052634700240056249000390058650600660062552016410069165000350233265000400236770000350240785600320244285600670247464-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20071121sz fot ||| 0|eng d a978303719540670a10.4171/0402doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aHarutyunyan, Gohar,eauthor.10aElliptic Mixed, Transmission and Singular Crack Problemsh[electronic resource] /cGohar Harutyunyan, B.-Wolfgang Schulze3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (777 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v41 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMixed, transmission, or crack problems belong to the analysis of
boundary value problems on manifolds with singularities. The
Zaremba problem with a jump between Dirichlet
and Neumann conditions along an interface on the boundary is a classical example. The central
theme of this book is to study mixed problems in standard Sobolev
spaces as well as in weighted edge spaces where the interfaces are interpreted as edges.
Parametrices and regularity of solutions are obtained within a systematic
calculus of boundary value problems on manifolds with conical or edge
singularities. This calculus allows singularities on the interface, and homotopies between
mixed and crack problems. Additional edge conditions are computed in terms
of relative index results. In a detailed final chapter, the intuitive ideas of the approach are
illustrated, and there is a discussion of future challenges. A special feature of
the text is the inclusion of many worked out examples which help the
reader to appreciate the scope of the theory and to treat new cases of practical interest.
This book is addressed to mathematicians and physicists interested
in models with singularities, associated boundary value problems,
and their solvability strategies based on pseudo-differential operators.
The material is also useful for
students in higher semesters and young researchers, as well as for
experienced specialists working in analysis on manifolds with
geometric singularities, the applications of index theory and
spectral theory, operator algebras with symbolic structures,
quantisation, and asymptotic analysis.07aDifferential equations2bicssc07aPartial differential equations2msc1 aSchulze, B.-Wolfgang,eauthor.40uhttps://doi.org/10.4171/040423cover imageuhttps://www.ems-ph.org/img/books/schulze_mini.jpg02422nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000350020624501140024126000820035530000340043733600260047133700260049733800360052334700240055949000390058350600660062252011410068865000350182965000400186465000290190470000280193385600320196185600670199365-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20071121sz fot ||| 0|eng d a978303719542070a10.4171/0422doi ach0018173 7aPBKJ2bicssc a35-xxa46-xx2msc1 aHaroske, Dorothee D.,eauthor.10aDistributions, Sobolev Spaces, Elliptic Equationsh[electronic resource] /cDorothee D. Haroske, Hans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (303 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIt is the main aim of this book to develop at an accessible, moderate
level an L2 theory for elliptic differential operators of second order on
bounded smooth domains in Euclidean n-space, including a priori
estimates for boundary-value problems in terms of (fractional) Sobolev
spaces on domains and on their boundaries, together with a related
spectral theory.
The presentation is preceded by an introduction to the classical theory
for the Laplace–Poisson equation, and some chapters providing required
ingredients such as the theory of distributions, Sobolev spaces and the
spectral theory in Hilbert spaces.
The book grew out of two-semester courses the authors have given
several times over a period of ten years at the Friedrich Schiller
University of Jena. It is addressed to graduate students and mathematicians
who have a working knowledge of calculus, measure theory
and the basic elements of functional analysis (as usually covered by
undergraduate courses) and who are seeking an accessible introduction
to some aspects of the theory of function spaces and its applications to
elliptic equations.07aDifferential equations2bicssc07aPartial differential equations2msc07aFunctional analysis2msc1 aTriebel, Hans,eauthor.40uhttps://doi.org/10.4171/042423cover imageuhttps://www.ems-ph.org/img/books/triebel_mini.jpg02533nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000330023024500980026326000820036130000340044333600260047733700260050333800360052934700240056549000510058950600660064052011510070665000320185765000350188965000330192465000240195765000660198185600320204785600680207967-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080212sz fot ||| 0|eng d a978303719544470a10.4171/0442doi ach0018173 7aPBKG2bicssc 7aPBKQ2bicssc a28-xxa26-xxa49-xx2msc1 aDe Lellis, Camillo,eauthor.10aRectifiable Sets, Densities, and Tangent Measuresh[electronic resource] /cCamillo De Lellis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (133 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe characterization of rectifiable sets through the existence of
densities is a pearl of geometric measure theory. The difficult proof,
due to Preiss, relies on many beautiful and deep ideas and novel
techniques. Some of them have already proven useful in other contexts,
whereas others have not yet been exploited. These notes give a simple
and short presentation of the former, and provide some perspective of
the latter.
This text emerged from a course on rectifiability given at the
University of Zürich. It is addressed both to researchers and students,
the only prerequisite is a solid knowledge in standard measure theory.
The first four chapters give an introduction to rectifiable sets and
measures in euclidean spaces, covering classical topics such as the area
formula, the theorem of Marstrand and the most elementary rectifiability
criterions. The fifth chapter is dedicated to a subtle rectifiability
criterion due to Marstrand and generalized by Mattila, and the last
three focus on Preiss' result. The aim is to provide a self-contained
reference for anyone interested in an overview of this fascinating topic.07aFunctional analysis2bicssc07aCalculus of variations2bicssc07aMeasure and integration2msc07aReal functions2msc07aCalculus of variations and optimal control; optimization2msc40uhttps://doi.org/10.4171/044423cover imageuhttps://www.ems-ph.org/img/books/delellis_mini.jpg02374nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000330019924501530023226000820038530000340046733600260050133700260052733800360055334700240058949000390061350600660065252011550071865000320187365000290190585600320193485600700196672-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080228sz fot ||| 0|eng d a978303719543770a10.4171/0432doi ach0018173 7aPBKG2bicssc a46-xx2msc1 aTimmermann, Thomas,eauthor.10aAn Invitation to Quantum Groups and Dualityh[electronic resource] :bFrom Hopf Algebras to Multiplicative Unitaries and Beyond /cThomas Timmermann3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (427 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides an introduction to the theory of quantum groups
with emphasis on their duality and on the setting of operator algebras.
Part I of the text presents the basic theory of Hopf algebras, Van
Daele’s duality theory of algebraic quantum groups, and Woronowicz’s
compact quantum groups, staying in a purely algebraic setting.
Part II focuses on quantum groups in the setting of operator algebras.
Woronowicz’s compact quantum groups are treated in the setting of
C*-algebras, and the fundamental multiplicative unitaries of Baaj and
Skandalis are studied in detail. An outline of Kustermans’ and Vaes’
comprehensive theory of locally compact quantum groups completes
this part. Part III leads to selected topics, such as coactions,
Baaj–Skandalis-duality, and approaches to quantum groupoids in the
setting of operator algebras.
The book is addressed to graduate students and non-experts from other
fields. Only basic knowledge of (multi-) linear algebra is required for
the first part, while the second and third part assume some familiarity
with Hilbert spaces, C*-algebras, and von Neumann algebras.07aFunctional analysis2bicssc07aFunctional analysis2msc40uhttps://doi.org/10.4171/043423cover imageuhttps://www.ems-ph.org/img/books/timmermann_mini.jpg02051nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000310019924500750023026000820030530000340038733600260042133700260044733800360047334700240050949000390053350600660057252008970063865000340153565000420156985600320161185600700164374-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080229sz fot ||| 0|eng d a978303719541370a10.4171/0412doi ach0018173 7aPBFD2bicssc a20-xx2msc1 aBogopolski, Oleg,eauthor.10aIntroduction to Group Theoryh[electronic resource] /cOleg Bogopolski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (187 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book quickly introduces beginners to general group theory and then focuses on three main themes:
finite group theory, including sporadic groups;
combinatorial and geometric group theory, including the Bass–Serre theory of groups acting on trees;
the theory of train tracks by Bestvina and Handel for automorphisms of free groups.
With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples.
Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc40uhttps://doi.org/10.4171/041423cover imageuhttps://www.ems-ph.org/img/books/bogopolski_mini.jpg02474nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018310000300019824501180022826000820034630000340042833600260046233700260048833800360051434700240055049000390057450600660061352012180067965000450189765000550194270000270199785600320202485600680205675-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080303sz fot ||| 0|eng d a978303719549970a10.4171/0492doi ach0018173 7aPBK2bicssc a32-xx2msc1 aJarnicki, Marek,eauthor.10aFirst Steps in Several Complex Variables: Reinhardt Domainsh[electronic resource] /cMarek Jarnicki, Peter Pflug3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (367 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties.
Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics.
The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis.07aCalculus & mathematical analysis2bicssc07aSeveral complex variables and analytic spaces2msc1 aPflug, Peter,eauthor.40uhttps://doi.org/10.4171/049423cover imageuhttps://www.ems-ph.org/img/books/jarnicki_mini.jpg02786nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200150018408400150019910000360021424500850025026000820033530000340041733600260045133700260047733800360050334700240053949000610056350600660062452015320069065000470222265000240226965000310229385600320232485600680235676-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080408sz fot ||| 0|eng d a978303719550570a10.4171/0502doi ach0018173 7aPBMP2bicssc 7aPB2bicssc a53-xx2msc1 aTaimanov, Iskander A.,eauthor.10aLectures on Differential Geometryh[electronic resource] /cIskander A. Taimanov3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (219 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDifferential geometry studies geometrical objects using analytical methods.
Like modern analysis itself, differential geometry originates in classical
mechanics. For instance, geodesics and minimal surfaces are defined via
variational principles and the curvature of a curve is easily interpreted as
the acceleration with respect to the path length parameter. Modern
differential geometry in its turn strongly contributed to modern physics.
This book gives an introduction to the basics of differential geometry, keeping
in mind the natural origin of many geometrical quantities, as well as
the applications of differential geometry and its methods to other sciences.
The text is divided into three parts. The first part covers the basics of curves
and surfaces, while the second part is designed as an introduction to smooth
manifolds and Riemannian geometry. In particular, Chapter 5 contains short
introductions to hyperbolic geometry and geometrical principles of special
relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary
differential equations is required. The third part is more advanced and
introduces into matrix Lie groups and Lie algebras, representation theory of
groups, symplectic and Poisson geometry, and applications of complex analysis
in surface theory.
The book is based on lectures the author held repeatedly at Novosibirsk State
University. It is addressed to students as well as to anyone who wants to learn
the basics of differential geometry.07aDifferential & Riemannian geometry2bicssc07aMathematics2bicssc07aDifferential geometry2msc40uhttps://doi.org/10.4171/050423cover imageuhttps://www.ems-ph.org/img/books/taimanov_mini.jpg03196nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400290018310000320021224501320024426000820037630000340045833600260049233700260051833800360054434700240058049000390060450600660064352018800070965000370258965000530262665000360267965000200271585600320273585600670276777-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080429sz fot ||| 0|eng d a978303719545170a10.4171/0452doi ach0018173 7aPBT2bicssc a60-xxa43-xxa62-xx2msc1 aFeldman, Gennadiy,eauthor.10aFunctional Equations and Characterization Problems on Locally Compact Abelian Groupsh[electronic resource] /cGennadiy Feldman3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (268 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v51 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book deals with the characterization of probability distributions. It is well
known that both the sum and the difference of two Gaussian independent
random variables with equal variance are independent as well. The converse statement was
proved independently by M. Kac and S. N. Bernstein. This result is a famous
example of a characterization theorem. In general, characterization problems
in mathematical statistics are statements in which the description of possible
distributions of random variables follows from properties of some functions in
these variables.
In recent years, a great deal of attention has been focused upon generalizing
the classical characterization theorems to random variables with values in
various algebraic structures such as locally compact Abelian groups, Lie
groups, quantum groups, or symmetric spaces. The present book is aimed at
the generalization of some well-known characterization theorems to the case
of independent random variables taking values in a locally compact Abelian
group X. The main attention is paid to the characterization of the Gaussian
and the idempotent distribution (group analogs of the Kac–Bernstein,
Skitovich–Darmois, and Heyde theorems). The solution of the corresponding
problems is reduced to the solution of some functional equations in the
class of continuous positive definite functions defined on the character group
of X. Group analogs of the Cramér and Marcinkiewicz theorems are also
studied.
The author is an expert in algebraic probability theory. His comprehensive
and self-contained monograph is addressed to mathematicians working in
probability theory on algebraic structures, abstract harmonic analysis,
and functional equations. The book concludes with comments and unsolved
problems that provide further stimulation for future research in the theory.07aProbability & statistics2bicssc07aProbability theory and stochastic processes2msc07aAbstract harmonic analysis2msc07aStatistics2msc40uhttps://doi.org/10.4171/045423cover imageuhttps://www.ems-ph.org/img/books/feldman_mini.jpg02977nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200160018408400220020010000300022224500800025226000820033230000340041433600260044833700260047433800360050034700240053649000510056050600660061152016770067765000300235465000350238465000480241965000380246785600320250585600660253778-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080819sz fot ||| 0|eng d a978303719554370a10.4171/0542doi ach0018173 7aPBPH2bicssc 7aTGB2bicssc a58-xxa57-xx2msc1 aFarber, Michael,eauthor.10aInvitation to Topological Roboticsh[electronic resource] /cMichael Farber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (143 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book discusses several selected topics of a new emerging area of research lying on the interface between topology and engineering. The first main topic of the book is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g. engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces we apply a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in the book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. The book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic of the book is topology of configuration spaces associated to polyhedra. The book gives an account of a beautiful work of S.R. Gal suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next we study the knot theory of a robot arm focusing on a recent important result of R. Connelly, E. Demain and G. Rote. Finally, the book investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant TC(X) measuring navigational complexity of configuration spaces.
The book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering.07aAnalytic topology2bicssc07aMechanical engineering2bicssc07aGlobal analysis, analysis on manifolds2msc07aManifolds and cell complexes2msc40uhttps://doi.org/10.4171/054423cover imageuhttps://www.ems-ph.org/img/books/farber_mini.jpg02339nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000340023024500770026426000820034130000340042333600260045733700260048333800360050934700240054549000510056950600660062052010190068665000280170565000360173365000380176965000230180765000230183085600320185385600680188579-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080901sz fot ||| 0|eng d a978303719552970a10.4171/0522doi ach0018173 7aPBMZ2bicssc 7aPBRD2bicssc a52-xxa05-xxa11-xx2msc1 aBarvinok, Alexander,eauthor.10aInteger Points in Polyhedrah[electronic resource] /cAlexander Barvinok3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (199 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is a self-contained exposition of several core aspects of the theory of rational polyhedra
with a view towards algorithmic applications to efficient counting of integer points,
a problem arising in many areas of pure and applied mathematics. The approach is based
on the consistent development and application of the apparatus of generating functions
and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic,
continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra–
Lenstra–Lovász lattice reduction algorithm, to recent advances such as the Berline–Vergne
local formula.
The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.07aFinite geometry2bicssc07aAlgebraic number theory2bicssc07aConvex and discrete geometry2msc07aCombinatorics2msc07aNumber theory2msc40uhttps://doi.org/10.4171/052423cover imageuhttps://www.ems-ph.org/img/books/barvinok_mini.jpg02446nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018424500630019926000820026230000340034433600260037833700260040433800360043034700240046649000830049050502920057350600660086552009740093165000340190565000240193970000330196385600320199685600680202880-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080611sz fot ||| 0|eng d a978303719547570a10.4171/0472doi ach0018173 7aPBFD2bicssc a81-xx2msc10aQuantum Groupsh[electronic resource] /cBenjamin Enriquez3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (140 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1200tLectures on tensor categories /rDamien Calaque, Pavel Etingof --tThe Drinfeld associator of gl(1 | 1) /rJens Lieberum --tIntegrable systems associated with elliptic algebras /rAlexander Odesskii, Vladimir Rubtsov --tOn the automorphisms of Uq+(ℊ) /rNicolás Andruskiewitsch.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius–Perron dimensions, and the classification of tensor categories.
The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of
algebra automorphisms of quantum groups. The preface sets the results presented in perspective.
Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.07aGroups & group theory2bicssc07aQuantum theory2msc1 aEnriquez, Benjamin,eeditor.40uhttps://doi.org/10.4171/047423cover imageuhttps://www.ems-ph.org/img/books/enriquez_mini.jpg03927nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018424501140019926000820031330000340039533600260042933700260045533800360048134700240051749000500054150512950059150600660188652013690195265000470332165000310336870000370339970000260343685600320346285600710349481-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080611sz fot ||| 0|eng d a978303719551270a10.4171/0512doi ach0018173 7aPBMP2bicssc a53-xx2msc10aRecent Developments in Pseudo-Riemannian Geometryh[electronic resource] /cDmitri V. Alekseevsky, Helga Baum3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (549 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)00tThe classification problem for pseudo-Riemannian symmetric spaces /rInes Kath, Martin Olbrich --tHolonomy groups of Lorentzian manifolds: classification, examples, and applications /rAnton Galaev, Thomas Leistner --tHypersymplectic manifolds /rAndrew Dancer, Andrew Swann --tAnti-self-dual conformal structures in neutral signature /rMaciej Dunajski, Simon West --tA neutral Kähler surface with applications in geometric optics /rBrendan Guilfoyle, Wilhelm Klingenberg --tA primer on the (2 + 1) Einstein universe /rThierry Barbot, Todd A. Drumm, Virginie Charette, William M. Goldman, Karin Melnick --tEssential conformal structures in Riemannian and Lorentzian geometry /rCharles Frances --tConformal transformations of pseudo-Riemannian manifolds /rWolfgang Kühnel, Hans-Bert Rademacher --tThe causal hierarchy of spacetimes /rEttore Minguzzi, Miguel Sánchez Caja --tGeodesics in semi-Riemannian manifolds: geometric properties and variational tools /rAnna Maria Candela, Miguel Sánchez Caja --tLorentzian symmetric spaces in supergravity /rJosé Miguel Figueroa-O’Farrill --tMetric bundles of split signature and type II supergravity /rFrederik Witt --tEinstein metrics with 2-dimensional Killing leaves and their physical interpretation /rGaetano Vilasi.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides an introduction to and survey of recent developments in
pseudo-Riemannian geometry, including applications in mathematical physics,
by leading experts in the field. Topics covered are:
Classification of pseudo-Riemannian symmetric spaces
Holonomy groups of Lorentzian and pseudo-Riemannian manifolds
Hypersymplectic manifolds
Anti-self-dual conformal structures in neutral signature and integrable systems
Neutral Kähler surfaces and geometric optics
Geometry and dynamics of the Einstein universe
Essential conformal structures and conformal transformations in pseudo-Riemannian geometry
The causal hierarchy of spacetimes
Geodesics in pseudo-Riemannian manifolds
Lorentzian symmetric spaces in supergravity
Generalized geometries in supergravity
Einstein metrics with Killing leaves
The book is addressed to advanced students as well as to researchers in
differential geometry, global analysis, general relativity and string
theory. It shows essential differences between the geometry on manifolds
with positive definite metrics and on those with indefinite metrics, and
highlights the interesting new geometric phenomena, which naturally arise
in the indefinite metric case. The reader finds a description of the present state of art
in the field as well as open problems, which can stimulate further research.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc1 aAlekseevsky, Dmitri V.,eeditor.1 aBaum, Helga,eeditor.40uhttps://doi.org/10.4171/051423cover imageuhttps://www.ems-ph.org/img/books/alekseevsky_mini.jpg02180nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000360020624501300024226000820037230000340045433600260048833700260051433800360054034700240057649000610060050600660066152008670072765000290159465000260162365000280164970000390167785600320171685600700174882-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080626sz fot ||| 0|eng d a978303719518570a10.4171/0182doi ach0018173 7aPBKN2bicssc a42-xxa65-xx2msc1 aMohlenkamp, Martin J.,eauthor.10aWavelets, Their Friends, and What They Can Do for Youh[electronic resource] /cMartin J. Mohlenkamp, María Cristina Pereyra3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (119 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSo what is all the fuss about wavelets?
You can find out by reading these notes. They will introduce you to the
central concepts surrounding wavelets and their applications. By
focusing on the essential ideas and arguments, they enable you to get
to the heart of the matter as quickly as possible. They then point
you to the appropriate places in the literature for detailed proofs and
real applications, so you can continue your study.
They begin with the notion of time-frequency analysis, present the
multiresolution analysis and basic wavelet construction, introduce you
to the many friends, relatives and mutations of wavelets, and finally
give a selection of applications.
They are suitable for beginning graduate students and above.
A preliminary chapter containing some of the prerequisite concepts
and definitions is included for reference.07aFourier analysis2bicssc07aFourier analysis2msc07aNumerical analysis2msc1 aPereyra, María Cristina,eauthor.40uhttps://doi.org/10.4171/018423cover imageuhttps://www.ems-ph.org/img/books/mohlenkamp_mini.jpg02637nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400220020110000390022324501130026226000820037530000340045733600260049133700260051733800360054334700240057949000510060350600660065452013180072065000310203865000270206965000280209665000400212485600320216485600670219683-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080704sz fot ||| 0|eng d a978303719565970a10.4171/0652doi ach0018173 7aPBMW2bicssc 7aPBFL2bicssc a14-xxa13-xx2msc1 aSchmitt, Alexander H. W.,eauthor.10aGeometric Invariant Theory and Decorated Principal Bundlesh[electronic resource] /cAlexander H. W. Schmitt3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (396 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness
of the number of quotients, and the variation of quotients.
In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map.
Via the universal Kobayashi–Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces.
The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles.
The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.07aAlgebraic geometry2bicssc07aFields & rings2bicssc07aAlgebraic geometry2msc07aCommutative rings and algebras2msc40uhttps://doi.org/10.4171/065423cover imageuhttps://www.ems-ph.org/img/books/schmitt_mini.jpg02838nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400290018410000280021324500830024126000820032430000340040633600260044033700260046633800360049234700240052849000390055250600660059152015910065765000320224865000290228065000330230965000260234285600320236885600760240084-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080902sz fot ||| 0|eng d a978303719519270a10.4171/0192doi ach0018173 7aPBKG2bicssc a46-xxa28-xxa42-xx2msc1 aTriebel, Hans,eauthor.10aFunction Spaces and Wavelets on Domainsh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (265 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v71 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWavelets have emerged as an important tool in analyzing functions
containing discontinuities and sharp spikes. They were developed
independently in the fields of mathematics, quantum physics, electrical
engineering, and seismic geology. Interchanges between these fields
during the last ten years have led to many new wavelet applications such
as image compression, turbulence, human vision, radar, earthquake
prediction, and pure mathematics applications such as solving partial
differential equations.
This book develops a theory of wavelet bases and wavelet frames for function spaces on various
types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the
exposition moves on to so-called thick domains (including Lipschitz
domains and snowflake domains). Especially, wavelet expansions and
extensions to corresponding spaces on Euclidean n-spaces are
developed. Finally, spaces on smooth and cellular domains and related
manifolds are treated.
Although the presentation relies on the recent theory of function spaces, basic notation and classical results are
repeated in order to make the text self-contained.
The book is addressed to two types of readers:
researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions, and scientists who wish to use wavelet bases in classical function spaces for various applications.
Adapted to the second type of readers, the preface contains a guide to where one finds basic definitions and key
assertions.07aFunctional analysis2bicssc07aFunctional analysis2msc07aMeasure and integration2msc07aFourier analysis2msc40uhttps://doi.org/10.4171/019423cover imageuhttps://www.ems-ph.org/img/books/triebel(Tracts7)_mini.jpg03383nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200160018308400220019910000270022124501340024826000820038230000340046433600260049833700260052433800360055034700240058649000390061050600660064952020170071565000310273265000470276365000280281065000260283870000360286485600320290085600650293285-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080902sz fot ||| 0|eng d a978303719526070a10.4171/0262doi ach0018173 7aPBS2bicssc 7aUAA2bicssc a65-xxa68-xx2msc1 aNovak, Erich,eauthor.10aTractability of Multivariate Problemsh[electronic resource] :bVolume I: Linear Information /cErich Novak, Henryk Woźniakowski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (395 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v61 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMultivariate problems occur in many applications.
These problems are defined on spaces of d-variate functions and
d can be huge – in the hundreds or even in the thousands.
Some high-dimensional problems can be solved efficiently to within ε,
i.e., the cost increases polynomially in ε−1 and d.
However, there are many multivariate problems
for which even the minimal cost increases exponentially in d.
This exponential dependence on d is called
intractability or the curse of dimensionality.
This is the first of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems.
It is devoted to algorithms using
linear information consisting of arbitrary linear functionals.
The theory for multivariate problems is developed
in various settings: worst case, average case, randomized and
probabilistic. A problem is tractable if its minimal cost is not
exponential in ε−1 and d. There are various notions of
tractability,
depending on how we measure the lack of exponential dependence.
For example, a problem is polynomially tractable if its minimal cost is
polynomial in ε−1 and d. The study of tractability was
initiated about 15 years ago. This is the first research
monograph on this subject.
Many multivariate problems suffer from the curse of dimensionality
when they are defined over classical (unweighted) spaces.
But many
practically important problems are solved today for huge d in a
reasonable time. One of the most intriguing challenges of theory is to
understand why this is possible. Multivariate problems may become tractable
if they are defined over weighted spaces with properly
decaying weights. In this case, all variables and groups of variables
are moderated by weights. The main purpose of this book is to study weighted spaces
and to obtain conditions on the weights that are necessary and sufficient
to achieve various notions of tractability.
The book is of interes...07aNumerical analysis2bicssc07aMathematical theory of computation2bicssc07aNumerical analysis2msc07aComputer science2msc1 aWoźniakowski, Henryk,eauthor.40uhttps://doi.org/10.4171/026423cover imageuhttps://www.ems-ph.org/img/books/novak_mini.jpg02455nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000310020624500970023726000820033430000340041633600260045033700260047633800360050234700240053849000390056250600660060152012410066765000310190865000280193965000380196785600320200585600680203786-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080901sz fot ||| 0|eng d a978303719548270a10.4171/0482doi ach0018173 7aPBPD2bicssc a55-xxa57-xx2msc1 atom Dieck, Tammo,eauthor.10aAlgebraic Topologyh[electronic resource] :bCorrected 2nd printing, 2010 /cTammo tom Dieck3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (578 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends to start an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results.
Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (masters) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.07aAlgebraic topology2bicssc07aAlgebraic topology2msc07aManifolds and cell complexes2msc40uhttps://doi.org/10.4171/048423cover imageuhttps://www.ems-ph.org/img/books/tomDieck_mini.jpg02109nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200160018308400220019910000320022124501310025326000820038430000340046633600260050033700260052633800360055234700240058849000510061250600660066352007770072965000310150665000480153765000280158565000240161385600320163785600660166987-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080924sz fot ||| 0|eng d a978303719567370a10.4171/0672doi ach0018173 7aPBS2bicssc 7aPHT2bicssc a65-xxa81-xx2msc1 aLubich, Christian,eauthor.10aFrom Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysish[electronic resource] /cChristian Lubich3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (153 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aQuantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations.
This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrödinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.07aNumerical analysis2bicssc07aQuantum physics (quantum mechanics)2bicssc07aNumerical analysis2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/067423cover imageuhttps://www.ems-ph.org/img/books/lubich_mini.jpg03971nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018424501130019926000820031230000340039433600260042833700260045433800360048034700240051649000540054050510910059450600660168552016660175165000270341765000400344470000350348485600320351985600700355188-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080924sz fot ||| 0|eng d a978303719562870a10.4171/0622doi ach0018173 7aPBFL2bicssc a16-xx2msc10aTrends in Representation Theory of Algebras and Related Topicsh[electronic resource] /cAndrzej Skowroński3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (722 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tFinite dimensional Hecke algebras /rSusumu Ariki --tSemi-invariants of quivers and their zero sets /rGrzegorz Bobiński, Christine Riedtmann, Andrzej Skowroński --tMaximal Cohen–Macaulay modules over surface singularities /rIgor Burban, Yuriy Drozd --tRank varieties /rJon F. Carlson --tPeriodic algebras /rKarin Erdmann, Andrzej Skowroński --tPreprojective algebras and cluster algebras /rChristof Geiss, Bernard Leclerc, Jan Schröer --tSymplectic reflection algebras /rIain G. Gordon --tAuslander–Reiten theory revisited /rOsamu Iyama --tCalabi–Yau categories and Poincaré duality /rPeter Jørgensen --tRepresentation types of algebras from the model theory point of view /rStanisław Kasjan --tCalabi–Yau triangulated categories /rBernhard Keller --tA panorama of diagram algebras /rSteffen Koenig --tSpectral analysis of finite dimensional algebras and singularities /rHelmut Lenzing, Luz de Teresa --tModuli of representations of quivers /rMarkus Reineke --tSelfinjective algebras of quasitilted type /rAndrzej Skowroński, Kunio Yamagata.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is concerned with recent trends in the representation
theory of algebras and its exciting interaction with geometry, topology,
commutative algebra, Lie algebras, quantum groups, homological algebra,
invariant theory, combinatorics, model theory and theoretical physics.
The collection of articles, written by leading researchers in the field,
is conceived as a sort of handbook providing easy access to the present state of knowledge and
stimulating further development.
The topics under discussion include diagram algebras,
Brauer algebras, cellular algebras, quasi-hereditary algebras,
Hall algebras, Hecke algebras, symplectic reflection algebras,
Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras,
cluster algebras, rank varieties, varieties of algebras and modules,
moduli of representations of quivers, semi-invariants of quivers,
Cohen–Macaulay modules, singularities, coherent sheaves,
derived categories, spectral representation theory, Coxeter polynomials,
Auslander–Reiten theory, Calabi–Yau triangulated categories,
Poincaré duality spaces, selfinjective algebras, periodic algebras,
stable module categories, Hochschild cohomologies, deformations of algebras,
Galois coverings of algebras, tilting theory,
algebras of small homological dimensions, representation types of algebras,
model theory.
The book consists of fifteen self-contained expository survey
articles and is addressed to researchers and graduate students
in algebra as well as
a broader mathematical community. They contain a large number of open
problems and give new perspectives for research in the field.07aFields & rings2bicssc07aAssociative rings and algebras2msc1 aSkowroński, Andrzej,eeditor.40uhttps://doi.org/10.4171/062423cover imageuhttps://www.ems-ph.org/img/books/skowronski_mini.jpg04312nam a22004095a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018424501480020626000820035430000340043633600260047033700260049633800360052234700240055849000540058250510900063650600660172652017640179265000310355665000200358765000480360770000350365570000290369070000270371970000280374670000330377485600320380785600630383989-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20081006sz fot ||| 0|eng d a978303719560470a10.4171/0602doi ach0018173 7aPBMW2bicssc a19-xxa58-xx2msc10aK-Theory and Noncommutative Geometryh[electronic resource] /cGuillermo Cortiñas, Joachim Cuntz, Max Karoubi, Ryszard Nest, Charles A. Weibel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (454 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tCategorical aspects of bivariant K-theory /rRalf Meyer --tInheritance of isomorphism conjectures under colimits /rArthur Bartels, Siegfried Echterhoff, Wolfgang Lück --tCoarse and equivariant co-assembly maps /rHeath Emerson, Ralf Meyer --tOn K1 of a Waldhausen category /rFernando Muro, Andrew Tonks --tTwisted K-theory – old and new /rMax Karoubi --tEquivariant cyclic homology for quantum groups /rChristian Voigt --tA Schwartz type algebra for the tangent groupoid /rPaulo Carrillo Rouse --tC*-algebras associated with the ax + b-semigroup over ℕ /rJoachim Cuntz --tOn a class of Hilbert C*-manifolds /rWend Werner --tDuality for topological abelian group stacks and T-duality /rUlrich Bunke, Thomas Schick, Markus Spitzweck, Andreas Thom --tDeformations of gerbes on smooth manifolds /rPaul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan --tTorsion classes of finite type and spectra /rGrigory Garkusha, Mike Prest --tParshin’s conjecture revisited /rThomas Geisser --tAxioms for the norm residue isomorphism /rCharles A. Weibel.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSince its inception 50 years ago, K-theory has been a tool for
understanding a wide-ranging family of mathematical structures and their
invariants: topological spaces, rings, algebraic varieties and operator
algebras are the dominant examples. The invariants range from
characteristic classes in cohomology, determinants of matrices, Chow
groups of varieties, as well as traces and indices of elliptic operators.
Thus K-theory is notable for its connections with other branches of
mathematics.
Noncommutative geometry develops tools which allow
one to think of noncommutative algebras in the same footing as commutative
ones: as algebras of functions on (noncommutative) spaces. The algebras
in question come from problems in various areas of mathematics and mathematical
physics; typical examples include algebras of pseudodifferential operators, group algebras,
and other algebras arising from quantum field theory.
To study noncommutative geometric problems one considers invariants of the relevant noncommutative
algebras. These invariants include algebraic and topological K-theory, and also cyclic homology,
discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative
version of de Rham cohomology and as an additive version of K-theory.
There are primary and secondary Chern characters which pass from
K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative
problems, and have applications ranging from index theorems to the detection of singularities of commutative
algebraic varieties.
The contributions to this volume represent
this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.07aAlgebraic geometry2bicssc07a$K$-theory2msc07aGlobal analysis, analysis on manifolds2msc1 aCortiñas, Guillermo,eeditor.1 aCuntz, Joachim,eeditor.1 aKaroubi, Max,eeditor.1 aNest, Ryszard,eeditor.1 aWeibel, Charles A.,eeditor.40uhttps://doi.org/10.4171/060423cover imageuhttps://www.ems-ph.org/img/books/cortinas.jpg03769nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018424501070020626000820031330000340039533600260042933700260045533800360048134700240051749000500054150512870059150600660187852011240194465000320306865000310310065000520313170000350318370000340321870000300325285600320328285600690331491-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20081022sz fot ||| 0|eng d a978303719557470a10.4171/0572doi ach0018173 7aPHGK2bicssc a01-xxa82-xx2msc10aBoltzmann’s Legacyh[electronic resource] /cGiovanni Gallavotti, Wolfgang L. Reiter, Jakob Yngvason3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (284 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)00tIntroduction /rGiovanni Gallavotti --tBoltzmann and the end of the mechanistic worldview /rJürgen Renn --tWhat if Boltzmann had known about quantum mechanics /rElliott H. Lieb --tEntropy, nonequilibrium, chaos and infinitesimals /rGiovanni Gallavotti --tFrom time-symmetric microscopic dynamics to time-asymmetric macroscopic behavior: an overview /rJoel L. Lebowitz --tWhat physical quantities make sense in nonequilibrium statistical mechanics? /rDavid Ruelle --tBoltzmann, ergodic theory, and chaos /rDonald S. Ornstein --t134 years of Boltzmann equation /rCarlo Cercignani --tH-theorem and beyond: Boltzmann's entropy in today's mathematics /rCédric Villani --tOn the Boltzmann equation for weakly nonlinear wave equations /rHerbert Spohn --tEntropy, probability and dynamics /rE.G.D. Cohen --tRealizing Boltzmann's dream: computer simulations in modern statistical mechanics /rChristoph Dellago, Harald A. Posch --tStatistical properties of the cluster dynamics of the systems of statistical mechanics /rAndrei Gabrielov, Vladimir Keilis-Borok, Yakov G. Sinai, Ilya Zaliapin --tBoltzmann and evolution: some basic questions of biology seen with atomistic glasses /rPeter Schuster --tLudwig Boltzmann – the restless prophet /rWolfgang L. Reiter.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aLudwig Eduard Boltzmann (1844–1906) was an
Austrian physicist famous for his founding contributions in the fields
of statistical mechanics and statistical thermodynamics. He was one of
the most important advocates for atomic theory when that scientific
model was still highly controversial. To commemorate the 100th
anniversary of his death in Duino, the International Symposium
“Boltzmann's Legacy” was held at the Erwin Schrödinger International
Institute for Mathematical Physics in June 2006.
This text covers a wide spectrum of topics ranging from equilibrium
statistical and nonequilibrium statistical physics, ergodic theory and
chaos to basic questions of biology and historical accounts of
Boltzmann's work. Besides the lectures presented at the symposium the
volume also contains contributions specially written for this occasion.
The articles give a broad overview of Boltzmann's legacy to the sciences
from the standpoint of some of present day's leading scholars in the field.
The book addresses students and researchers in mathematics, physics and
the history of science.07aStatistical physics2bicssc07aHistory and biography2msc07aStatistical mechanics, structure of matter2msc1 aGallavotti, Giovanni,eeditor.1 aReiter, Wolfgang L.,eeditor.1 aYngvason, Jakob,eeditor.40uhttps://doi.org/10.4171/057423cover imageuhttps://www.ems-ph.org/img/books/boltzmann_mini.jpg02573nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400290018410000390021324501050025226000820035730000340043933600260047333700260049933800360052534700240056149000530058550600660063852012370070465000310194165000450197265000400201765000480205785600320210585600740213793-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090110sz fot ||| 0|eng d a978303719568070a10.4171/0682doi ach0018173 7aPHRD2bicssc a83-xxa35-xxa58-xx2msc1 aChristodoulou, Demetrios,eauthor.10aThe Formation of Black Holes in General Relativityh[electronic resource] /cDemetrios Christodoulou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (599 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity.
A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves.
The theorems proved in the present monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler–Lagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable.
This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations.07aGeneral relativity2bicssc07aRelativity and gravitational theory2msc07aPartial differential equations2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/068423cover imageuhttps://www.ems-ph.org/img/books/christodoulou3_mini.jpg02784nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018310000270019824501400022526000820036530000340044733600260048133700260050733800360053334700240056949000560059350600660064952015200071565000350223565000310227070000340230185600320233585600670236794-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20081201sz fot ||| 0|eng d a978303719559870a10.4171/0592doi ach0018173 7aPBX2bicssc a01-xx2msc1 aBeery, Janet,eauthor.10aThomas Harriot’s Doctrine of Triangular Numbers: the ‘Magisteria Magna’h[electronic resource] /cJanet Beery, Jacqueline Stedall3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (144 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThomas Harriot (c. 1560–1621) was a mathematician and astronomer, known
not only for his work in algebra and geometry, but also for his
wide-ranging interests in ballistics, navigation, and optics (he
discovered the sine law of refraction now known as Snell’s law).
By about 1614, Harriot had developed finite difference interpolation
methods for navigational tables. In 1618 (or slightly later) he composed
a treatise entitled ‘De numeris triangularibus et inde de
progressionibus arithmeticis, Magisteria magna’, in which he derived
symbolic interpolation formulae and showed how to use them. This
treatise was never published and is here reproduced for the first time.
Commentary has been added to help the reader to follow Harriot’s
beautiful but almost completely nonverbal presentation. The introductory
essay preceding the treatise gives an overview of the contents of the
‘Magisteria’ and describes its influence on Harriot’s contemporaries and
successors over the next sixty years. Harriot’s method was not
superseded until Newton, apparently independently, made a similar
discovery in the 1660s. The ideas in the ‘Magisteria’ were spread
primarily through personal communication and unpublished manuscripts,
and so, quite apart from their intrinsic mathematical interest, their
survival in England during the seventeenth century provides an important
case study in the dissemination of mathematics through informal networks
of friends and acquaintances.07aHistory of mathematics2bicssc07aHistory and biography2msc1 aStedall, Jacqueline,eauthor.40uhttps://doi.org/10.4171/059423cover imageuhttps://www.ems-ph.org/img/books/harriot_mini.jpg04487nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018424500950020626000820030130000340038333600260041733700260044333800360046934700240050549000830052950515200061250600660213252016670219865000290386565000410389465000550393570000370399085600320402785600660405996-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090325sz fot ||| 0|eng d a978303719555070a10.4171/0552doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc10aHandbook of Teichmüller Theory, Volume IIh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (883 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1300tIntroduction to Teichmüller theory, old and new, II /rAthanase Papadopoulos --tThe Weil–Petersson metric geometry /rScott A. Wolpert --tInfinite dimensional Teichmüller spaces /rAlastair Fletcher, Vladimir Markovic --tA construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy /rYoichi Imayoshi --tThe uniformization problem /rRobert Silhol --tRiemann surfaces, ribbon graphs and combinatorial classes /rGabriele Mondello --tCanonical 2-forms on the moduli space of Riemann surfaces /rNariya Kawazumi --tQuasi-homomorphisms on mapping class groups /rKoji Fujiwara --tLefschetz fibrations on 4-manifolds /rMustafa Korkmaz, András I. Stipsicz --tIntroduction to measurable rigidity of mapping class groups /rYoshikata Kida --tAffine groups of flat surfaces /rMartin Möller --tBraid groups and Artin groups /rLuis Paris --tComplex projective structures /rDavid Dumas --tCircle packing and Teichmüller space /rSadayoshi Kojima --t(2+1) Einstein spacetimes of finite type /rRiccardo Benedetti, Francesco Bonsante --tTrace coordinates on Fricke spaces of some simple hyperbolic surfaces /rWilliam M. Goldman --tSpin networks and SL(2,ℂ)-character varieties /rSean Lawton, Elisha Peterson --tGrothendieck’s reconstruction principle and 2-dimensional topology and geometry /rFeng Luo --tDessins d’enfants and origami curves /rFrank Herrlich, Gabriela Schmithüsen --tThe Teichmüller theory of the solenoid /rDragomir Šarić.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis multi-volume set deals with Teichmüller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmüller theory. The aim is to give a complete panorama of this generalized Teichmüller theory and of its applications in various fields of mathematics.
The volumes consist of chapters, each of which is dedicated to a specific topic. The present volume has 19 chapters and is divided into four parts:
The metric and the analytic theory (uniformization, Weil–Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space).
The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups).
Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line).
The Grothendieck–Teichmüller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmüller theory of the soleniod).
This handbook is an essential reference for graduate students and researchers interested in Teichmüller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis.
The authors are leading experts in the field.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/055423cover imageuhttps://www.ems-ph.org/img/books/irma13_mini.jpg02115nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400220018310000320020524501120023726000820034930000340043133600260046533700260049133800360051734700240055349000610057750600660063852008350070465000410153965000230158065000180160370000300162185600320165185600700168397-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090408sz fot ||| 0|eng d a978303719566670a10.4171/0662doi ach0018173 7aPBV2bicssc a05-xxa51-xx2msc1 aPayne, Stanley E.,eauthor.10aFinite Generalized Quadranglesh[electronic resource] :bSecond Edition /cStanley E. Payne, Joseph A. Thas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (299 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aGeneralized quadrangles (GQ) were formally introduced by J. Tits in 1959 in order to describe geometric properties of simple groups of Lie type of rank 2. After its appearance in 1984, Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ. It presents the whole story of the subject from the very beginning in a book of modest length.
This second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that introduces major new results pertaining to GQ, especially in those areas in which the authors of this work have made a contribution.
The first edition has been out of print for many years, and the new edition makes again available this classical reference in the rapidly increasing field of finite geometries.07aCombinatorics & graph theory2bicssc07aCombinatorics2msc07aGeometry2msc1 aThas, Joseph A.,eauthor.40uhttps://doi.org/10.4171/066423cover imageuhttps://www.ems-ph.org/img/books/payne_thas-mini.jpg05051nam a22004575a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016707200170018307200170020007200160021708400360023324501820026926000820045130000340053333600260056733700260059333800360061934700240065550517220067950600660240152016820246765000310414965000350418065000510421565000320426665000280429865000400432665000260436665000440439270000280443670000300446485600320449485600670452698-091109CH-001817-320091109150325.0a fot 1|| 0|cr nn mmmmamaa091109e20090615sz fot 1|| 0|eng d a978303719556770a10.4171/0562doi ach0018173 7aPBS2bicssc 7aPBKJ2bicssc 7aPBWD2bicssc 7aPHB2bicssc a65-xxa35-xxa68-xxa92-xx2msc10a6th International Congress on Industrial and Applied Mathematics Zürich, Switzerland, 16-20 July 2007h[electronic resource] :bInvited Lectures /cRolf Jeltsch, Gerhard Wanner3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (530 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tA level set method for the numerical simulation of damage evolution /rGrégoire Allaire, François Jouve, Nicolas Van Goethem --tDissipation inequalities in systems theory: An introduction and recent results /rChristian Ebenbauer, Tobias Raff, Frank Allgöwer --tSome nonlinear problems involving non-local diffusions /rLuis A. Caffarelli --tHigh-order methods for PDEs: Recent advances and new perspectives /rClaudio Canuto --tRadar imaging /rMargaret Cheney --tAdaptive approximations by greedy algorithms /rAlbert Cohen --tMultiscale analysis of density functional theory /rWeinan E --tFrictional contact in solid mechanics /rMichel Fortin, Carl Robitaille, André Fortin, Ali Rezgui --tNumerical methods for fully nonlinear elliptic equations /rRoland Glowinski --tAsymptotic solutions of Hamilton–Jacobi equations for large time and related topics /rKenji Nishihara --tHyperbolic conservation laws. Past and future /rBarbara Lee Keyfitz --tSecond-order PDE’s and deterministic games /rRobert V. Kohn, Sylvia Serfaty --tControllability and observability: From ODEs to quasilinear hyperbolic systems /rTatsien Li --tOrder-value optimization and new applications /rJosé Mario Martínez --tConformation dynamics /rChristof Schütte, Frank Noe, Eike Meerbach, Philipp Metzner, Carsten Hartmann --tMCMC methods for sampling function space /rAlexandros Beskos, Andrew M. Stuart --tChaotic itinerancy reality in the dynamic brain – episodic memory formation /rIchiro Tsuda --tVisibility and invisibility /rGunther Uhlmann --tOptimal algorithms for discretized partial differential equations /rJinchao Xu --tLeonhard Euler: His life, the man, and his works /rWalter Gautschi.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe International Council for Industrial and Applied Mathematics (ICIAM)
is the worldwide organisation of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4
years, are run under the auspices of the Council with the aim to advance
the applications of mathematics in all parts of the world. The 6th ICIAM Congress was held in Zürich, Switzerland, 16–20 July 2007, and was attended by more than 3000 scientists from 47 countries.
This volume collects the invited lectures of this
Congres, the appreciations of the ICIAM Prize winners’ achievements and the Euler
Lecture celebrating the 300th anniversary of Euler. The authors of these
papers are leading researchers of their fields, rigorously selected by a
distinguished international program committee. The book presents an
overview of contemporary applications of mathematics, new perspectives
and open problems. Topics embrace analysis of and numerical methods for:
linear and nonlinear partial differential equations
multiscale modeling
nonlinear problems involving integral operators
controllability and observability
asymptotic solutions of Hamilton–Jacobi equations
contact problems in solid mechanics
topology optimization of structures
dissipation inequalities in systems theory
greedy algorithms
sampling in function space
order-value optimization
parabolic partial differential equations and deterministic games
Moreover, particular applications involve risk in financial markets,
radar imaging, brain dynamics, complex geometric optics applied to
acoustics and electromagnetics.07aNumerical analysis2bicssc07aDifferential equations2bicssc07aMathematics for scientists & engineers2bicssc07aTheoretical methods2bicssc07aNumerical analysis2msc07aPartial differential equations2msc07aComputer science2msc07aBiology and other natural sciences2msc1 aJeltsch, Rolf,eeditor.1 aWanner, Gerhard,eeditor.40uhttps://doi.org/10.4171/056423cover imageuhttps://www.ems-ph.org/img/books/ICIAM07_mini.jpg02717nam a22003375a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400150018410000310019924500870023026000820031730000340039933600260043333700260045933800360048534700240052149000500054550600660059552015360066165000350219765000450223285600320227785600700230999-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090608sz fot ||| 0|eng d a978303719553670a10.4171/0532doi ach0018173 7aPBKJ2bicssc a83-xx2msc1 aRingström, Hans,eauthor.10aThe Cauchy Problem in General Relativityh[electronic resource] /cHans Ringström3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (307 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe general theory of relativity is a theory of manifolds equipped with
Lorentz metrics and fields which describe the matter content. Einstein’s
equations equate the Einstein tensor (a curvature quantity associated
with the Lorentz metric) with the stress energy tensor (an object constructed
using the matter fields). In addition, there are equations
describing the evolution of the matter. Using symmetry as a guiding
principle, one is naturally led to the Schwarzschild and
Friedmann–Lemaître–Robertson–Walker solutions,
modelling an isolated system and
the entire universe respectively. In a different approach, formulating
Einstein’s equations as an initial value problem allows a closer study of
their solutions. This book first provides a definition of the concept of
initial data and a proof of the correspondence between initial data and
development. It turns out that some initial data allow non-isometric
maximal developments, complicating the uniqueness issue. The second
half of the book is concerned with this and related problems, such as
strong cosmic censorship.
The book presents complete proofs of several classical results that play a
central role in mathematical relativity but are not easily accessible to
those wishing to enter the subject. Prerequisites are a good knowledge
of basic measure and integration theory as well as the fundamentals of
Lorentz geometry. The necessary background from the theory of partial
differential equations and Lorentz geometry is included.07aDifferential equations2bicssc07aRelativity and gravitational theory2msc40uhttps://doi.org/10.4171/053423cover imageuhttps://www.ems-ph.org/img/books/ringstroem_mini.jpg02821nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003200207245017800239260008200417300003400499336002600533337002600559338003600585347002400621490003900645506006600684520137900750650003302129650005202162650002902214700003102243700002902274700003202303856003202335856006802367100-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090708sz fot ||| 0|eng d a978303719570370a10.4171/0702doi ach0018173 7aPHDD2bicssc a82-xxa46-xx2msc1 aAlbeverio, Sergio,eauthor.10aThe Statistical Mechanics of Quantum Lattice Systemsh[electronic resource] :bA Path Integral Approach /cSergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Röckner3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (392 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v81 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aQuantum statistical mechanics plays a major role in many fields
such as, for instance, thermodynamics, plasma physics, solid-state
physics, and the study of stellar structure.
While the theory of quantum harmonic oscillators is relatively simple,
the case of anharmonic oscillators, a mathematical model of a localized quantum
particle, is more complex and challenging.
Moreover, infinite
systems of interacting quantum anharmonic oscillators possess
interesting ordering properties with respect to quantum
stabilization.
This book presents a rigorous approach to the
statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice.
The text is addressed to both mathematicians and physicists, especially those who are concerned with
the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here
a concise collection of facts, concepts, and tools relevant for the
application of path integrals and other methods based on measure and
integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum
anharmonic crystals. The methods developed in
the book are also applicable to other problems involving infinitely
many variables, for example, in biology and economics.07aAnalytical mechanics2bicssc07aStatistical mechanics, structure of matter2msc07aFunctional analysis2msc1 aKondratiev, Yuri,eauthor.1 aKozitsky, Yuri,eauthor.1 aRöckner, Michael,eauthor.40uhttps://doi.org/10.4171/070423cover imageuhttps://www.ems-ph.org/img/books/roeckner_mini.jpg02561nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184245014300206260008200349300003400431336002600465337002600491338003600517347002400553505034700577506006600924520087500990650003101865650002801896650003101924700002701955700002801982700003102010700003602041856003202077856006602109102-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090624sz fot ||| 0|eng d a978303719569770a10.4171/0692doi ach0018173 7aPBS2bicssc a65-xxa01-xx2msc10aEssays on the Complexity of Continuous Problemsh[electronic resource] /cErich Novak, Ian H. Sloan, Joseph F. Traub, Henryk Woźniakowski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (105 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tHenryk Woźniakowski and the complexity of continuous problems /rErich Novak --tComplexity as a new challenge for mathematicians /rHenryk Woźniakowski --tA brief history of information-based complexity /rJoseph F. Traub --tHow high is high-dimensional? /rIan H. Sloan --tWhat is information-based complexity? /rHenryk Woźniakowski.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book contains five essays
on the complexity of continuous problems, written
for a wider audience.
Henryk Woźniakowski and the complexity of continuous problems
Complexity as a new challenge for mathematicians
A brief history of information-based complexity
How high is high-dimensional?
What is information-based complexity?
The first four essays are based on talks
presented in 2008 when Henryk Woźniakowski received
an honorary doctoral degree of
the Friedrich Schiller University of Jena.
The focus is on introduction and history of the complexity of continuous
problems, as well as on recent
progress concerning the complexity of high-dimensional numerical
problems. The last essay provides a brief and informal introduction to
the basic notions and concepts of information-based complexity addressed
to a general readership.07aNumerical analysis2bicssc07aNumerical analysis2msc07aHistory and biography2msc1 aNovak, Erich,eeditor.1 aSloan, Ian H.,eeditor.1 aTraub, Joseph F.,eeditor.1 aWoźniakowski, Henryk,eeditor.40uhttps://doi.org/10.4171/069423cover imageuhttps://www.ems-ph.org/img/books/essays_mini.jpg02982nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003600200245024300236260008200479300003400561336002600595337002600621338003600647347002400683490003900707506006600746520153100812650003102343650002802374700003102402700003402433700003802467856003202505856007102537103-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090808sz fot ||| 0|eng d a978303719564270a10.4171/0642doi ach0018173 7aPBMW2bicssc a14-xx2msc1 aBeltrametti, Mauro C.,eauthor.10aLectures on Curves, Surfaces and Projective Varietiesh[electronic resource] :bA Classical View of Algebraic Geometry First corrected reprint, June 2012 /cMauro C. Beltrametti, Ettore Carletti, Dionisio Gallarati, Giacomo Monti Bragadin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (506 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions.
The text is aimed at students of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed.
The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc1 aCarletti, Ettore,eauthor.1 aGallarati, Dionisio,eauthor.1 aMonti Bragadin, Giacomo,eauthor.40uhttps://doi.org/10.4171/064423cover imageuhttps://www.ems-ph.org/img/books/beltrametti_mini.jpg02989nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003000199245013500229260008200364300003400446336002600480337002600506338003600532347002400568490003900592506006600631520176700697650003702464650005302501856003202554856006502586104-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090815sz fot ||| 0|eng d a978303719571070a10.4171/0712doi ach0018173 7aPBT2bicssc a60-xx2msc1 aWoess, Wolfgang,eauthor.10aDenumerable Markov Chainsh[electronic resource] :bGenerating Functions, Boundary Theory, Random Walks on Trees /cWolfgang Woess3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (368 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMarkov chains are the first and most important examples of random processes.
This book is about time-homogeneous Markov chains that evolve with discrete time
steps on a countable state space. Measure theory is not avoided, careful and
complete proofs are provided.
A specific feature is the systematic use, on a relatively elementary level, of generating
functions associated with transition probabilities for analyzing Markov chains. Basic
definitions and facts include the construction of the trajectory space and are followed
by ample material concerning recurrence and transience, the convergence and ergodic
theorems for positive recurrent chains. There is a side-trip to the Perron–Frobenius theorem.
Special attention is given to reversible Markov chains and to basic mathematical
models of “population evolution” such as birth-and-death chains, Galton–Watson
process and branching Markov chains.
A good part of the second half is devoted to the introduction of the basic language
and elements of the potential theory of transient Markov chains. Here the construction
and properties of the Martin boundary for describing positive harmonic functions
are crucial. In the long final chapter on nearest neighbour random walks on (typically
infinite) trees the reader can harvest from the seed of methods laid out so far, in order
to obtain a rather detailed understanding of a specific, broad class of Markov chains.
The level varies from basic to more advanced, addressing an audience from master’s
degree students to researchers in mathematics, and persons who want to teach the
subject on a medium or advanced level. A specific characteristic of the book is the rich
source of classroom-tested exercises with solutions.07aProbability & statistics2bicssc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/071423cover imageuhttps://www.ems-ph.org/img/books/woess_mini.jpg03037nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002800207245007500235260008200310300003400392336002600426337002600452338003600478347002400514490008300538506006600621520178000687650002402467650004602491650005302537856003202590856006502622105-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090829sz fot ||| 0|eng d a978303719546870a10.4171/0462doi ach0018173 7aPBWL2bicssc a37-xxa60-xx2msc1 aWeber, Michel,eauthor.10aDynamical Systems and Processesh[electronic resource] /cMichel Weber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (773 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book presents in a concise and accessible way, as well as in
a common setting, various tools and methods arising from spectral
theory, ergodic theory and stochastic processes theory, which
form the basis of and contribute interactively a great deal to the
current research on almost everywhere convergence problems.
The text is divided into four parts.
Part I is devoted to spectral results such as von Neumann’s theorem, spectral regularizations inequalities and
their link with square functions and entropy numbers of ergodic averages.
The representation of a weakly
stationary process as Fourier transform of some random orthogonal measure,
and a study of Gaposhkin’s
spectral criterion conclude this part.
Classical results such as mixing in dynamical systems,
Birkhoff's pointwise theorem, dominated ergodic theorems,
oscillations functions of ergodic averages, transference
principle, Wiener–Wintner theorem, Banach principle, continuity principle,
Bourgain's entropy criteria, Burton–Denker’s central limit
theorem are covered in part II.
The metric entropy method and the majorizing measure method, including a
succinct study of Gaussian processes, are treated in part III, with
applications to suprema of random polynomials.
Part IV contains a study of Riemann sums and of the convergence
properties of the system {f(nkx), k ≥ 1}, as well as a probabilistic approach concerning divisors with applications.
Researchers working in dynamical systems and at the crossroads of
spectral theory, ergodic theory and stochastic processes will find the
tools, methods and results presented in this book of great interest.
It is written in a style accessible to graduate students throughout.07aStochastics2bicssc07aDynamical systems and ergodic theory2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/046423cover imageuhttps://www.ems-ph.org/img/books/weber_mini.jpg03316nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245011700207260008200324300003400406336002600440337002600466338003600492347002400528490008300552505070100635506006601336520125301402650003102655650002802686650002402714700002802738700003302766700003302799856003202832856006602864106-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090924sz fot ||| 0|eng d a978303719573470a10.4171/0732doi ach0018173 7aPBMW2bicssc a14-xxa81-xx2msc10aRenormalization and Galois Theoriesh[electronic resource] /cAlain Connes, Frédéric Fauvet, Jean-Pierre Ramis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (279 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1500tNoncommutative geometry and motives (à quoi servent les endomotifs?) /rCaterina Consani --tRenormalisation of non-commutative field theories /rVincent Rivasseau, Fabien Vignes-Tourneret --tMould expansions for the saddle-node and resurgence monomials /rDavid Sauzin --tGalois theory, motives and transcendental numbers /rYves André --tThe combinatorics of Bogoliubov’s recursion in renormalization /rKurusch Ebrahimi-Fard, Dominique Manchon --t(Non)commutative Hopf algebras of trees and (quasi)symmetric functions /rMichael E. Hoffman --tFormal differential equations and renormalization /rFrédéric Menous --tFeynman integrals and multiple polylogarithms /rStefan Weinzierl.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is the outcome of a CIRM Workshop on Renormalization
and Galois Theories held in Luminy, France, in March 2006.
The subject of this workshop was the interaction and relationship
between four currently very active areas: renormalization in quantum
field theory (QFT), differential Galois theory, noncommutative
geometry, motives and Galois theory.
The last decade has seen a burst of new techniques to cope with
the various mathematical questions involved in QFT, with notably the
development of a Hopf-algebraic approach and insights into the
classes of numbers and special functions that systematically appear
in the calculations of perturbative QFT (pQFT). The analysis of
the ambiguities of resummation of the divergent series of pQFT,
an old problem, has been renewed, using recent results on Gevrey
asymptotics, generalized Borel summation, Stokes phenomenon
and resurgent functions.
The purpose of the present book is to highlight, in the context of
renormalization, the convergence of these various themes,
orchestrated by diverse Galois theories. It contains three lecture
courses together with five research articles and will be useful to both
reseachers and graduate students in mathematics and physics.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aQuantum theory2msc1 aConnes, Alain,eeditor.1 aFauvet, Frédéric,eeditor.1 aRamis, Jean-Pierre,eeditor.40uhttps://doi.org/10.4171/073423cover imageuhttps://www.ems-ph.org/img/books/connes_mini.jpg03060nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003100207245011400238260008200352300003400434336002600468337002600494338003600520347002400556490003900580506006600619520180000685650003502485650002302520650002802543700002802571856003202599856006702631107-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20091001sz fot ||| 0|eng d a978303719574170a10.4171/0742doi ach0018173 7aPBRH2bicssc a11-xxa14-xx2msc1 aBöckle, Gebhard,eauthor.10aCohomological Theory of Crystals over Function Fieldsh[electronic resource] /cGebhard Böckle, Richard Pink3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (195 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v91 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book develops a new cohomological theory for schemes in positive
characteristic p and it applies this theory to give a purely algebraic proof of a
conjecture of Goss on the rationality of certain L-functions arising in the
arithmetic of function fields. These L-functions are power series over a certain
ring A, associated to any family of Drinfeld A-modules or, more generally, of
A-motives on a variety of finite type over the finite field Fp. By analogy to the
Weil conjecture, Goss conjectured that these L-functions are in fact rational
functions. In 1996 Taguchi and Wan gave a first proof of Goss’s conjecture by
analytic methods à la Dwork.
The present text introduces A-crystals, which can be viewed as generalizations
of families of A-motives, and studies their cohomology. While A-crystals are
defined in terms of coherent sheaves together with a Frobenius map, in many
ways they actually behave like constructible étale sheaves. A central result is a
Lefschetz trace formula for L-functions of A-crystals, from which the rationality
of these L-functions is immediate. Beyond its application to Goss’s L-functions,
the theory of A-crystals is closely related to the work of Emerton and Kisin on
unit root F-crystals, and it is essential in an Eichler–Shimura type isomorphism
for Drinfeld modular forms as constructed by the first author.
The book is intended for researchers and advanced graduate students
interested in the arithmetic of function fields and/or cohomology theories for
varieties in positive characteristic. It assumes a good working knowledge in
algebraic geometry as well as familiarity with homological algebra and derived
categories, as provided by standard textbooks. Beyond that the presentation is
largely self-contained.07aAnalytic number theory2bicssc07aNumber theory2msc07aAlgebraic geometry2msc1 aPink, Richard,eauthor.40uhttps://doi.org/10.4171/074423cover imageuhttps://www.ems-ph.org/img/books/boeckle_mini.jpg02873nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003300199245009000232260008200322300003400404336002600438337002600464338003600490347002400526490005600550506006600606520165200672650003502324650003102359700003002390856003202420856007102452108-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20091030sz fot ||| 0|eng d a978303719558170a10.4171/0582doi ach0018173 7aPBX2bicssc a01-xx2msc1 aSpringer, Tonny A.,eauthor.10aHans Freudenthal, Selectah[electronic resource] /cTonny A. Springer, Dirk van Dalen3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (661 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHans Freudenthal (1905–1990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics.
The present Selecta are devoted to Freudenthal’s mathematical oeuvre, they contain a selection of his major contributions. Included are fundamental contributions to topology such as the foundation of the theory of ends (in the thesis of 1931), the introduction (in 1937) of the suspension and its use in stability results for homotopy groups of spheres. In group theory there is work on topological groups (of the 1930s) and on various aspects of the theory of Lie groups, such as a paper on automorphisms of 1941. From the later work of the 1950s and 1960s, papers on geometric aspects of Lie theory (geometries associated to exceptional groups, space problems) have been included. Freudenthal’s versatility is further demonstrated by a choice from his foundational and historical work: papers on intuitionistic logic and topology, a paper on axiomatic geometry reappraising Hilbert’s Grundlagen, and a paper summarizing his development of Lincos, a universal (“cosmic”) language.
The book also contains a sketch of Freudenthal’s life. Most of the selected papers are accompanied by brief comments.07aHistory of mathematics2bicssc07aHistory and biography2msc1 avan Dalen, Dirk,eauthor.40uhttps://doi.org/10.4171/058423cover imageuhttps://www.ems-ph.org/img/books/freudenthal_mini.jpg03086nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003200199245009500231260008200326300003400408336002600442337002600468338003600494347002400530490006100554506006600615520187300681650004502554650004802599856003202647856006902679109-131128CH-001817-320131128234500.0a fot ||| 0|cr nn mmmmamaa131128e20131213sz fot ||| 0|eng d a978303719628170a10.4171/1282doi ach0018173 7aPBK2bicssc a58-xx2msc1 aKhalkhali, Masoud,eauthor.10aBasic Noncommutative Geometryh[electronic resource] :bSecond edition /cMasoud Khalkhali3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (257 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis text provides an introduction to noncommutative geometry and some of its applications. It can be used either as a textbook for a graduate course or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and
homological algebra at a first year graduate level is helpful.
Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry
and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes–Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well.
Two new sections have been added to this second edition: one concerns the Gauss–Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative two torus, and the second is a brief introduction to Hopf cyclic cohomology. The bibliography has been extended and some new examples are presented.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/128423cover imageuhttps://www.ems-ph.org/img/books/khalkhali_mini.jpg02501nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003100207245010900238260008200347300003400429336002600463337002600489338003600515347002400551490005000575506006600625520123600691650003501927650005501962650004002017856003202057856006202089110-100226CH-001817-320100226234500.0a fot ||| 0|cr nn mmmmamaa100226e20100226sz fot ||| 0|eng d a978303719576570a10.4171/0762doi ach0018173 7aPBKJ2bicssc a32-xxa35-xx2msc1 aStraube, Emil J.,eauthor.10aLectures on the ℒ2-Sobolev Theory of the ∂-Neumann problemh[electronic resource] /cEmil J. Straube3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (214 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides a thorough and self-contained introduction to the ∂-Neumann problem, leading up to current research, in the context of the ℒ2-Sobolev theory on bounded pseudoconvex domains in ℂn. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrödinger International Institute for Mathematical Physics and at Texas A&M University.
The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic ℒ2-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research.
Prerequisites are a solid background in basic complex and functional analysis, including the elementary ℒ2-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.07aDifferential equations2bicssc07aSeveral complex variables and analytic spaces2msc07aPartial differential equations2msc40uhttps://doi.org/10.4171/076423cover imageuhttps://www.ems-ph.org/img/books/straube.jpg04363nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168245013700183260008200320300003400402336002600436337002600462338003600488347002400524505164800548506006602196520155602262650002403818700002603842700003103868700003003899856003203929856006403961111-100412CH-001817-320100412234500.0a fot 1|| 0|cr nn mmmmamaa100412e20100424sz fot 1|| 0|eng d a978303719577270a10.4171/0772doi ach0018173 7aPB2bicssc10aEuropean Congress of Mathematics Amsterdam, 14–18 July, 2008h[electronic resource] /cA.C.M. Ran, Herman te Riele, Jan Wiegerinck3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (488 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tUniqueness of bounded solutions to aggregation equations by optimal transport methods /rJosé A. Carrillo, Jesús Rosado --tOn the computation of the coefﬁcients of modular forms /rBas Edixhoven --tEffective equidistribution and spectral gap /rManfred Einsiedler --tSurvey on aspherical manifolds /rWolfgang Lück --tWheeled props in algebra, geometry and quantization /rSergei A. Merkulov --tPositive deﬁnite functions in distance geometry /rOleg R. Musin --tFrom sparse graphs to nowhere dense structures: decompositions, independence, dualities and limits /rJaroslav Nešetřil, Patrice Ossona de Mendez --tBundle gerbes and surface holonomy /rJürgen Fuchs, Thomas Nikolaus, Christoph Schweigert, Konrad Waldorf --tTopological ﬁeld theories in 2 dimensions /rConstantin Teleman --tThe revolution of 1907 – Brouwer’s dissertation /rDirk van Dalen --tNew developments in combinatorial number theory and applications /rJean Bourgain --tLarge random planar maps and their scaling limits /rJean-François Le Gall --tGeometry and non-archimedean integrals /rFrançois Loeser --tFeynman integrals and motives /rMatilde Marcolli --tTopological quantum ﬁeld theory: 20 years later /rNicolai Reshetikhin --tComputational complexity and numerical stability of linear problems /rOlga Holtz, Noam Shomron --tHigh-dimensional distributions with convexity properties /rBo'az Klartag --tSome recent results about the sixth problem of Hilbert: hydrodynamic limits of the Boltzmann equation /rLaure Saint-Raymond --tGraded algebras associated to algebraic algebras need not be algebraic /rAgata Smoktunowicz.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000) and Stockholm (2004), the Fifth European Congress of Mathematics (5ECM) took place in Amsterdam, The Netherlands, July 14–18, 2008, with about 1000 participants from 68 different countries.
Ten plenary and thirty-three invited lectures were delivered. Three science lectures outlined applications of mathematics in other sciences: climate change, quantum information theory and population dynamics. As in the four preceding EMS congresses, ten EMS prizes were granted to very promising young mathematicians. In addition, the Felix Klein Prize was awarded, for the second time, for an application of mathematics to a concrete and difficult industrial problem. There were twenty-two minisymposia, spread over the whole mathematical area. Two round table meetings were organized: one on industrial mathematics and one on mathematics and developing countries.
As part of the 44th Nederlands Mathematisch Congres, which was embedded in 5ECM, the so-called Brouwer lecture was presented. It is the Netherland's most prestigious award in mathematics, organized every three years by the Royal Dutch Mathematical Society. Information about Brouwer was given in an invited historical lecture during the congress.
These proceedings contain a selection of the contributions to the congress, providing a permanent record of the best what mathematics offers today.07aMathematics2bicssc1 aRan, A.C.M.,eeditor.1 ate Riele, Herman,eeditor.1 aWiegerinck, Jan,eeditor.40uhttps://doi.org/10.4171/077423cover imageuhttps://www.ems-ph.org/img/books/5ECM_mini.jpg02842nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001600185084002900201100002800230245021700258260008200475300003400557336002600591337002600617338003600643347002400679490006100703506006600764520122300830650003502053650003102088650002802119650004002147650002502187700004302212700003202255700003502287856003202322856006602354112-100420CH-001817-320100420234500.0a fot ||| 0|cr nn mmmmamaa100420e20100430sz fot ||| 0|eng d a978303719578970a10.4171/0782doi ach0018173 7aPBKJ2bicssc 7aPBS2bicssc a65-xxa35-xxa47-xx2msc1 aHolden, Helge,eauthor.10aSplitting Methods for Partial Differential Equations with Rough Solutionsh[electronic resource] :bAnalysis and MATLAB programs /cHelge Holden, Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, Nils Henrik Risebro3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (234 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aOperator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks.
Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated web page that provides MATLAB codes for many of the examples.
The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.07aDifferential equations2bicssc07aNumerical analysis2bicssc07aNumerical analysis2msc07aPartial differential equations2msc07aOperator theory2msc1 aKarlsen, Kenneth Hvistendahl,eauthor.1 aLie, Knut-Andreas,eauthor.1 aRisebro, Nils Henrik,eauthor.40uhttps://doi.org/10.4171/078423cover imageuhttps://www.ems-ph.org/img/books/holden_mini.jpg03077nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003000221245013000251260008200381300003400463336002600497337002600523338003600549347002400585490003900609506006600648520169300714650003502407650004602442650004102488650003102529650004402560856003202604856006702636113-100519CH-001817-320100519234500.0a fot ||| 0|cr nn mmmmamaa100519e20100519sz fot ||| 0|eng d a978303719581970a10.4171/0812doi ach0018173 7aPBKQ2bicssc a37-xxa34-xxa53-xxa70-xx2msc1 aZehnder, Eduard,eauthor.10aLectures on Dynamical Systemsh[electronic resource] :bHamiltonian Vector Fields and Symplectic Capacities /cEduard Zehnder3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (363 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at the ETH Zurich.
The first part centres around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale’s theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum.
The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times.
The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed.
There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.07aCalculus of variations2bicssc07aDynamical systems and ergodic theory2msc07aOrdinary differential equations2msc07aDifferential geometry2msc07aMechanics of particles and systems2msc40uhttps://doi.org/10.4171/081423cover imageuhttps://www.ems-ph.org/img/books/zehnder_mini.jpg02629nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245013500252260008200387300003400469336002600503337002600529338003600555347002400591490004000615506006600655520125700721650003101978650003802009650004002047650004602087650002402133856003202157856006602189114-100601CH-001817-320100601234500.0a fot ||| 0|cr nn mmmmamaa100601e20100601sz fot ||| 0|eng d a978303719586470a10.4171/0862doi ach0018173 7aPBPD2bicssc a57-xxa16-xxa18-xxa81-xx2msc1 aTuraev, Vladimir,eauthor.10aHomotopy Quantum Field Theoryh[electronic resource] :bWith Appendices by Michael Müger and Alexis Virelizier /cVladimir Turaev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (290 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v101 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHomotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space.
This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on 2-dimensional and 3-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Müger and A. Virelizier summarize their work in this area.
The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.07aAlgebraic topology2bicssc07aManifolds and cell complexes2msc07aAssociative rings and algebras2msc07aCategory theory; homological algebra2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/086423cover imageuhttps://www.ems-ph.org/img/books/turaev_mini.jpg02055nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100002800220245011400248260008200362300003400444336002600478337002600504338003600530347002400566490004000590506006600630520073400696650003101430650002901461650003901490650002601529650002601555856003201581856006801613115-100601CH-001817-320100601234500.0a fot ||| 0|cr nn mmmmamaa100601e20100601sz fot ||| 0|eng d a978303719585770a10.4171/0852doi ach0018173 7aPBS2bicssc a46-xxa41-xxa42-xxa68-xx2msc1 aTriebel, Hans,eauthor.10aBases in Function Spaces, Sampling, Discrepancy, Numerical integrationh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (305 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v111 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean n-space and n-cubes. This
is used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity.
This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation
theory, and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).07aNumerical analysis2bicssc07aFunctional analysis2msc07aApproximations and expansions2msc07aFourier analysis2msc07aComputer science2msc40uhttps://doi.org/10.4171/085423cover imageuhttps://www.ems-ph.org/img/books/triebel_mini2.jpg04562nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185245010300214260008200317300003400399336002600433337002600459338003600485347002400521490008300545505231000628506006602938520090803004650004703912650003103959650002403990650004504014700003104059856003204090856006604122116-100610CH-001817-320100610234500.0a fot ||| 0|cr nn mmmmamaa100610e20100610sz fot ||| 0|eng d a978303719579670a10.4171/0792doi ach0018173 7aPBMP2bicssc a53-xxa81-xxa83-xx2msc10aHandbook of Pseudo-Riemannian Geometry and Supersymmetryh[electronic resource] /cVicente Cortés3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (964 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1600tQuaternion-Kähler spaces, hyper-Kähler cones, and the c-map /rMartin Roček, Cumrun Vafa, Stefan Vandoren --tDifferential forms on quaternionic Kähler manifolds /rGregor Weingart --tSasakian geometry, holonomy, and supersymmetry /rCharles P. Boyer, Krzysztof Galicki† --tSpecial geometry for arbitrary signatures /rMaría A. Lledó, Óscar Maciá, Antoine Van Proeyen, Veeravalli S. Varadarajan --tSpecial geometry, black holes and Euclidean supersymmetry /rThomas Mohaupt --tGeneralized geometry – an introduction /rNigel Hitchin --tGeneralizing geometry – algebroids and sigma models /rAlexei Kotov, Thomas Strobl --tA potential for generalized Kähler geometry /rUlf Lindström, Martin Roček, Rikard von Unge, Maxim Zabzine --tNon-integrable geometries, torsion, and holonomy /rIlka Agricola --tConnections with totally skew-symmetric torsion and nearly-Kähler geometry /rPaul-Andi Nagy --tHomogeneous nearly Kähler manifolds /rJean-Baptiste Butruille --tNearly pseudo-Kähler and nearly para-Kähler six-manifolds /rLars Schäfer, Fabian Schulte-Hengesbach --tQuaternionic geometries from superconformal symmetry /rAndrew Swann --tTwistor and reflector spaces of almost para-quaternionic manifolds /rStefan Ivanov, Ivan Minchev, Simeon Zamkovoy --tPara-pluriharmonic maps and twistor spaces /rMatthias Krahe --tMaximally homogeneous para-CR manifolds of semisimple type /rDmitri V. Alekseevsky, Costantino Medori, Adriano Tomassini --tRecent developments in pseudo-Riemannian holonomy theory /rAnton Galaev, Thomas Leistner --tGeometric applications of irreducible representations of Lie groups /rAntonio J. Di Scala, Thomas Leistner, Thomas Neukirchner --tSurface holonomy /rKonrad Waldorf --tClassification results for pseudo-Riemannian symmetric spaces /rInes Kath --tPseudo-Kähler and para-Kähler symmetric spaces /rDmitri V. Alekseevsky --tPrehomogeneous affine representations and flat pseudo-Riemannian manifolds /rOliver Baues --tThe conformal analog of Calabi–Yau manifolds /rHelga Baum --tNondegenerate conformal structures, CR structures and quaternionic CR structures on manifolds /rYoshinobu Kamishima --tLinear wave equations on Lorentzian manifolds /rChristian Bär --tSurvey of D-branes and K-theory /rDaniel S. Freed.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are:
special geometry and supersymmetry
generalized geometry
geometries with torsion
para-geometries
holonomy theory
symmetric spaces and spaces of constant curvature
conformal geometry
wave equations on Lorentzian manifolds
D-branes and K-theory
The intended audience consists of advanced students and researchers working in differential geometry, string theory and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kähler geometry or generalized geometry.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aQuantum theory2msc07aRelativity and gravitational theory2msc1 aCortés, Vicente,eeditor.40uhttps://doi.org/10.4171/079423cover imageuhttps://www.ems-ph.org/img/books/cortes_mini.jpg03322nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100002700206245015300233260008200386300003400468336002600502337002600528338003600554347002400590490004000614506006600654520200400720650004702724650002802771650002602799700003602825856003202861856006702893118-100703CH-001817-320100703234500.0a fot ||| 0|cr nn mmmmamaa100703e20100703sz fot ||| 0|eng d a978303719584070a10.4171/0842doi ach0018173 7aUAA2bicssc a65-xxa68-xx2msc1 aNovak, Erich,eauthor.10aTractability of Multivariate Problemsh[electronic resource] :bVolume II: Standard Information for Functionals /cErich Novak, Henryk Woźniakowski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (675 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v121 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis three-volume set is a comprehensive study of the
tractability of multivariate problems.
The present second volume deals with algorithms using
standard information consisting of function values
for the approximation of linear and selected nonlinear
functionals. An important
example is numerical multivariate integration.
The proof techniques used in volumes I and II
are quite different.
It is especially hard to establish meaningful lower error
bounds for the approximation of functionals
by using finitely many function values.
Here, the concept
of decomposable reproducing kernels is
helpful, allowing it to find matching lower and upper error bounds
for some linear functionals.
It is then possible to conclude tractability results
from such error bounds.
Tractability results even for linear functionals are very rich in
variety. There are infinite-dimensional Hilbert spaces for which
the approximation with an arbitrarily small error
of all linear functionals requires only one function
value. There are Hilbert spaces for which all
nontrivial linear functionals suffer from the curse of dimensionality.
This holds for unweighted spaces, where the role of all variables and
groups of variables is the same. For weighted spaces one can monitor the
role of all variables and groups of variables. Necessary and
sufficient conditions on the decay of the weights are given to obtain various
notions of tractability.
The text contains extensive
chapters on discrepancy and integration,
decomposable kernels and lower bounds,
the Smolyak/sparse grid algorithms,
lattice rules and the
CBC (component-by-component) algorithms.
This is done in various settings.
Path integration and quantum computation are also discussed.
The book is of interest for researchers working in computational
mathematics, especially in approximation of high-dimensional
problems. It is also well suited for graduate courses and
seminars. 61 open problems...07aMathematical theory of computation2bicssc07aNumerical analysis2msc07aComputer science2msc1 aWoźniakowski, Henryk,eauthor.40uhttps://doi.org/10.4171/084423cover imageuhttps://www.ems-ph.org/img/books/novakII_mini.jpg02230nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100002600221245009800247260008200345300003400427336002600461337002600487338003600513347002400549490005100573506006600624520088100690650003101571650005501602650002301657650005501680650002601735856003201761856006301793119-100820CH-001817-320100820234500.0a fot ||| 0|cr nn mmmmamaa100820e20100907sz fot ||| 0|eng d a978303719593270a10.4171/0932doi ach0018173 7aPBUH2bicssc a90-xxa05-xxa15-xxa68-xx2msc1 aOnn, Shmuel,eauthor.10aNonlinear Discrete Optimizationh[electronic resource] :bAn Algorithmic Theory /cShmuel Onn3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (147 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases.
The monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.07aLinear programming2bicssc07aOperations research, mathematical programming2msc07aCombinatorics2msc07aLinear and multilinear algebra; matrix theory2msc07aComputer science2msc40uhttps://doi.org/10.4171/093423cover imageuhttps://www.ems-ph.org/img/books/onn_mini.jpg04850nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184245021100199260008200410300003400492336002600526337002600552338003600578347002400614505186100638506006602499520167102565650003504236650003104271700002904302700003504331700003204366856003204398856005804430120-100902CH-001817-320100902234500.0a fot ||| 0|cr nn mmmmamaa100902e20100824sz fot ||| 0|eng d a978303719589570a10.4171/0892doi ach0018173 7aPBX2bicssc a01-xx2msc10amath.ch/100h[electronic resource] :bSchweizerische Mathematische Gesellschaft – Société Mathématique Suisse – Swiss Mathematical Society 1910 /cBruno Colbois, Christine Riedtmann, Viktor Schroeder3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (526 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tMathématiques et Mathématiciens en Suisse (1850–1950) /rMichel Plancherel (1885–1967) --t100 Jahre Schweizerische Mathematische Gesellschaft /rErwin Neuenschwander --tEin Mathematikstudium in den Fünfzigerjahren /rChristian Blatter --tAndreas Speiser (1885–1970) /rJohann Jakob Burckhardt (1903–2006), Adolf Schnyder --tHeinz Huber und das Längenspektrum /rPeter Buser --tA glimpse of the de Rham era /rSrishti Chatterji, Manuel Ojanguren --tLes mathématiques appliquées à l'École polytechnique de Lausanne /rJean Descloux, Dominique de Werra --tMichel Kervaire (1927–2007) /rShalom Eliahou, Pierre de la Harpe, Jean-Claude Hausmann, Claude Weber --tAlexander M. Ostrowski (1893–1986): His life, work, and students /rWalter Gautschi --tNumerical analysis in Zurich – 50 years ago /rMartin H. Gutknecht --tArmand Borel (1923–2003) /rAndré Haefliger --tBericht über meine Zeit in der Schweiz in den Jahren 1948–1950 /rFriedrich Hirzebruch --tMichel Plancherel, une vie pour les mathématiques et pour le prochain /rNorbert Hungerbühler, Martine Schmutz --tZur Geschichte des Mathematischen Instituts der Universität Freiburg (Schweiz) /rHeinrich Kleisli --tMartin Eichler – Leben und Werk /rJürg Kramer --tMathematik an der Universität Bern im 19. und 20. Jahrhundert /rPeter Mani --tAn interview with Beno Eckmann /rMartin Raussen, Alain Valette --tWege von Frauen: Mathematikerinnen in der Schweiz /rChristine Riedtmann --tL'Institut de mathématiques de Neuchâtel 1950–90 /rAlain Robert --tHermann Weyl, Heinz Hopf und das Jahr 1930 an der ETH /rUrs Stammbach --tRolf Nevanlinna in Zurich /rKurt Strebel --tQuelques souvenirs sur le troisième cycle romand de mathématiques et le séminaire des Plans-sur-Bex /rClaude Weber --tJürgen Moser (1928–1999) /rEduard Zehnder.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book includes twenty-three essays to celebrate the 100th anniversary of the Swiss Mathematical Society. The life and work of outstanding mathematicians, extraordinary conferences held in Switzerland such as the three International Congresses of Mathematicians, the influence of women in Swiss mathematics are among the topics. The articles, including many photographs, old and recent, give a vivid picture of hundred years of mathematical life in Switzerland.
Dieses Buch ist eine Festschrift zum 100-jährigen Bestehen der Schweizerischen Mathematischen Gesellschaft. Es enthält dreiundzwanzig Beiträge zur Mathematik in der Schweiz.
Geschichtliches und Biographisches über herausragende Mathematiker an Schweizer Universitäten, grosse Tagungen wie etwa die drei Internationalen Mathematiker-Kongresse, die Rolle der Frauen in der Schweizer Mathematik sind nur einige Themen. Insgesamt vermitteln die verschiedenen Essays zusammen mit den zahlreichen Abbildungen ein höchst lebendiges und anschauliches Panorama eines Jahrhunderts Schweizer Mathematik.
Cet ouvrage a été édité pour marquer le 100e anniversaire de la Société Mathématique Suisse. Il rassemble vingt-trois articles consacrés aux mathématiques en Suisse. Parmi beaucoup d'autres choses, les écrits évoquent la vie et l'œuvre de grands mathématiciens des universités suisses, les grands événements, dont les trois Congrès internationaux de mathématiques, ou encore la présence des femmes dans les mathématiques suisses. Agrémenté de nombreuses photos, anciennes et récentes, ce livre donne une image très vivante de cent années de vie mathématique en Suisse.07aHistory of mathematics2bicssc07aHistory and biography2msc1 aColbois, Bruno,eeditor.1 aRiedtmann, Christine,eeditor.1 aSchroeder, Viktor,eeditor.40uhttps://doi.org/10.4171/089423cover imageuhttps://www.ems-ph.org/img/books/smg.jpg02188nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003100207245007900238260008200317300003300399336002600432337002600458338003600484347002400520490006100544506006600605520097500671650003401646650004201680650002301722856003201745856006101777121-101003CH-001817-320101003234500.0a fot ||| 0|cr nn mmmmamaa101003e20100929sz fot ||| 0|eng d a978303719590170a10.4171/0902doi ach0018173 7aPBFD2bicssc a20-xxa11-xx2msc1 aHarada, Koichiro,eauthor.10a“Moonshine” of Finite Groupsh[electronic resource] /cKoichiro Harada3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (83 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is an almost verbatim reproduction of the author’s lecture notes written
in 1983–84 at the Ohio State University, Columbus, Ohio, USA. A substantial
update is given in the bibliography. Over the last 20 plus years, there has
been an energetic activity in the field of finite simple group theory related to
the monster simple group. Most notably, influential works have been
produced in the theory of vertex operator algebras whose research was
stimulated by the moonshine of the finite groups. Still, we can ask the same
questions now just as we did some 30–40 years ago: What is the monster
simple group? Is it really related to the theory of the universe as it was
vaguely so envisioned? What lays behind the moonshine phenomena of the
monster group? It may appear that we have only scratched the surface.
These notes are primarily reproduced for the benefit of young readers
who wish to start learning about modular functions used in moonshine.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc07aNumber theory2msc40uhttps://doi.org/10.4171/090423cover imageuhttps://www.ems-ph.org/img/books/harada.jpg03293nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003400207245014000241260008200381300003400463336002600497337002600523338003600549347002400585490004000609506006600649520185400715650004702569650003802616650003102654700003002685700003002715700003102745700002602776856003202802856006102834122-100929CH-001817-320100929234500.0a fot ||| 0|cr nn mmmmamaa100929e20100929sz fot ||| 0|eng d a978303719582670a10.4171/0822doi ach0018173 7aPBMP2bicssc a57-xxa53-xx2msc1 aBessières, Laurent,eauthor.10aGeometrisation of 3-Manifoldsh[electronic resource] /cLaurent Bessières, Gérard Besson, Michel Boileau, Sylvain Maillot, Joan Porti3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (247 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v131 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints.
Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another.
A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ℒ-functional and κ-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.07aDifferential & Riemannian geometry2bicssc07aManifolds and cell complexes2msc07aDifferential geometry2msc1 aBesson, Gérard,eauthor.1 aBoileau, Michel,eauthor.1 aMaillot, Sylvain,eauthor.1 aPorti, Joan,eauthor.40uhttps://doi.org/10.4171/082423cover imageuhttps://www.ems-ph.org/img/books/besson.jpg02676nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003700213245008800250260008200338300003400420336002600454337002600480338003600506347002400542490005600566506006600622520140800688650003502096650003102131650001802162650003102180856003202211856007102243123-101201CH-001817-320101201234500.0a fot ||| 0|cr nn mmmmamaa101201e20101201sz fot ||| 0|eng d a978303719587170a10.4171/0872doi ach0018173 7aPBX2bicssc a01-xxa51-xxa53-xx2msc1 aPapadopoulos, Athanase,eauthor.10aNikolai I. Lobachevsky, Pangeometryh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (322 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aLobachevsky wrote his Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models.
Besides its historical importance, Lobachevsky’s Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a source book and as a repository of inspiration.
The present edition provides the first complete English translation of the Pangeometry that appears in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.07aHistory of mathematics2bicssc07aHistory and biography2msc07aGeometry2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/087423cover imageuhttps://www.ems-ph.org/img/books/lobachevsky_mini.jpg03410nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184245011900199260008200318300003400400336002600434337002600460338003600486347002400522490005400546505135200600506006601952520077902018650002002797650002802817700002702845700003502872700003202907856003202939856006502971124-101215CH-001817-320101215234500.0a fot ||| 0|cr nn mmmmamaa101215e20101230sz fot ||| 0|eng d a978303719507970a10.4171/0072doi ach0018173 7aPBF2bicssc a14-xx2msc10aClassification of Algebraic Varietiesh[electronic resource] /cCarel Faber, Gerard van der Geer, Eduard Looijenga3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (346 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tStable varieties with a twist /rDan Abramovich, Brendan Hassett --tBasic properties of log canonical centers /rFlorin Ambro --tBurniat surfaces I: fundamental groups and moduli of primary Burniat surfaces /rIngrid Bauer, Fabrizio Catanese --tMinimal models, flips and finite generation: a tribute to V.V. Shokurov and Y.-T. Siu /rCaucher Birkar, Mihai Paun --tRemarks on an example of K. Ueno /rFrédéric Campana --tSpecial orbifolds and birational classification: a survey /rFrédéric Campana --tBirational geometry of threefolds /rJungkai Alfred Chen --tEmptiness of homogeneous linear systems with ten general base points /rCiro Ciliberto, Olivia Dumitrescu, Rick Miranda, Joaquim Roé --tFinite generation of adjoint rings after Lazic: an introduction /rAlessio Corti --tLog canonical thresholds on varieties with bounded singularities /rTommaso de Fernex, Lawrence Ein, Mircea Mustaţă --tBrill–Noether geometry on moduli spaces of spin curves /rGavril Farkas --tOn the bimeromorphic geometry of compact complex contact threefolds /rKristina Frantzen, Thomas Peternell --tIntroduction to the theory of quasi-log varieties /rOsamu Fujino --tOn Kawamata’s theorem /rOsamu Fujino --tRemarks on the cone of divisors /rYujiro Kawamata --tp-elementary subgroups of the Cremona group of rank 3 /rYuri Prokhorov.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aFascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field.
Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas.
This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.07aAlgebra2bicssc07aAlgebraic geometry2msc1 aFaber, Carel,eeditor.1 avan der Geer, Gerard,eeditor.1 aLooijenga, Eduard,eeditor.40uhttps://doi.org/10.4171/007423cover imageuhttps://www.ems-ph.org/img/books/faber_mini.jpg02717nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002900199245018800228260008200416300003400498336002600532337002600558338003600584347002400620490004000644506006600684520145900750650004502209650002802254856003202282856006502314125-101201CH-001817-320101201234500.0a fot ||| 0|cr nn mmmmamaa101201e20101201sz fot ||| 0|eng d a978303719591870a10.4171/0912doi ach0018173 7aPBK2bicssc a65-xx2msc1 aBörm, Steffen,eauthor.10aEfficient Numerical Methods for Non-local Operatorsh[electronic resource] :bℋ2-Matrix Compression, Algorithms and Analysis Corrected 2nd printing, September 2013 /cSteffen Börm3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (441 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHierarchical matrices present an efficient way of treating dense matrices
that arise in the context of integral equations, elliptic partial
differential equations, and control theory.
While a dense n × n matrix in standard representation requires
n2 units of storage, a hierarchical matrix can approximate the
matrix in a compact representation requiring only O(nk log n) units
of storage, where k is a parameter controlling the accuracy.
Hierarchical matrices have been successfully applied to approximate
matrices arising in the context of boundary integral methods, to
construct preconditioners for partial differential equations, to
evaluate matrix functions and to solve matrix equations used in control
theory.
ℋ2-matrices
offer a refinement of hierarchical matrices: using a
multilevel representation of submatrices, the efficiency can be
significantly improved, particularly for large problems.
This books gives an introduction to the basic concepts and presents a
general framework that can be used to analyze the complexity and
accuracy of ℋ2-matrix techniques.
Starting from basic ideas of numerical linear
algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers
in numerical mathematics and scientific computing. Special techniques are only required
in isolated sections, e.g., for certain classes of model problems.07aCalculus & mathematical analysis2bicssc07aNumerical analysis2msc40uhttps://doi.org/10.4171/091423cover imageuhttps://www.ems-ph.org/img/books/börm_mini.jpg02372nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003200221245010800253260008200361300003400443336002600477337002600503338003600529347002400565490006100589506006600650520099800716650003401714650004001748650005501788650002501843650003101868856003201899856006701931126-110225CH-001817-320110225234510.0a fot ||| 0|cr nn mmmmamaa110225e20110225sz fot ||| 0|eng d a978303719580270a10.4171/0802doi ach0018173 7aPBFD2bicssc a22-xxa32-xxa47-xxa53-xx2msc1 aNeretin, Yurii A.,eauthor.10aLectures on Gaussian Integral Operators and Classical Groupsh[electronic resource] /cYurii A. Neretin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (571 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis.
Topics covered include the theory of various Fourier-like integral operators as Segal–Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces.
The heart of the book is the Weil representation of
the symplectic group (real and complex realizations, relations with theta-functions
and modular forms, $p$-adic and adelic constructions) and representations
in Hilbert spaces of holomorphic functions of several complex variables.
The book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. The reader is supposed to be familiar with standard university courses in linear algebra, functional analysis, and complex analysis.07aGroups & group theory2bicssc07aTopological groups, Lie groups2msc07aSeveral complex variables and analytic spaces2msc07aOperator theory2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/080423cover imageuhttps://www.ems-ph.org/img/books/neretin_mini.jpg02999nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003400199245014500233260008200378300003400460336002600494337002600520338003600546347002400582490005600606506006600662520176800728650003502496650003102531856003202562856006702594127-110329CH-001817-320110329234510.0a fot ||| 0|cr nn mmmmamaa110329e20110329sz fot ||| 0|eng d a978303719592570a10.4171/0922doi ach0018173 7aPBX2bicssc a01-xx2msc1 aStedall, Jacqueline,eauthor.10aFrom Cardano’s great art to Lagrange’s reflections: filling a gap in the history of algebrah[electronic resource] /cJacqueline Stedall3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (236 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy ‘Réflexions sur la résolution algébrique des équations’: that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra.
Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage.
The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (from 1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (from 1707 to 1770) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation.07aHistory of mathematics2bicssc07aHistory and biography2msc40uhttps://doi.org/10.4171/092423cover imageuhttps://www.ems-ph.org/img/books/stedall_mini.jpg02716nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003000214245012800244260008200372300003400454336002600488337002600514338003600540347002400576490006100600506006600661520134800727650002702075650004002102650002802142650004302170700003002213856003202243856006702275128-110524CH-001817-320110524234510.0a fot ||| 0|cr nn mmmmamaa110524e20110611sz fot ||| 0|eng d a978303719596370a10.4171/0962doi ach0018173 7aPBFL2bicssc a13-xxa14-xxa17-xx2msc1 aCalaque, Damien,eauthor.10aLectures on Duflo Isomorphisms in Lie Algebra and Complex Geometryh[electronic resource] /cDamien Calaque, Carlo A. Rossi3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (114 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDuflo isomorphism first appeared in Lie theory and representation theory. It is
an isomorphism between invariant polynomials of a Lie algebra and the center
of its universal enveloping algebra, generalizing the pioneering work of
Harish-Chandra on semi-simple Lie algebras. Later on, Duflo’s result was refound by
Kontsevich in the framework of deformation quantization, who also observed
that there is a similar isomorphism between Dolbeault cohomology of holomorphic
polyvector fields on a complex manifold and its Hochschild cohomology.
The present book, which arose from a series of lectures by the first author at
ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds.
All notions mentioned above are introduced and explained in the book, the only
prerequisites being basic linear algebra and differential geometry. In addition
to standard notions such as Lie (super)algebras, complex manifolds, Hochschild
and Chevalley–Eilenberg cohomologies, spectral sequences, Atiyah and Todd
classes, the graphical calculus introduced by Kontsevich in his seminal work on
deformation quantization is addressed in details.
The book is well-suited for graduate students in mathematics and mathematical
physics as well as for researchers working in Lie theory, algebraic geometry and
deformation theory.07aFields & rings2bicssc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc07aNonassociative rings and algebras2msc1 aRossi, Carlo A.,eauthor.40uhttps://doi.org/10.4171/096423cover imageuhttps://www.ems-ph.org/img/books/calaque_mini.jpg03016nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184245012000220260008200340300003400422336002600456337002600482338003600508347002400544490005000568505040500618506006601023520124601089650004502335650004802380650002302428650002902451650002402480700002902504856003202533856006502565129-110706CH-001817-320110706234510.0a fot ||| 0|cr nn mmmmamaa110706e20110706sz fot ||| 0|eng d a978303719508670a10.4171/0082doi ach0018173 7aPBK2bicssc a58-xxa11-xxa46-xxa81-xx2msc10aNoncommutative Geometry and Physics: Renormalisation, Motives, Index Theoryh[electronic resource] /cAlan L. Carey3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (280 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)00tNotes on Feynman integrals and renormalization /rChristoph Bergbauer --tIntroduction to motives /rSujatha Ramdorai, Jorge Plazas, Matilde Marcolli --tA short survey on pre-Lie algebras /rDominique Manchon --tDivergent multiple sums and integrals with constraints: a comparative study /rSylvie Paycha --tSpectral triples: examples and index theory /rAlan L. Carey, John Phillips, Adam Rennie.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis collection of expository articles grew out of the workshop “Number Theory and Physics” held in March 2009 at the The Erwin Schrödinger International Institute for Mathematical Physics, Vienna. The common theme of the articles is the influence of ideas from noncommutative geometry (NCG) on subjects ranging from number theory to Lie algebras, index theory, and mathematical physics.
Matilde Marcolli’s article gives a survey of relevant aspects of NCG in number theory, building on an introduction to motives for beginners by Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index theory from the viewpoint of NCG is described in the article by Alan Carey, John Phillips and Adam Rennie. As developed by Alain Connes and Dirk Kreimer, NCG also provides insight into novel algebraic structures underlying many analytic aspects of quantum field theory. Dominique Manchon's article on pre-Lie algebras fits into this developing research area. This interplay of algebraic and analytic techniques
also appears in the articles by Christoph Bergbauer, who introduces renormalisation theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalisation and zeta function techniques.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aNumber theory2msc07aFunctional analysis2msc07aQuantum theory2msc1 aCarey, Alan L.,eeditor.40uhttps://doi.org/10.4171/008423cover imageuhttps://www.ems-ph.org/img/books/carey_mini.jpg02762nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002800207245017300235260008200408300003400490336002600524337002600550338003600576347002400612490004000636506006600676520138200742650003102124650002802155650004602183700003302229700002902262856003202291856006502323130-110815CH-001817-320110815234510.0a fot ||| 0|cr nn mmmmamaa110815e20110811sz fot ||| 0|eng d a978303719583370a10.4171/0832doi ach0018173 7aPBPD2bicssc a55-xxa18-xx2msc1 aBrown, Ronald,eauthor.10aNonabelian Algebraic Topologyh[electronic resource] :bFiltered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /cRonald Brown, Philip J. Higgins, Rafael Sivera3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (703 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v151 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe main theme of this book is that the use of filtered spaces rather than
just topological spaces allows the development of basic algebraic topology in
terms of higher homotopy groupoids; these algebraic structures better
reflect the geometry of subdivision and composition than those commonly in
use. Exploration of these uses of higher dimensional versions of groupoids
has been largely the work of the first two authors since the mid 1960s.
The structure of the book is intended to make it useful to a wide class of
students and researchers for learning and evaluating these methods, primarily
in algebraic topology but also in higher category theory and its applications
in analogous areas of mathematics, physics and computer science.
Part I explains the intuitions and theory in dimensions 1 and 2, with many
figures and diagrams, and a detailed account of the theory of crossed
modules. Part II develops the applications of crossed complexes. The engine
driving these applications is the work of Part III on cubical ω-groupoids,
their relations to crossed complexes, and their homotopically defined examples
for filtered spaces. Part III also includes a chapter suggesting further
directions and problems, and three appendices give accounts of some
relevant aspects of category theory. Endnotes for each chapter give further
history and references.07aAlgebraic topology2bicssc07aAlgebraic topology2msc07aCategory theory; homological algebra2msc1 aHiggins, Philip J.,eauthor.1 aSivera, Rafael,eauthor.40uhttps://doi.org/10.4171/083423cover imageuhttps://www.ems-ph.org/img/books/brown_mini.jpg02839nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003000199245008800229260008200317300003400399336002600433337002600459338003600485347002400521490004000545506006600585520161000651650004502261650005502306700002702361856003202388856006902420131-110815CH-001817-320110815234510.0a fot ||| 0|cr nn mmmmamaa110815e20110811sz fot ||| 0|eng d a978303719598770a10.4171/0982doi ach0018173 7aPBK2bicssc a32-xx2msc1 aJarnicki, Marek,eauthor.10aSeparately Analytic Functionsh[electronic resource] /cMarek Jarnicki, Peter Pflug3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (306 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v161 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe story of separately holomorphic functions began about 100 years ago.
During the second half of the 19th century, it became known that a separately
continuous function is not necessarily continuous as a function of all
variables. At the beginning of the 20th century, the study of separately
holomorphic functions started due to the fundamental work of Osgood and
Hartogs.
This book provides the first self-contained and complete presentation of the
study of separately holomorphic functions, starting from its birth up to
current research. Most of the results presented have never been published
before in book form. The text is divided into two parts. A more elementary
one deals with separately holomorphic functions “without singularities”,
another addresses the situation of existing singularities. A discussion of the
classical results related to separately holomorphic functions leads to the
most fundamental result, the classical cross theorem as well as various
extensions and generalizations to more complicated “crosses”. Additionally,
several applications for other classes of “separately regular” functions are
given.
A solid background in basic complex analysis is a prerequisite. In order to
make the book self-contained, all the results needed for its understanding
are collected in special introductory chapters and referred to at the beginning
of each section.
The book is addressed to students and researchers in several complex
variables as well as to mathematicians and theoretical physicists who are
interested in this area of mathematics.07aCalculus & mathematical analysis2bicssc07aSeveral complex variables and analytic spaces2msc1 aPflug, Peter,eauthor.40uhttps://doi.org/10.4171/098423cover imageuhttps://www.ems-ph.org/img/books/jarnicki2_mini.jpg02589nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100003100220245011700251260008200368300003400450336002600484337002600510338003600536347002400572490006100596506006600657520109300723650004501816650004801861650002801909650004301937650005501980700002902035700002802064856003202092856006702124132-110806CH-001817-320110806234510.0a fot ||| 0|cr nn mmmmamaa110806e20110806sz fot ||| 0|eng d a978303719597070a10.4171/0972doi ach0018173 7aPBK2bicssc a58-xxa14-xxa17-xxa32-xx2msc1 aCarmeli, Claudio,eauthor.10aMathematical Foundations of Supersymmetryh[electronic resource] /cClaudio Carmeli, Lauren Caston, Rita Fioresi3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (300 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSupersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation.
The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, with a special attention to giving detailed proofs and many clarifying examples. It is aimed ideally at a second year graduate student. After the first three introductory chapters, the text divides into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices, the first introducing Lie superalgebras and representations of classical Lie superalgebras, the second collecting some relevant facts on categories, sheafification of functors and commutative algebra, and the third explaining the notion of Fréchet space in the super context.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aAlgebraic geometry2msc07aNonassociative rings and algebras2msc07aSeveral complex variables and analytic spaces2msc1 aCaston, Lauren,eauthor.1 aFioresi, Rita,eauthor.40uhttps://doi.org/10.4171/097423cover imageuhttps://www.ems-ph.org/img/books/carmeli_mini.jpg03172nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245010600200260008200306300003400388336002600422337002600448338003600474347002400510490005400534505113900588506006601727520074401793650002402537650005302561700002802614700003002642700002902672856003202701856006502733133-110815CH-001817-320110815234510.0a fot ||| 0|cr nn mmmmamaa110815e20110810sz fot ||| 0|eng d a978303719572770a10.4171/0722doi ach0018173 7aPBWL2bicssc a60-xx2msc10aSurveys in Stochastic Processesh[electronic resource] /cJochen Blath, Peter Imkeller, Sylvie Rœlly3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (263 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tOptimal switching, systems of reflected BSDEs and systems of variational inequalities with inter-connected obstacles /rSaïd Hamadène --tThe COGARCH: a review, with news on option pricing and statistical inference /rClaudia Klüppelberg, Ross Maller, Alexander Szimayer --tSome properties of quasi-stationary distributions for finite Markov chains /rServet Martínez, Jaime San Martín --tThe parabolic Anderson model with heavy-tailed potential /rPeter Mörters --tFrom exploration paths to mass excursions – variations on a theme of Ray and Knight /rEtienne Pardoux, Anton Wakolbinger --tGaussian approximation of functionals: Malliavin calculus and Stein’s method /rGesine Reinert --tMerging and stability for time inhomogeneous finite Markov chains /rLaurent Saloff-Coste, Jessica Zúñiga --tSome mathematical aspects of market impact modeling /rAlexander Schied, Alla Slynko --tThe self-avoiding walk: A brief survey /rGordon Slade --t$L^p$-independence of growth bounds of Feynman–Kac semigroups /rMasayoshi Takeda --tSome recent progress on functional inequalities and applications /rFeng-Yu Wang.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 33rd Bernoulli Society Conference on “Stochastic Processes and Their Applications” was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries, who communicated recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology.
The present book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection
is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume.07aStochastics2bicssc07aProbability theory and stochastic processes2msc1 aBlath, Jochen,eeditor.1 aImkeller, Peter,eeditor.1 aRœlly, Sylvie,eeditor.40uhttps://doi.org/10.4171/072423cover imageuhttps://www.ems-ph.org/img/books/blath_mini.jpg03045nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003100200245012900231260008200360300003400442336002600476337002600502338003600528347002400564490005100588506006600639520178700705650003502492650004002527700003002567856003202597856006602629134-110729CH-001817-320110729234510.0a fot ||| 0|cr nn mmmmamaa110729e20110902sz fot ||| 0|eng d a978303719595670a10.4171/0952doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aNakanishi, Kenji,eauthor.10aInvariant Manifolds and Dispersive Hamiltonian Evolution Equationsh[electronic resource] /cKenji Nakanishi, Wilhelm Schlag3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (258 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein–Gordon and Schrödinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter.
One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. Our entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount.
This monograph is based on recent research by the authors and the proofs rely on an interplay between the variational structure of the ground states on the one hand, and the nonlinear hyperbolic dynamics near these states on the other hand. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion.
These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein–Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.07aDifferential equations2bicssc07aPartial differential equations2msc1 aSchlag, Wilhelm,eauthor.40uhttps://doi.org/10.4171/095423cover imageuhttps://www.ems-ph.org/img/books/schlag_mini.jpg04233nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245011300200260008200313300003400395336002600429337002600455338003600481347002400517490005400541505112400595506006601719520185601785650002703641650004003668700003503708700003003743856003203773856006603805135-110909CH-001817-320110909234510.0a fot ||| 0|cr nn mmmmamaa110909e20110924sz fot ||| 0|eng d a978303719601470a10.4171/1012doi ach0018173 7aPBFL2bicssc a16-xx2msc10aRepresentations of Algebras and Related Topicsh[electronic resource] /cAndrzej Skowroński, Kunio Yamagata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (740 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tOn generalized cluster categories /rClaire Amiot --tModule categories for finite group algebras /rDavid J. Benson, Srikanth B. Iyengar, Henning Krause --tOn cluster theory and quantum dilogarithm identities /rBernhard Keller --tQuantum loop algebras, quiver varieties, and cluster algebras /rBernard Leclerc --tWeighted projective lines and applications /rHelmut Lenzing --tCohomology of block algebras of finite groups /rMarkus Linckelmann --tAlgebras with separating Auslander–Reiten components /rPiotr Malicki, Andrzej Skowroński --tClassification problems in noncommutative algebraic geometry and representation theory /rIzuru Mori --tPeriodicities in cluster algebras and dilogarithm identities /rTomoki Nakanishi --tThe Tits forms of tame algebras and their roots /rJosé Antonio Peña, Andrzej Skowroński --tThe minimal representation-infinite algebras which are special biserial /rClaus Michael Ringel --tCoalgebras of tame comodule type, comodule categories, and a tame-wild dichotomy problem /rDaniel Simson --tSingularities of orbit closures in module varieties /rGrzegorz Zwara.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is concerned with recent trends in the representation
theory of algebras and its exciting interaction with geometry, topology,
commutative algebra, Lie algebras, combinatorics, quantum algebras,
and theoretical physics.
The collection of articles, written by leading researchers in the field,
is conceived as a sort of handbook providing easy access
to the present state of knowledge and
stimulating
further development.
The topics under discussion include
quivers,
quivers with potential,
bound quiver algebras,
Jacobian algebras,
cluster algebras and categories,
Calabi–Yau algebras and categories,
triangulated and derived categories,
quantum loop algebras,
Nakajima quiver varieties,
Yang–Baxter equations,
T-systems and Y-systems,
dilogarithm and quantum dilogarithm identities,
stable module categories,
localizing and colocalizing subcategories,
cohomologies of groups,
support varieties,
fusion systems,
Hochschild cohomologies,
weighted projective lines,
coherent sheaves,
Kleinian and Fuchsian singularities,
stable categories of vector bundles,
nilpotent operators,
Artin–Schelter regular algebras,
Fano algebras,
deformations of algebras,
module varieties,
degenerations of modules,
singularities of orbit closures,
coalgebras and comodules,
representation types of algebras and coalgebras,
Tits and Euler forms of algebras,
Galois coverings of algebras,
tilting and cluster tilting theory,
algebras of small homological dimensions,
Auslander–Reiten theory.
The book consists of thirteen self-contained expository survey
and research articles and is addressed to researchers and graduate
students in algebra as well as a broader mathematical community.
They contain a large number of examples and open problems
and give new perspectives for research in the field.07aFields & rings2bicssc07aAssociative rings and algebras2msc1 aSkowroński, Andrzej,eeditor.1 aYamagata, Kunio,eeditor.40uhttps://doi.org/10.4171/101423cover imageuhttps://www.ems-ph.org/img/books/icra14_mini.jpg03154nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003200214245008300246260008200329300003400411336002600445337002600471338003600497347002400533506006600557520193600623650003102559650004402590650004602634650002602680856003202706856006602738136-110924CH-001817-320110924234522.0a fot ||| 0|cr nn mmmmamaa110924e20110925sz fot ||| 0|eng d a978303719588870a10.4171/0882doi ach0018173 7aPBCD2bicssc a03-xxa18-xxa68-xx2msc1 aGirard, Jean-Yves,eauthor.10aThe Blind Spoth[electronic resource] :bLectures on Logic /cJean-Yves Girard3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (550 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThese lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic.
The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is “more equal than the other”: one thus discovers essentialist blind spots.
Starting with Gödel’s paradox (1931) – so to speak, the incompleteness of answers with respect to questions – the book proceeds with paradigms inherited from Gentzen’s cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra.
Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity.
This highly original course on logic by one of the world’s leading proof theorists challenges mathematicians, computer scientists, physicists and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.07aMathematical logic2bicssc07aMathematical logic and foundations2msc07aCategory theory; homological algebra2msc07aComputer science2msc40uhttps://doi.org/10.4171/088423cover imageuhttps://www.ems-ph.org/img/books/girard_mini.jpg03286nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003200206245013500238260008200373300003400455336002600489337002600515338003600541347002400577490005600601506006600657520200600723650003502729650003102764650004202795856003202837856006702869137-111013CH-001817-320111013234510.0a fot ||| 0|cr nn mmmmamaa111013e20111020sz fot ||| 0|eng d a978303719604570a10.4171/1042doi ach0018173 7aPBX2bicssc a01-xxa20-xx2msc1 aNeumann, Peter M.,eauthor.10aThe mathematical writings of Évariste Galoish[electronic resource] :bCorrected 2nd printing, September 2013 /cPeter M. Neumann3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (421 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAlthough Évariste Galois was only 20 years old when he died, shot in a mysterious early-morning duel in 1832, his ideas, when they were published 14 years later, changed the course of algebra. He invented what is now called Galois Theory, the modern form of what was classically the Theory of Equations. For that purpose, and in particular to formulate a precise condition for solubility of equations by radicals, he also invented groups and began investigating their theory. His main writings were published in French in 1846 and there have been a number of French editions culminating in the great work published by Bourgne & Azra in 1962 containing transcriptions of every page and fragment of the manuscripts that survive. Very few items have been available in English up to now.
The present work contains English translations of almost all the Galois material. They are presented alongside a new transcription of the original French, and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the Testamentary Letter and the First Memoir (in which Galois expounded the ideas now called Galois Theory), which are the most famous of the manuscripts. There follow the less well known manuscripts, namely the Second Memoir and the many fragments. A short epilogue devoted to myths and mysteries concludes the text.
The book is written as a contribution to the history of mathematics but with mathematicans as well as historians in mind. It makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the 19th century, presented in its original form. The primary aim is to establish a text of what Galois wrote. Exegesis would fill another book or books, and little of that is to be f...07aHistory of mathematics2bicssc07aHistory and biography2msc07aGroup theory and generalizations2msc40uhttps://doi.org/10.4171/104423cover imageuhttps://www.ems-ph.org/img/books/neumann_mini.jpg02687nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002900199245010100228260008200329300003400411336002600445337002600471338003600497347002400533490004000557506006600597520147800663650004502141650002602186700002702212856003202239856006602271141-111105CH-001817-320111105234510.0a fot ||| 0|cr nn mmmmamaa111105e20111105sz fot ||| 0|eng d a978303719599470a10.4171/0992doi ach0018173 7aPBK2bicssc a31-xx2msc1 aBjörn, Anders,eauthor.10aNonlinear Potential Theory on Metric Spacesh[electronic resource] /cAnders Björn, Jana Björn3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (415 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v171 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe p-Laplace equation is the main prototype for nonlinear elliptic problems
and forms a basis for various applications, such as injection moulding of
plastics, nonlinear elasticity theory and image processing. Its solutions,
called p-harmonic functions, have been studied in various contexts since
the 1960s, first on Euclidean spaces and later on Riemannian manifolds,
graphs and Heisenberg groups. Nonlinear potential theory of p-harmonic
functions on metric spaces has been developing since the 1990s and
generalizes and unites these earlier theories.
This monograph gives a unified treatment of the subject and covers most
of the available results in the field, so far scattered over a large number
of research papers. The aim is to serve both as an introduction to the area
for an interested reader and as a reference text for an active researcher.
The presentation is rather self-contained, but the reader is assumed to
know measure theory and functional analysis.
The first half of the book deals with Sobolev type spaces, so-called
Newtonian spaces, based on upper gradients on general metric spaces. In
the second half, these spaces are used to study p-harmonic functions
on metric spaces and a nonlinear potential theory is developed under some
additional, but natural, assumptions on the underlying metric space.
Each chapter contains historical notes with relevant references and an
extensive index is provided at the end of the book.07aCalculus & mathematical analysis2bicssc07aPotential theory2msc1 aBjörn, Jana,eauthor.40uhttps://doi.org/10.4171/099423cover imageuhttps://www.ems-ph.org/img/books/björn_mini.jpg02393nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003500200245011800235260008200353300003400435336002600469337002600495338003600521347002400557490003900581506006600620520115200686650002701838650004001865700003001905856003201935856007601967142-111212CH-001817-320111212234510.0a fot ||| 0|cr nn mmmmamaa111212e20111213sz fot ||| 0|eng d a978303719602170a10.4171/1022doi ach0018173 7aPBFL2bicssc a16-xx2msc1 aSkowroński, Andrzej,eauthor.10aFrobenius Algebras Ih[electronic resource] :bBasic Representation Theory /cAndrzej Skowroński, Kunio Yamagata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (661 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is the first of two volumes which will provide a comprehensive introduction
to the modern representation theory of Frobenius algebras. The first
part of the book serves as a general introduction to basic results and techniques
of the modern representation theory of finite dimensional associative
algebras over fields, including the Morita theory of equivalences and dualities
and the Auslander–Reiten theory of irreducible morphisms and almost
split sequences.
The second part is devoted to fundamental classical and recent results concerning
the Frobenius algebras and their module categories. Moreover, the
prominent classes of Frobenius algebras, the Hecke algebras of Coxeter
groups and the finite dimensional Hopf algebras over fields are exhibited.
This volume is self-contained and the only prerequisite is a basic knowledge
of linear algebra. It includes complete proofs of all results presented and provides
a rich supply of examples and exercises.
The text is primarily addressed to graduate students starting research in
the representation theory of algebras as well mathematicians working in
other fields.07aFields & rings2bicssc07aAssociative rings and algebras2msc1 aYamagata, Kunio,eauthor.40uhttps://doi.org/10.4171/102423cover imageuhttps://www.ems-ph.org/img/books/skowronski_text1_mini.jpg02411nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002600213245010000239260008200339300003400421336002600455337002600481338003600507347002400543490005100567506006600618520112400684650003101808650002801839650004001867650004601907856003201953856006401985143-111229CH-001817-320111229234510.0a fot ||| 0|cr nn mmmmamaa111229e20120114sz fot ||| 0|eng d a978303719600770a10.4171/1002doi ach0018173 7aPBS2bicssc a65-xxa35-xxa37-xx2msc1 aFaou, Erwan,eauthor.10aGeometric Numerical Integration and Schrödinger Equationsh[electronic resource] /cErwan Faou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (146 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe goal of geometric numerical integration is the simulation of evolution
equations possessing geometric properties over long times. Of particular importance
are Hamiltonian partial differential equations typically arising in application
fields such as quantum mechanics or wave propagation phenomena. They
exhibit many important dynamical features such as energy preservation and
conservation of adiabatic invariants over long time. In this setting, a natural
question is how and to which extent the reproduction of such long time qualitative
behavior can be ensured by numerical schemes.
Starting from numerical examples, these notes provide a detailed analysis of the
Schrödinger equation in a simple setting (periodic boundary conditions, polynomial
nonlinearities) approximated by symplectic splitting methods. Analysis
of stability and instability phenomena induced by space and time discretization
are given, and rigorous mathematical explanations for them.
The book grew out of a graduate level course and is of interest to researchers
and students seeking an introduction to the subject matter.07aNumerical analysis2bicssc07aNumerical analysis2msc07aPartial differential equations2msc07aDynamical systems and ergodic theory2msc40uhttps://doi.org/10.4171/100423cover imageuhttps://www.ems-ph.org/img/books/faou_mini.jpg02956nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003200207245007700239260008200316300003400398336002600432337002600458338003600484347002400520490003800544506006600582520173500648650002902383650004102412650005502453856003202508856006602540144-111229CH-001817-320111229234510.0a fot ||| 0|cr nn mmmmamaa111229e20120102sz fot ||| 0|eng d a978303719575870a10.4171/0752doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc1 aPenner, Robert C.,eauthor.10aDecorated Teichmüller Theoryh[electronic resource] /cRobert C. Penner3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (377 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aThe QGM Master Class Series (QGM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThere is an essentially “tinker-toy” model of a trivial bundle over the classical Teichmüller space of a punctured surface, called the decorated Teichmüller space, where the fiber over a point is the space of all tuples of horocycles, one
about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizationsleading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules.
This volume gives the story and wider context of these decorated Teichmüller
spaces as developed by the author over the last two decades in a series of
papers, some of them in collaboration. Sometimes correcting errors or typos,
sometimes simplifying proofs and sometimes articulating more general formulations
than the original research papers, this volume is self-contained and
requires little formal background. Based on a master’s course at Aarhus University,
it gives the first treatment of these works in monographic form.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc40uhttps://doi.org/10.4171/075423cover imageuhttps://www.ems-ph.org/img/books/penner_mini.jpg02765nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184245008800206260008200294300003400376336002600410337002600436338003600462347002400498490008300522505062000605506006601225520090401291650002102195650001802216650003802234700003702272856003202309856006202341145-120118CH-001817-320120118234510.0a fot ||| 0|cr nn mmmmamaa120118e20120118sz fot ||| 0|eng d a978303719605270a10.4171/1052doi ach0018173 7aPBM2bicssc a51-xxa57-xx2msc10aStrasbourg Master Class on Geometryh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (461 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1800tNotes on non-Euclidean geometry /rNorbert A’Campo, Athanase Papadopoulos --tCrossroads between hyperbolic geometry and number theory /rFrançoise Dal’Bo --tIntroduction to origamis in Teichmüller space /rFrank Herrlich --tFive lectures on 3-manifold topology /rPhilipp Korablev, Sergey V. Matveev --tAn introduction to globally symmetric spaces /rGabriele Link --tGeometry of the representation spaces in SU(2) /rJulien Marché --tAlgorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs /rCarlo Petronio --tAn introduction to asymptotic geometry /rViktor Schroeder.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmüller theory, Lie groups and asymptotic geometry.
The text is addressed to students and mathematicians who wish to learn the subject. It can also be used as a reference book and as a textbook for short courses on geometry.07aGeometry2bicssc07aGeometry2msc07aManifolds and cell complexes2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/105423cover imageuhttps://www.ems-ph.org/img/books/irma_18.jpg03167nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084002200202100003100224245011100255260008200366300003400448336002600482337002600508338003600534347002400570490005300594506006600647520178600713650003502499650004702534650004002581650003102621700003002652856003202682856006702714146-120207CH-001817-320120207234510.0a fot ||| 0|cr nn mmmmamaa120207e20120209sz fot ||| 0|eng d a978303719606970a10.4171/1062doi ach0018173 7aPBKJ2bicssc 7aPBMP2bicssc a35-xxa53-xx2msc1 aKrieger, Joachim,eauthor.10aConcentration Compactness for Critical Wave Mapsh[electronic resource] /cJoachim Krieger, Wilhelm Schlag3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (490 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWave maps are the simplest wave equations taking their values in a Riemannian
manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only
difference being that lengths are measured with respect to the metric $g$. By
Noether's theorem, symmetries of the Lagrangian imply conservation laws for
wave maps, such as conservation of energy.
In coordinates, wave maps are given by a system of semilinear wave equations.
Over the past 20 years important methods have emerged which address the
problem of local and global wellposedness of this system. Due to weak dispersive
effects, wave maps defined on Minkowski spaces of low dimensions, such as $\mathbb R^{2+1}_{t,x}$, present particular technical difficulties. This class of wave maps has the additional important feature of being energy critical, which refers to the fact that
the energy scales exactly like the equation.
Around 2000 Daniel Tataru and Terence Tao, building on earlier work of
Klainerman–Machedon, proved that smooth data of small energy lead to global
smooth solutions for wave maps from 2+1 dimensions into target manifolds
satisfying some natural conditions. In contrast, for large data, singularities may
occur in finite time for $M =\mathbb S^2$ as target. This monograph establishes that for
$\mathbb H$ as target the wave map evolution of any smooth data exists globally as a
smooth function.
While we restrict ourselves to the hyperbolic plane as target the implementation
of the concentration-compactness method, the most challenging piece of this
exposition, yields more detailed information on the solution. This monograph
will be of interest to experts in nonlinear dispersive equations, in particular to
those working on geometric evolution equations.07aDifferential equations2bicssc07aDifferential & Riemannian geometry2bicssc07aPartial differential equations2msc07aDifferential geometry2msc1 aSchlag, Wilhelm,eauthor.40uhttps://doi.org/10.4171/106423cover imageuhttps://www.ems-ph.org/img/books/krieger_mini.jpg02076nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100002800221245011900249260008200368300003400450336002600484337002600510338003600536347002400572490006100596506006600657520072400723650003201447650002901479650003901508650002601547650002601573856003201599856007101631147-120316CH-001817-320120316234500.0a fot ||| 0|cr nn mmmmamaa120316e20120316sz fot ||| 0|eng d a978303719607670a10.4171/1072doi ach0018173 7aPBKG2bicssc a46-xxa41-xxa42-xxa68-xx2msc1 aTriebel, Hans,eauthor.10aFaber Systems and Their Use in Sampling, Discrepancy, Numerical Integrationh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (115 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author’s book Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration (EMS, 2010) from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.
The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory.07aFunctional analysis2bicssc07aFunctional analysis2msc07aApproximations and expansions2msc07aFourier analysis2msc07aComputer science2msc40uhttps://doi.org/10.4171/107423cover imageuhttps://www.ems-ph.org/img/books/triebel-mini-lec.jpg02501nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003500213245008900248260008200337300003400419336002600453337002600479338003600505347002400541490003800565506006600603520122200669650002001891650004601911650004301957650003802000856003202038856006902070148-120316CH-001817-320120316234500.0a fot ||| 0|cr nn mmmmamaa120316e20120316sz fot ||| 0|eng d a978303719608370a10.4171/1082doi ach0018173 7aPBF2bicssc a18-xxa17-xxa57-xx2msc1 aMazorchuk, Volodymyr,eauthor.10aLectures on Algebraic Categorificationh[electronic resource] /cVolodymyr Mazorchuk3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (128 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aThe QGM Master Class Series (QGM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe term “categorification” was introduced by Louis Crane in 1995 and refers to
the process of replacing set-theoretic notions by the corresponding category-theoretic
analogues.
This text mostly concentrates on algebraical aspects of the theory, presented
in the historical perspective, but also contains several topological applications,
in particular, an algebraic (or, more precisely, representation-theoretical) approach
to categorification. It consists of fifteen sections corresponding to fifteen
one-hour lectures given during a Master Class at Aarhus University, Denmark in
October 2010. There are some exercises collected at the end of the text and a
rather extensive list of references. Video recordings of all (but one) lectures are
available from the Master Class website.
The book provides an introductory overview of the subject rather than a fully
detailed monograph. Emphasis is on definitions, examples and formulations of
the results. Most proofs are either briefly outlined or omitted. However, complete
proofs can be found by tracking references. It is assumed that the reader is
familiar with the basics of category theory, representation theory, topology and
Lie algebra.07aAlgebra2bicssc07aCategory theory; homological algebra2msc07aNonassociative rings and algebras2msc07aManifolds and cell complexes2msc40uhttps://doi.org/10.4171/108423cover imageuhttps://www.ems-ph.org/img/books/mazorchuk_mini.jpg02469nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003400206245010100240260008200341300003400423336002600457337002600483338003600509347002400545490005100569506006600620520119100686650003701877650005301914650005201967856003202019856006802051149-120503CH-001817-320120503234500.0a fot ||| 0|cr nn mmmmamaa120503e20120511sz fot ||| 0|eng d a978303719609070a10.4171/1092doi ach0018173 7aPBT2bicssc a60-xxa82-xx2msc1 aSznitman, Alain-Sol,eauthor.10aTopics in Occupation Times and Gaussian Free Fieldsh[electronic resource] /cAlain-Sol Sznitman3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (121 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book grew out of a graduate course at ETH Zurich during the Spring term
2011. It explores various links between such notions as occupation times of
Markov chains, Gaussian free fields, Poisson point processes of Markovian loops,
and random interlacements, which have been the object of intensive research
over the last few years. These notions are developed in the convenient set-up
of finite weighted graphs endowed with killing measures.
The book first discusses elements of continuous-time Markov chains, Dirichlet
forms, potential theory, together with some consequences for Gaussian free
fields. Next, isomorphism theorems and generalized Ray-Knight theorems,
which relate occupation times of Markov chains to Gaussian free fields, are pre-
sented. Markovian loops are constructed and some of their key properties
derived. The field of occupation times of Poisson point processes of Markovian
loops is investigated. Of special interest are its connection to the Gaussian free
field, and a formula of Symanzik. Finally, links between random interlacements
and Markovian loops are discussed, and some further connections with
Gaussian free fields are mentioned.07aProbability & statistics2bicssc07aProbability theory and stochastic processes2msc07aStatistical mechanics, structure of matter2msc40uhttps://doi.org/10.4171/109423cover imageuhttps://www.ems-ph.org/img/books/sznitman_mini.jpg02684nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002500213245007200238260008200310300003400392336002600426337002600452338003600478347002400514490006100538506006600599520143700665650004102102650002302143650004202166650001802208856003202226856006402258152-120613CH-001817-320120613234500.0a fot ||| 0|cr nn mmmmamaa120613e20120613sz fot ||| 0|eng d a978303719610670a10.4171/1102doi ach0018173 7aPBV2bicssc a05-xxa20-xxa51-xx2msc1 aThas, Koen,eauthor.10aA Course on Elation Quadranglesh[electronic resource] /cKoen Thas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (129 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe notion of elation generalized quadrangle is a natural generalization to
the theory of generalized quadrangles of the important notion of translation
planes in the theory of projective planes. Almost any known class of finite
generalized quadrangles can be constructed from a suitable class of elation
quadrangles.
In this book the author considers several aspects of the theory of elation generalized
quadrangles. Special attention is given to local Moufang conditions
on the foundational level, exploring for instance a question of Knarr from
the 1990s concerning the very notion of elation quadrangles. All the known
results on Kantor’s prime power conjecture for finite elation quadrangles are
gathered, some of them published here for the first time. The structural theory
of elation quadrangles and their groups is heavily emphasized. Other related
topics, such as p-modular cohomology, Heisenberg groups and existence problems
for certain translation nets, are briefly touched.
The text starts from scratch and is essentially self-contained. Many alternative
proofs are given for known theorems. Containing dozens of exercises at
various levels, from very easy to rather difficult, this course will stimulate
undergraduate and graduate students to enter the fascinating and rich world
of elation quadrangles. The more accomplished mathematician will especially
find the final chapters challenging.07aCombinatorics & graph theory2bicssc07aCombinatorics2msc07aGroup theory and generalizations2msc07aGeometry2msc40uhttps://doi.org/10.4171/110423cover imageuhttps://www.ems-ph.org/img/books/thas_mini.jpg04157nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245009600207260008200303300003400385336002600419337002600445338003600471347002400507490008300531505142300614506006602037520143202103650002903535650004103564650005503605700003703660856003203697856006603729153-120609CH-001817-320120609234500.0a fot ||| 0|cr nn mmmmamaa120609e20120608sz fot ||| 0|eng d a978303719603870a10.4171/1032doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc10aHandbook of Teichmüller Theory, Volume IIIh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (874 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1700tIntroduction to Teichmüller theory, old and new, III /rAthanase Papadopoulos --tQuasiconformal and BMO-quasiconformal homeomorphisms /rJean-Pierre Otal --tEarthquakes on the hyperbolic plane /rJun Hu --tKerckhoff’s lines of minima in Teichmüller space /rCaroline Series --tA tale of two groups: arithmetic groups and mapping class groups /rLizhen Ji --tSimplicial actions of mapping class groups /rJohn D. McCarthy, Athanase Papadopoulos --tOn the coarse geometry of the complex of domains /rValentina Disarlo --tMinimal generating sets for the mapping class group /rMustafa Korkmaz --tFrom mapping class groups to monoids of homology cobordisms: a survey /rKazuo Habiro, Gwénaël Massuyeau --tA survey of Magnus representations for mapping class groups and homology cobordisms of surfaces /rTakuya Sakasai --tAsymptotically rigid mapping class groups and Thompson groups /rLouis Funar, Christophe Kapoudjian, Vlad Sergiescu --tAn introduction to moduli spaces of curves and their intersection theory /rDimitri Zvonkine --tHomology of the open moduli space of curves /rIb Madsen --tOn the $L^p$-cohomology and the geometry of metrics on moduli spaces of curves /rLizhen Ji, Steven Zucker --tThe Weil–Petersson metric and the renormalized volume of hyperbolic 3-manifolds /rKirill Krasnov, Jean-Marc Schlenker --tDiscrete Liouville equation and Teichmüller theory /rRinat Kashaev.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with 3-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas towards a unique subject is a manifestation of the unity and harmony of mathematics.
The present volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in the fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems.
The metric and the analytic theory.
The group theory.
The algebraic topology of mapping class groups and moduli spaces.
Teichmüller theory and mathematical physics.
The handbook is addressed to graduate students and researchers in all the fields mentioned.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/103423cover imageuhttps://www.ems-ph.org/img/books/irma17_mini.jpg04216nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245010500221260008200326300003400408336002600442337002600468338003600494347002400530490005400554505175300608506006602361520110702427650003103534650002803565650002303593650005503616650003103671700002903702856003203731856006703763154-120815CH-001817-320120815234500.0a fot ||| 0|cr nn mmmmamaa120815e20120815sz fot ||| 0|eng d a978303719614470a10.4171/1142doi ach0018173 7aPBMW2bicssc a14-xxa11-xxa32-xxa53-xx2msc10aContributions to Algebraic Geometryh[electronic resource] :bImpanga Lecture Notes /cPiotr Pragacz3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (516 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tThe influence of Oscar Zariski on algebraic geometry /rPiotr Blass --tThe geometry of T-varieties /rKlaus Altmann, Nathan Ilten, Lars Petersen, Hendrik Süß, Robert Vollmert --tIntroduction to equivariant cohomology in algebraic geometry /rDave Anderson --tRecent developments and open problems in linear series /rThomas Bauer, Cristiano Bocci, Susan Cooper, Sandra Di Rocco, Marcin Dumnicki, Brian Harbourne, Anders Lindquist, Hans Z. Munthe-Kaas, Alex Küronya, Rick Miranda, Joaquim Roé, Henry K. Schenck, Tomasz Szemberg, Zach Teitler --tModuli of map germs, Thom polynomials and the Green–Griffiths conjecture /rGergely Bérczi --tThe Minimal Model Program revisited /rPaolo Cascini, Vladimir Lazić --tInvariants of hypersurfaces and logarithmic differential forms /rSławomir Cynk, Sławomir Rams --tPrym varieties and their moduli /rGavril Farkas --tOn generalized Wrońskians /rLetterio Gatto, Inna Scherbak --tLines crossing a tetrahedron and the Bloch group /rKevin Hutchinson, Masha Vlasenko --tOn complex and symplectic toric stacks /rAndreas Hochenegger, Frederik Witt --tDeformation along subsheaves, II /rClemens Jörder, Stefan Kebekus --tSome degenerations of $G_2$ and Calabi–Yau varieties /rMichał Kapustka --tNotes on Kebekus’ lectures on differential forms on singular spaces /rMateusz Michałek --tLecture notes on K3 and Enriques surfaces Notes by Sławomir Rams /rShigeru Mukai --tIMPANGA lecture notes on log canonical thresholds Notes by Tomasz Szemberg /rMircea Mustaţă --tOn Schur function expansions of Thom polynomials /rÖzer Öztürk, Piotr Pragacz --tA note on the kernel of the norm map /rMarek Szyjewski --tSeshadri and packing constants /rHalszka Tutaj-Gasińska.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Będlewo. The following spectrum of topics is covered:
K3 surfaces and Enriques surfaces;
Prym varieties and their moduli;
invariants of singularities in birational geometry;
differential forms on singular spaces;
Minimal Model Program;
linear systems;
toric varieties;
Seshadri and packing constants;
equivariant cohomology;
Thom polynomials;
arithmetic questions.
The main purpose of the volume is to give comprehensive introductions to the above topics through texts starting from an elementary level and ending with the discussion of current research. The first four topics are represented by the notes from the minicourses held during the conference. In the articles the reader will find classical results and methods, as well as modern ones. The book is addressed to researchers and graduate students in algebraic geometry, singularity theory and algebraic topology. Most of the material exposed in the volume has not yet appeared in book form.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aNumber theory2msc07aSeveral complex variables and analytic spaces2msc07aDifferential geometry2msc1 aPragacz, Piotr,eeditor.40uhttps://doi.org/10.4171/114423cover imageuhttps://www.ems-ph.org/img/books/pragacz_mini.jpg03782nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084002200202245009600224260008200320300003400402336002600436337002600462338003600488347002400524490005400548505190000602506006602502520050402568650003003072650003603102650002803138650002303166700002703189700002903216700002903245856003203274856006603306155-121009CH-001817-320121009234500.0a fot ||| 0|cr nn mmmmamaa121009e20121019sz fot ||| 0|eng d a978303719619970a10.4171/1192doi ach0018173 7aPBMS2bicssc 7aPBRD2bicssc a14-xxa11-xx2msc10aGeometry and Arithmetich[electronic resource] /cCarel Faber, Gavril Farkas, Robin de Jong3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (383 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tNef divisors on $\M_{0,n}$ from GIT /rValery Alexeev, David Swinarski --tInoue type manifolds and Inoue surfaces: a connected component of the moduli space of surfaces with $K^2=7, p_g = 0$ /rIngrid Bauer, Fabrizio Catanese --tNon-rationality of the symmetric sextic Fano threefold /rArnaud Beauville --tBrill–Noether loci of stable rank-two vector bundles on a general curve /rCiro Ciliberto, Flaminio Flamini --tMordell–Weil groups and Zariski triples /rJosé Ignacio Cogolludo-Agustín, Remke Kloosterman --tApproximate computations with modular curves /rJean-Marc Couveignes, Bas Edixhoven --tA remark on a conjecture of Paranjape and Ramanan /rFriedrich Eusen, Frank-Olaf Schreyer --tOn extensions of the Torelli map /rAngela Gibney --tThe classes of singular moduli in the generalized Jacobian /rBenedict H. Gross --tThe Eisenstein motive for the cohomology of GSp2(ℤ) /rGünter Harder --tCohomology of the moduli stack of coherent sheaves on a curve /rJochen Heinloth --tNew methods for bounding the number of points on curves over finite fields /rEverett W. Howe, Kristin E. Lauter --tWildly ramified actions and surfaces of general type arising from Artin–Schreier curves /rHiroyuki Ito, Stefan Schröer --tA note on a supersingular K3 surface in characteristic 2 /rToshiyuki Katsura, Shigeyuki Kondō --tThe intuitive definition of Du Bois singularities /rSándor J. Kovács --tBundles of rank 2 with small Clifford index on algebraic curves /rH. Lange, Peter E. Newstead --tDescendents on local curves: Stationary theory /rRahul Pandharipande, A. Pixton --tA remark on Getzler’s semi-classical approximation /rDan Petersen --tOn the modular curve X0(23) /rRené Schoof --tDegree 4 unramified cohomology with finite coefficients and torsion codimension 3 cycles /rClaire Voisin --tPoincaré duality and unimodularity /rYuri G. Zarhin.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume contains 21 articles written by leading experts in the fields of algebraic and arithmetic geometry. The treated topics range over a variety of themes, including moduli spaces of curves and abelian varieties, algebraic cycles, vector bundles and coherent sheaves, curves over finite fields, and algebraic surfaces, among others.
The volume originates from the conference “Geometry and Arithmetic”, which was held on the island of Schiermonnikoog in The Netherlands in September 2010.07aAnalytic geometry2bicssc07aAlgebraic number theory2bicssc07aAlgebraic geometry2msc07aNumber theory2msc1 aFaber, Carel,eeditor.1 aFarkas, Gavril,eeditor.1 ade Jong, Robin,eeditor.40uhttps://doi.org/10.4171/119423cover imageuhttps://www.ems-ph.org/img/books/farkas_mini.jpg01965nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003000206245007900236260008200315300003400397336002600431337002600457338003600483347002400519490003900543506006600582520075000648650002101398650001801419650004201437700002701479856003201506856006501538158-121002CH-001817-320121002234501.0a fot ||| 0|cr nn mmmmamaa121002e20121010sz fot ||| 0|eng d a978303719612070a10.4171/1122doi ach0018173 7aPBM2bicssc a51-xxa20-xx2msc1 aNowak, Piotr W.,eauthor.10aLarge Scale Geometryh[electronic resource] /cPiotr W. Nowak, Guoliang Yu3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (203 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aLarge scale geometry is the study of geometric objects viewed from a great distance.
The idea of large scale geometry can be traced back to Mostow’s work on rigidity and the work of Švarc, Milnor and Wolf on growth of groups. In the last decades, large scale geometry has found important applications in group theory, topology, geometry, higher index theory, computer science, and large data analysis.
This book provides a friendly approach to the basic theory of this exciting and fast growing subject and offers a glimpse of its applications to topology, geometry, and higher index theory.
The authors have made a conscientious effort to make the book accessible to advanced undergraduate students, graduate students, and non-experts.07aGeometry2bicssc07aGeometry2msc07aGroup theory and generalizations2msc1 aYu, Guoliang,eauthor.40uhttps://doi.org/10.4171/112423cover imageuhttps://www.ems-ph.org/img/books/nowak_mini.jpg02891nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002700199245015200226260008200378300003400460336002600494337002600520338003600546347002400582490004000606506006600646520163300712650003102345650002802376700003602404856003202440856006902472159-121029CH-001817-320121029234500.0a fot ||| 0|cr nn mmmmamaa121029e20121029sz fot ||| 0|eng d a978303719616870a10.4171/1162doi ach0018173 7aPBS2bicssc a65-xx2msc1 aNovak, Erich,eauthor.10aTractability of Multivariate Problemsh[electronic resource] :bVolume III: Standard Information for Operators /cErich Novak, Henryk Woźniakowski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (604 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v181 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis three-volume set is a comprehensive study of the tractability of multivariate problems. Volume I covers algorithms using linear information consisting of arbitrary continuous linear functionals. Volumes II and III are devoted to algorithms using standard information consisting of function values. Approximation of linear and selected nonlinear functionals is dealt with in volume II, and linear and selected nonlinear operators are studied in volume III. To a large extent, volume III can be read independently of volumes I and II.
The most important example studied in volume III is the approximation of multivariate functions. It turns out that many other linear and some nonlinear problems are closely related to the approximation of multivariate functions. While the lower bounds obtained in volume I for the class of linear information also yield lower bounds for the standard class of function values, new techniques for upper bounds are presented in volume III. One of the main issues here is to verify when the power of standard information is nearly the same as the power of linear information. In particular, for the approximation problem defined over Hilbert spaces, the power of standard and linear information is the same in the randomized and average case (with Gaussian measures) settings, whereas in the worst case setting this is not true.
The book is of interest to researchers working in computational mathematics, especially in approximation of high-dimensiona problems. It may be well suited for graduate courses and seminars. The text contains 58 open problems for future research in tractability.07aNumerical analysis2bicssc07aNumerical analysis2msc1 aWoźniakowski, Henryk,eauthor.40uhttps://doi.org/10.4171/116423cover imageuhttps://www.ems-ph.org/img/books/novak_III_mini.jpg04041nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245011900221260008200340300003400422336002600456337002600482338003600508347002400544490008300568505132100651506006601972520124402038650003103282650002803313650005503341650003803396650004803434700003303482700002703515856003203542856006903574160-121218CH-001817-320121218234500.0a fot ||| 0|cr nn mmmmamaa121218e20121218sz fot ||| 0|eng d a978303719618270a10.4171/1182doi ach0018173 7aPBMW2bicssc a14-xxa32-xxa57-xxa58-xx2msc10aSingularities in Geometry and Topologyh[electronic resource] :bStrasbourg 2009 /cVincent Blanlœil, Toru Ohmoto3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (370 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2000tOptical caustics and their modelling as singularities /rAlain Joets --tOn local equisingularity /rHelmut A. Hamm --tJet schemes of homogeneous hypersurfaces /rShihoko Ishii, Akiyoshi Sannai, Kei-ichi Watanabe --tSingularities in relativity /rTatsuhiko Koike --tOn the universal degenerating family of Riemann surfaces /rYukio Matsumoto --tAlgebraic local cohomologies and local $b$-functions attached to semiquasihomogeneous singularities with $L(f)=2$ /rYayoi Nakamura, Shinichi Tajima --tA note on the Chern–Schwartz–MacPherson class /rToru Ohmoto --tOn mixed projective curves /rMutsuo Oka --tInvariants of splice quotient singularities /rTomohiro Okuma --tA note on the toric duality between the cyclic quotient surface singularities $A_{n,q}$ and $A_{n,n - q}$ /rOswald Riemenschneider --tNearby cycles and characteristic classes of singular spaces /rJörg Schürmann --tResidues of singular holomorphic distributions /rTatsuo Suwa --tTwo birational invariants in statistical learning theory /rSumio Watanabe --tFrobenius morphisms of noncommutative blowups /rTakehiko Yasuda --tBivariant motivic Hirzebruch class and a zeta function of motivic Hirzebruch class /rShoji Yokura --tMinimality of hyperplane arrangements and basis of local system cohomology /rMasahiko Yoshinaga.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume arises from 5th Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers working on singularities in algebraic geometry, analytic geometry and topology, mainly from France and Japan. Besides, it also organized a special session, JSPS Forum on Singularities and Applications, which was aimed to introduce some recent applications of singularity theory to physics and statistics.
This book comprises research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented in the Forum are also added. Topics covered include splice surface singularities, b-functions, equisingularity, degenerating families of Riemann surfaces, hyperplane arrangements, mixed singularities, jet schemes, noncommutative blow-ups, characteristic classes of singular spaces, and applications to geometric optics, cosmology and learning theory.
Graduate students who wish to learn about various approaches to singularities, as well as experts in the field and researchers in other areas of mathematics and science will find the contributions to this volume a rich source for further study and research.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aSeveral complex variables and analytic spaces2msc07aManifolds and cell complexes2msc07aGlobal analysis, analysis on manifolds2msc1 aBlanlœil, Vincent,eeditor.1 aOhmoto, Toru,eeditor.40uhttps://doi.org/10.4171/118423cover imageuhttps://www.ems-ph.org/img/books/blanloeil_mini.jpg03690nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185245010100214260008200315300003400397336002600431337002600457338003600483347002400519490005400543505096900597506006601566520141401632650003103046650002803077650004003105650004003145700003103185856003203216856006803248161-130107CH-001817-320130107234500.0a fot ||| 0|cr nn mmmmamaa130107e20130107sz fot ||| 0|eng d a978303719615170a10.4171/1152doi ach0018173 7aPBMW2bicssc a14-xxa13-xxa16-xx2msc10aDerived Categories in Algebraic Geometryh[electronic resource] :bTokyo 2011 /cYujiro Kawamata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (354 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tCategorical representability and intermediate Jacobians of Fano threefolds /rMarcello Bernardara, Michele Bolognesi --tFourier–Mukai functors: a survey /rAlberto Canonaco, Paolo Stellari --tFlops and about: a guide /rSabin Cautis --tA note on derived categories of Fermat varieties /rAkira Ishii, Kazushi Ueda --tHomology of infinite loop spaces /rDmitry Kaledin --tCluster algebras and derived categories /rBernhard Keller --tSome derived equivalences between noncommutative schemes and algebras /rIzuru Mori --tLagrangian-invariant sheaves and functors for abelian varieties /rAlexander Polishchuk --tGeneric vanishing filtrations and perverse objects in derived categories of coherent sheaves /rMihnea Popa --tThe fundamental group is not a derived invariant /rChristian Schnell --tIntroduction and open problems of Donaldson–Thomas theory /rYukinobu Toda --tNotes on formal deformations of abelian categories /rMichel Van den Bergh.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics.
The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories.
This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aCommutative rings and algebras2msc07aAssociative rings and algebras2msc1 aKawamata, Yujiro,eeditor.40uhttps://doi.org/10.4171/115423cover imageuhttps://www.ems-ph.org/img/books/kawamata_mini.jpg02351nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003000199245011100229260008200340300003400422336002600456337002600482338003600508347002400544490005600568506006600624520115700690650003501847650003101882856003201913856006801945162-130121CH-001817-320130121234500.0a fot ||| 0|cr nn mmmmamaa130121e20130124sz fot ||| 0|eng d a978303719613770a10.4171/1132doi ach0018173 7aPBX2bicssc a01-xx2msc1 aRoquette, Peter,eauthor.10aContributions to the History of Number Theory in the 20th Centuryh[electronic resource] /cPeter Roquette3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (289 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 20th century was a time of great upheaval and great progress, mathematics not excluded. In order to get the overall picture of trends, developments and results it is illuminating to look at their manifestations
locally, in the personal life and work of people living at the time. The university archives of Göttingen harbor a wealth of papers, letters and manuscripts
from several generations of mathematicians – documents which tell us the
story of the historic developments from a local point of view.
The present
book offers a number of essays based on documents from Göttingen and
elsewhere – essays which are not yet contained in the author’s Collected Works. These little pieces, independent from each other, are meant as
contributions to the imposing mosaic of history of number theory. They are
written for mathematicians but with no special background requirements.
Involved are the names of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grün, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether,
Abraham Robinson, Ernst Steinitz, Hermann Weyl and others.07aHistory of mathematics2bicssc07aHistory and biography2msc40uhttps://doi.org/10.4171/113423cover imageuhttps://www.ems-ph.org/img/books/roquette_mini.jpg03047nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184245010400206260008200310300003400392336002600426337002600452338003600478347002400514490005000538505080200588506006601390520096501456650003502421650003102456650002402487700003402511700003002545856003202575856006602607163-130412CH-001817-320130412234500.0a fot ||| 0|cr nn mmmmamaa130412e20130411sz fot ||| 0|eng d a978303719621270a10.4171/1212doi ach0018173 7aPBX2bicssc a01-xxa81-xx2msc10aErwin Schrödinger – 50 Years Afterh[electronic resource] /cWolfgang L. Reiter, Jakob Yngvason3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (195 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)00tErwin Schrödinger – personal reminiscences /rWalter Thirring --tSchrödinger and the genesis of wave mechanics /rJürgen Renn --tDo we understand quantum mechanics – finally? /rJürg M. Fröhlich, Baptiste Schubnel --tSchrödinger’s cat and her laboratory cousins /rAnthony J. Leggett --tDigital and open system quantum simulation with trapped ions /rMarkus Müller, Peter Zoller --tOptomechanical Schrödinger cats – a case for space /rRainer Kaltenbaek, Markus Aspelmeyer --tA quantum discontinuity: The Schrödinger–Bohr dialogue /rHelge Kragh --tThe debate between Hendrik A. Lorentz and Schrödinger on wave mechanics /rAnne J. Kox --tA few reasons why Louis de Broglie discovered matter waves and yet did not discover Schrödinger’s equation /rOlivier Darrigol.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aErwin Schrödinger (1887–1961) was an Austrian physicist famous for the equation named after him and which earned him the Nobel Prize in 1933. This book contains lectures presented at the international symposium Erwin Schrödinger – 50 Years After held at the Erwin Schrödinger International Institute for Mathematical Physics in January 2011 to commemorate the 50th anniversary of Schrödinger’s death.
The text covers a broad spectrum of topics ranging from personal reminiscences to foundational questions of quantum mechanics and historical accounts of Schrödinger’s work. Besides the lectures presented at the symposium the volume also contains articles specially written for this occasion.
The contributions give an overview of Schrödinger’s legacy to the sciences from the standpoint of some of present day’s leading scholars in the field.
The book addresses students and researchers in mathematics, physics and the history of science.07aHistory of mathematics2bicssc07aHistory and biography2msc07aQuantum theory2msc1 aReiter, Wolfgang L.,eeditor.1 aYngvason, Jakob,eeditor.40uhttps://doi.org/10.4171/121423cover imageuhttps://www.ems-ph.org/img/books/reiter_mini.jpg02914nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002900207245012500236260008200361300003400443336002600477337002600503338003600529347002400565490003900589506006600628520160800694650002902302650004102331650005502372700002802427856003202455856006502487164-130506CH-001817-320130506234500.0a fot ||| 0|cr nn mmmmamaa130506e20130506sz fot ||| 0|eng d a978303719611370a10.4171/1112doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc1 aBruna, Joaquim,eauthor.10aComplex Analysish[electronic resource] :bTranslated from the Catalan by Ignacio Monreal /cJoaquim Bruna, Julià Cufí3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (576 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe theory of functions of a complex variable is a central theme in mathematical
analysis that has links to several branches of mathematics. Understanding
the basics of the theory is necessary for anyone who wants to have a general
mathematical training or for anyone who wants to use mathematics in applied
sciences or technology.
The book presents the basic theory of analytic functions of a complex variable
and their points of contact with other parts of mathematical analysis. This results
in some new approaches to a number of topics when compared to the current
literature on the subject.
Some issues covered are: a real version of the Cauchy–Goursat theorem, theorems
of vector analysis with weak regularity assumptions, an approach to the
concept of holomorphic functions of real variables, Green’s formula with multiplicities,
Cauchy’s theorem for locally exact forms, a study in parallel of Poisson’s
equation and the inhomogeneous Cauchy–Riemann equations, the relationship
between Green’s function and conformal mapping, the connection between
the solution of Poisson’s equation and zeros of holomorphic functions, and the
Whittaker–Shannon theorem of information theory.
The text can be used as a manual for complex variable courses of various levels
and as a reference book. The only prerequisites for reading it is a working knowledge
of the topology of the plane and the differential calculus for functions of
several real variables. A detailed treatment of harmonic functions also makes the
book useful as an introduction to potential theory.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aCufí, Julià,eauthor.40uhttps://doi.org/10.4171/111423cover imageuhttps://www.ems-ph.org/img/books/bruna_mini.jpg02987nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003100206245018000237260008200417300003400499336002600533337002600559338003600585347002400621490004000645506006600685520152800751650004502279650004102324650004002365700003602405700002702441700003302468856003202501856006802533165-130524CH-001817-320130524234500.0a fot ||| 0|cr nn mmmmamaa130524e20130529sz fot ||| 0|eng d a978303719622970a10.4171/1222doi ach0018173 7aPBK2bicssc a30-xxa35-xx2msc1 aBojarski, Bogdan,eauthor.10aInfinitesimal Geometry of Quasiconformal and Bi-Lipschitz Mappings in the Planeh[electronic resource] /cBogdan Bojarski, Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (214 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v191 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is intended for researchers interested in new aspects of local
behavior of plane mappings and their applications. The presentation is
self-contained, but the reader is assumed to know basic complex and real
analysis.
The study of the local and boundary behavior of quasiconformal and bi-Lipschitz mappings in the plane forms the core of the book. The concept
of the infinitesimal space is used to investigate the behavior of a mapping
at points without differentiability. This concept, based on compactness
properties, is applied to regularity problems of quasiconformal mappings
and quasiconformal curves, boundary behavior, weak and asymptotic
conformality, local winding properties, variation of quasiconformal
mappings, and criteria of univalence. Quasiconformal and bi-Lipschitz
mappings are instrumental for understanding elasticity, control theory
and tomography and the book also offers a new look at the classical
areas such as the boundary regularity of a conformal map. Complicated
local behavior is illustrated by many examples.
The text offers a detailed development of the background for graduate
students and researchers. Starting with the classical methods to study
quasiconformal mappings, this treatment advances to the concept of
the infinitesimal space and then relates it to other regularity properties
of mappings in Part II. The new unexpected connections between quasiconformal
and bi-Lipschitz mappings are treated in Part III. There is an
extensive bibliography.07aCalculus & mathematical analysis2bicssc07aFunctions of a complex variable2msc07aPartial differential equations2msc1 aGutlyanskii, Vladimir,eauthor.1 aMartio, Olli,eauthor.1 aRyazanov, Vladimir,eauthor.40uhttps://doi.org/10.4171/122423cover imageuhttps://www.ems-ph.org/img/books/bojarski_mini.jpg02382nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100002800214245010100242260008200343300003400425336002600459337002600485338003600511347002400547490004000571506006600611520111500677650003201792650002901824650004001853650002601893856003201919856006901951166-130529CH-001817-320130529234500.0a fot ||| 0|cr nn mmmmamaa130529e20130529sz fot ||| 0|eng d a978303719623670a10.4171/1232doi ach0018173 7aPBKG2bicssc a46-xxa35-xxa42-xx2msc1 aTriebel, Hans,eauthor.10aLocal Function Spaces, Heat and Navier–Stokes Equationsh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (241 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v201 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn this book a new approach is presented to exhibit relations between
Sobolev spaces, Besov spaces, and Hölder–Zygmund spaces on the one hand
and Morrey–Campanato spaces on the other. Morrey–Campanato spaces
extend the notion of functions of bounded mean oscillation. These spaces
play an important role in the theory of linear and nonlinear PDEs.
Chapters 1–3 deal with local smoothness spaces in Euclidean n-space based
on the Morrey–Campanato refinement of the Lebesgue spaces. The presented
approach relies on wavelet decompositions. This is applied in Chapter 4
to Gagliardo–Nirenberg inequalities. Chapter 5 deals with linear and nonlinear
heat equations in global and local function spaces. The obtained assertions
about function spaces and nonlinear heat equations are used in Chapter 6 to
study Navier–Stokes equations.
The book is addressed to graduate students and mathematicians having a
working knowledge of basic elements of (global) function spaces, and who
are interested in applications to nonlinear PDEs with heat and Navier–Stokes
equations as prototypes.07aFunctional analysis2bicssc07aFunctional analysis2msc07aPartial differential equations2msc07aFourier analysis2msc40uhttps://doi.org/10.4171/123423cover imageuhttps://www.ems-ph.org/img/books/triebel20_mini.jpg02640nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002700213245012300240260008200363300003400445336002600479337002600505338003600531347002400567490004000591506006600631520128300697650004501980650004602025650004102071650002802112700003002140856003202170856006402202167-130808CH-001817-320130808234500.0a fot ||| 0|cr nn mmmmamaa130808e20130807sz fot ||| 0|eng d a978303719624370a10.4171/1242doi ach0018173 7aPBK2bicssc a37-xxa34-xxa65-xx2msc1 aNipp, Kaspar,eauthor.10aInvariant Manifolds in Discrete and Continuous Dynamical Systemsh[electronic resource] /cKaspar Nipp, Daniel Stoffer3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (225 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v211 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn this book dynamical systems are investigated from a geometric
viewpoint. Admitting an invariant manifold is a strong geometric property
of a dynamical system. This text presents rigorous results on invariant
manifolds and gives examples of possible applications.
In the first part discrete dynamical systems in Banach spaces are
considered. Results on the existence and smoothness of attractive and
repulsive invariant manifolds are derived. In addition, perturbations
and approximations of the manifolds and the foliation of the adjacent
space are treated. In the second part analogous results for continuous
dynamical systems in finite dimensions are established. In the third part
the theory developed is applied to problems in numerical analysis
and to singularly perturbed systems of ordinary differential equations.
The mathematical approach is based on the so-called graph transform,
already used by Hadamard in 1901. The aim is to establish invariant
manifold results in a simple setting providing quantitative estimates.
The book is targeted at researchers in the field of dynamical systems
interested in precise theorems easy to apply. The application part
might also serve as an underlying text for a student seminar in
mathematics.07aCalculus & mathematical analysis2bicssc07aDynamical systems and ergodic theory2msc07aOrdinary differential equations2msc07aNumerical analysis2msc1 aStoffer, Daniel,eauthor.40uhttps://doi.org/10.4171/124423cover imageuhttps://www.ems-ph.org/img/books/nipp_mini.jpg02917nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168084003600183100003400219245016900253260008200422300003500504336002600539337002600565338003600591347002400627490005600651506006600707520138400773650002402157650001702181650002302198650004302221650004202264700003402306700003402340700003702374856003202411856006402443168-131118CH-001817-320131118234500.0a fot ||| 0|cr nn mmmmamaa131118e20131115sz fot ||| 0|eng d a978303719626770a10.4171/1262doi ach0018173 7aPB2bicssc a00-xxa05-xxa17-xxa20-xx2msc1 aBuekenhout, Francis,eauthor.10aJacques Tits, Œuvres – Collected Works Volumes I–IVh[electronic resource] /cFrancis Buekenhout, Bernhard Mühlherr, Jean-Pierre Tignol, Hendrik van Maldeghem3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (3963 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aJacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize
(jointly with John Thompson) in 2008. The impact of his contributions
in algebra, group theory and geometry made over a span of more than
five decades is incalculable. Many fundamental developments in several
fields of mathematics have their origin in ideas of Tits. A number of
Tits’ papers mark the starting point of completely new directions of
research. Outstanding examples are papers on quadratic forms, on
Kac–Moody groups and on what subsequently became known as the
Tits-alternative.
These volumes contain an almost complete collection of Tits’
mathematical writings. They include, in particular, a number of
published and unpublished manuscripts which have not been easily
accessible until now. This collection of Tits’ contributions in one
place makes the evolution of his mathematical thinking visible. The
development of his theory of buildings and BN-pairs and its bearing
on the theory of algebraic groups, for example, reveal a fascinating
story. Along with Tits’ mathematical writings, these volumes contain
biographical data, survey articles on aspects of Tits’ work and
comments by the editors on the content of some of his papers.
With the publication of these volumes, a major piece of 20th century
mathematics is being made available to a wider audience.07aMathematics2bicssc07aGeneral2msc07aCombinatorics2msc07aNonassociative rings and algebras2msc07aGroup theory and generalizations2msc1 aMühlherr, Bernhard,eauthor.1 aTignol, Jean-Pierre,eauthor.1 avan Maldeghem, Hendrik,eauthor.40uhttps://doi.org/10.4171/126423cover imageuhttps://www.ems-ph.org/img/books/tits_mini.jpg02308nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003400214245009500248260008200343300003400425336002600459337002600485338003600511347002400547490005100571506006600622520097700688650004701665650003101712650005501743650004801798856003201846856006801878169-131031CH-001817-320131031234500.0a fot ||| 0|cr nn mmmmamaa131031e20131213sz fot ||| 0|eng d a978303719627470a10.4171/1272doi ach0018173 7aPBMP2bicssc a53-xxa32-xxa58-xx2msc1 aLabourie, François,eauthor.10aLectures on Representations of Surface Groupsh[electronic resource] /cFrançois Labourie3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (145 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe subject of these notes is the character variety of representations of a surface group in a Lie group. We emphasize the various points of view (combinatorial, differential, algebraic) and are interested in the description of its smooth points, symplectic structure, volume and connected components. We also show how a three manifold bounded by the surface leaves a trace in this character variety.
These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, we do not
insist in the details of the differential geometric constructions and refer to classical textbooks, while in the more advanced chapters proofs occasionally are
provided only for special cases where they convey the flavor of the general arguments. These notes could also be used by researchers entering this fast
expanding field as motivation for further studies proposed in a concluding paragraph of every chapter.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aSeveral complex variables and analytic spaces2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/127423cover imageuhttps://www.ems-ph.org/img/books/labourie_mini.jpg06591nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001400168084001500182245020000197260008200397300003400479336002600513337002600539338003600565347002400601505379600625506006604421520136304487650003605850650001705886700003005903700003305933700003305966700003505999700003106034700003206065856003206097856006406129170-131114CH-001817-320131114234501.0a fot 1|| 0|cr nn mmmmamaa131114e20140103sz fot 1|| 0|eng d a978303719620570a10.4171/1202doi ach0018173 7aP2bicssc a00-xx2msc10aEuropean Congress of Mathematics Kraków, 2 – 7 July, 2012h[electronic resource] /cRafał Latała, Andrzej Ruciński, Paweł Strzelecki, Jacek Świątkowski, Dariusz Wrzosek, Piotr Zakrzewski3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (824 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tSome mathematical aspects of water waves /rAdrian Constantin --tContinuous dissipative Euler flows and a conjecture of Onsager /rCamillo De Lellis, László Székelyhidi Jr. --tPersistent Homology: Theory and Practice /rHerbert Edelsbrunner, Dmitriy Morozov --tIn a Search for a Structure, Part 1: On Entropy /rMisha Gromov --tClassification of Algebraic Varieties /rChristopher D. Hacon --tRepresentations of affine Kac–Moody groups over local and global fields: a survey of some recent results /rAlexander Braverman, David Kazhdan --tEmergence of the Abrikosov lattice in several models with two dimensional Coulomb interaction /rSylvia Serfaty --tDependent Classes E72 /rSaharon Shelah --tChaining and the Geometry of Stochastic Processes /rMichel Talagrand --tDuflo isomorphism, the Kashiwara–Vergne conjecture and Drinfeld associators /rAnton Alekseev --tCoagulation with limited aggregations /rJean Bertoin --tThe Cremona group in two variables /rSerge Cantat --tVariational models for image inpainting /rVicent Caselles --tKAM theory and its applications: from conservative to dissipative systems /rAlessandra Celletti --tLe programme de Langlands $p$-adique /rPierre Colmez --tMirror Symmetry and Fano Manifolds /rTom Coates, Alessio Corti, Sergey Galkin, Vasily Golyshev, Alexander Kasprzyk --tOn flat bundles in characteristic 0 and $p > 0$ /rHélène Esnault --tCombinatorial realisation of cycles and small covers /rAlexander A. Gaifullin --tRemarks on the global regularity for solutions to the incompressible Navier–Stokes equations /rIsabelle Gallagher --tWhy the empirical sciences need statistics so desperately /rOlle Häggström --tComputing the Schrodinger equation with no fear of commutators /rArieh Iserles --tDynamics of non-archimedean Polish groups /rAlexander S. Kechris --tCluster algebras and cluster monomials /rBernhard Keller --tWeak solutions to the complex Monge–Ampère equation /rSławomir Kołodziej --tReinforced random walk /rGady Kozma --tOn blow-up curves for semilinear wave equations /rFrank Merle --tCommuting higher rank ordinary differential operators /rAndrey Mironov --tStochastic calculus with respect to the fractional Brownian motion /rDavid Nualart --tSampling, Interpolation, Translates /rAlexander Olevskii --tMultidimensional periodic and almost-periodic spectral problems /rLeonid Parnovski --tEffective equations for quantum dynamics /rBenjamin Schlein --tCombinatorics of asymptotic representation theory /rPiotr Śniady --tOn scale-invariant solutions of the Navier–Stokes equations /rHao Jia, Vladimír Šverák --tRamsey-theoretic analysis of the conditional structure of weakly-null sequences /rStevo Todorčević --tUniqueness results for minimal surfaces and constant mean curvature surfaces in Riemannian manifolds /rSimon Brendle --tStability in geometric and functional inequalities /rAlessio Figalli --tClassification and rigidity for von Neumann algebras /rAdrian Ioana --tA nonlinear variational problem in relativistic quantum mechanics /rMathieu Lewin --tGrid Diagrams in Heegaard Floer Theory /rCiprian Manolescu --tRandom maps and continuum random 2-dimensional geometries /rGrégory Miermont --tApproximate (Abelian) groups /rTom Sanders --tShearing and mixing in parabolic flows /rCorinna Ulcigrai --tOptimal control theory and some applications to aerospace problems /rEmmanuel Trélat --tMathematics and geometric ornamentation in the medieval Islamic world /rJan P. Hogendijk --tSome mathematical aspects of the planet Earth /rJosé Francisco Rodrigues --tTuring's Mathematical Work /rP.D. Welch --tCounting Berg partitions via Sturmian words and substitution tilings /rArtur Siemaszko, Maciej P. Wojtkowski.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe European Congress of Mathematics, held every four years, has become a well-established major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004) and Amsterdam (2008), the Sixth European Congress of Mathematics (6ECM) took place in Kraków, Poland, July 2–7, 2012, with about 1000 participants from all over the world.
Ten plenary, thirty-three invited lectures and three special lectures formed the core of the program. As at all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: the Felix Klein Prize for a remarkable solution of an industrial problem, and – for the first time – the Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by twenty-four minisymposia with nearly 100 talks, spread over all areas of mathematics. Six panel discussions were organized, covering a variety of issues ranging from the financing of mathematical research to gender imbalance in mathematics.
These proceedings present extended versions of most of the invited talks which were delivered during the congress, providing a permanent record of the best what mathematics offers today.07aMathematics and science2bicssc07aGeneral2msc1 aLatała, Rafał,eeditor.1 aRuciński, Andrzej,eeditor.1 aStrzelecki, Paweł,eeditor.1 aŚwiątkowski, Jacek,eeditor.1 aWrzosek, Dariusz,eeditor.1 aZakrzewski, Piotr,eeditor.40uhttps://doi.org/10.4171/120423cover imageuhttps://www.ems-ph.org/img/books/6ECM_mini.gif02481nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245008000252260008200332300003400414336002600448337002600474338003600500347002400536490005100560506006600611520116500677650003401842650004001876650002301916650002801939650004301967856003202010856006502042172-140124CH-001817-320140124234500.0a fot ||| 0|cr nn mmmmamaa140124e20140118sz fot ||| 0|eng d a978303719630470a10.4171/1302doi ach0018173 7aPBFD2bicssc a13-xxa05-xxa14-xxa17-xx2msc1 aMarsh, Robert J.,eauthor.10aLecture Notes on Cluster Algebrash[electronic resource] /cRobert J. Marsh3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (121 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aCluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally
positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field, while giving a taste of the
wide connections between cluster algebras and other areas of mathematics.
The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in
order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included. The book ends with a
description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial
geometry.07aGroups & group theory2bicssc07aCommutative rings and algebras2msc07aCombinatorics2msc07aAlgebraic geometry2msc07aNonassociative rings and algebras2msc40uhttps://doi.org/10.4171/130423cover imageuhttps://www.ems-ph.org/img/books/marsh_mini.jpg02601nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003400200245015300234260008200387300003400469336002600503337002600529338003600555347002400591490005100615506006600666520126500732650003501997650004002032700003502072700003102107856003202138856006902170173-140123CH-001817-320140123234500.0a fot ||| 0|cr nn mmmmamaa140123e20140118sz fot ||| 0|eng d a978303719629870a10.4171/1292doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aGallagher, Isabelle,eauthor.10aFrom Newton to Boltzmann: Hard Spheres and Short-range Potentialsh[electronic resource] /cIsabelle Gallagher, Laure Saint-Raymond, Benjamin Texier3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (148 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe question addressed in this monograph is the relationship between the
time-reversible Newton dynamics for a system of particles interacting via
elastic collisions, and the irreversible Boltzmann dynamics which gives a
statistical description of the collision mechanism. Two types of elastic
collisions are considered: hard spheres, and compactly supported potentials..
Following the steps suggested by Lanford in 1974, we describe the transition
from Newton to Boltzmann by proving a rigorous convergence result in short
time, as the number of particles tends to infinity and their size simultaneously
goes to zero, in the Boltzmann-Grad scaling.
Boltzmann’s kinetic theory rests on the assumption that particle independence
is propagated by the dynamics. This assumption is central to the issue of
appearance of irreversibility. For finite numbers of particles, correlations are
generated by collisions. The convergence proof establishes that for initially
independent configurations, independence is statistically recovered in the
limit.
This book is intended for mathematicians working in the fields of partial
differential equations and mathematical physics, and is accessible to graduate
students with a background in analysis.07aDifferential equations2bicssc07aPartial differential equations2msc1 aSaint-Raymond, Laure,eauthor.1 aTexier, Benjamin,eauthor.40uhttps://doi.org/10.4171/129423cover imageuhttps://www.ems-ph.org/img/books/gallagher_mini.gif02538nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245012900200260008200329300003400411336002600445337002600471338003600497347002400533490005400557505076300611506006601374520046301440650002701903650004001930700003101970700003002001700003502031856003202066856006602098174-140106CH-001817-320140106234500.0a fot ||| 0|cr nn mmmmamaa140106e20140103sz fot ||| 0|eng d a978303719625070a10.4171/1252doi ach0018173 7aPBFL2bicssc a16-xx2msc10aAdvances in Representation Theory of Algebrash[electronic resource] /cDavid J. Benson, Henning Krause, Andrzej Skowroński3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (378 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tInfinite dimensional tilting theory /rLidia Angeleri Hügel --tA survey of modules of constant Jordan type and vector bundles on projective space /rDavid J. Benson --tOn representation-finite algebras and beyond /rKlaus Bongartz --tQuiver Hecke algebras and categorification /rJonathan Brundan --tOrdered exchange graphs /rThomas Brüstle, Dong Yang --tIntroduction to Donaldson–Thomas invariants /rSergey Mozgovoy --tCluster algebras and singular supports of perverse sheaves /rHiraku Nakajima --tRepresentations and cohomology of finite group schemes /rJulia Pevtsova --tSuperdecomposable pure-injective modules /rMike Prest --tExact model categories, approximation theory, and cohomology of quasi-coherent sheaves /rJan Šťovíček.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume presents a collection of articles devoted to representations
of algebras and related topics. Dististinguished experts in this field
presented their work at the International Conference on Representations
of Algebras which took place 2012 in Bielefeld. Many of the expository
surveys are included here. Researchers of representation theory
will find in this volume interesting and stimulating contributions to
the development of the subject.07aFields & rings2bicssc07aAssociative rings and algebras2msc1 aBenson, David J.,eeditor.1 aKrause, Henning,eeditor.1 aSkowroński, Andrzej,eeditor.40uhttps://doi.org/10.4171/125423cover imageuhttps://www.ems-ph.org/img/books/benson_mini.jpg02478nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003200214245011200246260008200358300003400440336002600474337002600500338003600526347002400562490006100586506006600647520109900713650003501812650004001847650004101887650004601928700003101974856003202005856006702037175-140303CH-001817-320140303234500.0a fot ||| 0|cr nn mmmmamaa140303e20140315sz fot ||| 0|eng d a978303719631170a10.4171/1312doi ach0018173 7aPBKJ2bicssc a35-xxa34-xxa37-xx2msc1 aGrébert, Benoît,eauthor.10aThe Defocusing NLS Equation and Its Normal Formh[electronic resource] /cBenoît Grébert, Thomas Kappeler3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (175 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrödinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium.
The book is not only intended for specialists working at the intersection of integrable PDEs and dynamical systems, but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion, each of its chapters and appendices can be read independently of each other.07aDifferential equations2bicssc07aPartial differential equations2msc07aOrdinary differential equations2msc07aDynamical systems and ergodic theory2msc1 aKappeler, Thomas,eauthor.40uhttps://doi.org/10.4171/131423cover imageuhttps://www.ems-ph.org/img/books/grebert_mini.jpg02959nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003600199245008000235260008200315300003400397336002600431337002600457338003600483347002400519490003900543506006600582520183000648650002102478650001802499856003202517856007202549176-140514CH-001817-320140514234500.0a fot ||| 0|cr nn mmmmamaa140514e20140510sz fot ||| 0|eng d a978303719638070a10.4171/1382doi ach0018173 7aPBM2bicssc a51-xx2msc1 aCasas-Alvero, Eduardo,eauthor.10aAnalytic Projective Geometryh[electronic resource] /cEduardo Casas-Alvero3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (636 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aProjective geometry is concerned with the properties of figures that are invariant by projecting and taking sections. It is considered one of the most beautiful parts of geometry and plays a central role because its specializations cover the whole of the affine, Euclidean and non-Euclidean geometries. The natural extension of projective geometry is projective algebraic geometry, a rich and active field of research. Regarding its applications, results and techniques of projective geometry are today intensively used in computer vision.
This book contains a comprehensive presentation of projective geometry, over the real and complex number fields, and its applications to affine and Euclidean geometries. It covers central topics such as linear varieties, cross ratio, duality, projective transformations, quadrics and their classifications – projective, affine and metric –, as well as the more advanced and less usual spaces of quadrics, rational normal curves, line complexes and the classifications of collineations, pencils of quadrics and correlations. Two appendices are devoted to the projective foundations of perspective and to the projective models of plane non-Euclidean geometries. The presentation uses modern language, is based on linear algebra and provides complete proofs. Exercises are proposed at the end of each chapter; many of them are beautiful classical results.
The material in this book is suitable for courses on projective geometry for undergraduate students, with a
working knowledge of a standard first course on linear algebra. The text is a valuable guide to graduate students and researchers working in areas using or related to projective geometry, such as algebraic geometry and computer vision, and to anyone wishing to gain an advanced view on geometry as a whole.07aGeometry2bicssc07aGeometry2msc40uhttps://doi.org/10.4171/138423cover imageuhttps://www.ems-ph.org/img/books/casas-alvero_mini.jpg03703nam a22004935a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001600183084002200199100003100221245025900252260008200511300003400593336002600627337002600653338003600679347002400715490007900739506006600818520180900884650002402693650003702717650003102754650001702785700003302802700003202835700002802867700002802895700003102923700003102954700002902985700003303014700003103047700003203078856003203110856006703142177-140429CH-001817-320140429234500.0a fot ||| 0|cr nn mmmmamaa140429e20140428sz fot ||| 0|eng d a978303719637370a10.4171/1372doi ach0018173 7aPB2bicssc 7aPBC2bicssc a01-xxa00-xx2msc1 aDeuflhard, Peter,eauthor.10aMATHEON – Mathematics for Key Technologiesh[electronic resource] /cPeter Deuflhard, Martin Grötschel, Dietmar Hömberg, Ulrich Horst, Jürg Kramer, Volker Mehrmann, Konrad Polthier, Frank Schmidt, Christof Schütte, Martin Skutella, Jürgen Sprekels3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (466 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series in Industrial and Applied Mathematics (ESIAM) ;x2523-5087 ;v11 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMathematics: intellectual endeavor, production factor, key technology, key to key technologies?
Mathematics is all of these! The last three of its facets have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, application-driven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies.
Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies.
This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of “showcases” are presented that illustrate a few success stories.07aMathematics2bicssc07aMathematical foundations2bicssc07aHistory and biography2msc07aGeneral2msc1 aGrötschel, Martin,eauthor.1 aHömberg, Dietmar,eauthor.1 aHorst, Ulrich,eauthor.1 aKramer, Jürg,eauthor.1 aMehrmann, Volker,eauthor.1 aPolthier, Konrad,eauthor.1 aSchmidt, Frank,eauthor.1 aSchütte, Christof,eauthor.1 aSkutella, Martin,eauthor.1 aSprekels, Jürgen,eauthor.40uhttps://doi.org/10.4171/137423cover imageuhttps://www.ems-ph.org/img/books/matheon_mini.jpg04822nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245009500207260008200302300003400384336002600418337002600444338003600470347002400506490008300530505171900613506006602332520179502398650002904193650004104222650005504263700003704318856003204355856007304387178-140530CH-001817-320140530234500.0a fot ||| 0|cr nn mmmmamaa140530e20140530sz fot ||| 0|eng d a978303719617570a10.4171/1172doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc10aHandbook of Teichmüller Theory, Volume IVh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (838 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1900tIntroduction to Teichmüller theory, old and new, IV /rAthanase Papadopoulos --tLocal and global aspects of Weil–Petersson geometry /rSumio Yamada --tSimple closed geodesics and the study of Teichmüller spaces /rHugo Parlier --tCurve complexes versus Tits buildings: structures and applications /rLizhen Ji --tExtremal length geometry /rHideki Miyachi --tCompactifications of Teichmüller spaces /rKen’ichi Ohshika --tArc geometry and algebra: foliations, moduli spaces, string topology and field theory /rRalph M. Kaufmann --tThe horoboundary and isometry group of Thurston’s Lipschitz metric /rCormac Walsh --tThe horofunction compactification of the Teichmüller metric /rLixin Liu, Weixu Su --tLipschitz algebras and compactifications of Teichmüller space /rHideki Miyachi --tOn the geodesic geometry of infinite-dimensional Teichmüller spaces /rZhong Li --tHolomorphic families of Riemann surfaces and monodromy /rHiroshige Shiga --tThe deformation of flat affine structures on the two-torus /rOliver Baues --tHigher Teichmüller spaces: from SL(2,$\mathbb{R}$) to other Lie groups /rMarc Burger, Alessandra Iozzi, Anna Wienhard --tThe theory of quasiconformal mappings in higher dimensions, I /rGaven J. Martin --tInfinite-dimensional Teichmüller spaces and modular groups /rKatsuhiko Matsuzaki --tTeichmüller spaces and holomorphic dynamics /rXavier Buff, Guizhen Cui, Lei Tan --tA survey of quantum Teichmüller space and Kashaev algebra /rRen Guo --tVariable Riemann surfaces /rOswald Teichmüller --tA commentary on Teichmüller’s paper Veränderliche Riemannsche Flächen /rAnnette A’Campo-Neuen, Norbert A’Campo, Lizhen Ji, Athanase Papadopoulos.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aTeichmüller theory is, since several decades, one of the most active research areas in
mathematics, with a very wide range of points of view, including Riemann surface theory,
hyperbolic geometry, low-dimensional topology, several complex variables, algebraic
geometry, arithmetic, partial differential equations, dynamical systems, representation
theory, symplectic geometry, geometric group theory, and mathematical physics.
The present book is the fourth volume in a Handbook of Teichmüller Theory project
that started as an attempt to present, in a most comprehensive and systematic way,
the various aspects of this theory with its relations to all the fields mentioned. The
handbook is addressed to researchers as well as graduate students.
The present volume is divided into five parts:
Part A: The metric and the analytic theory.
Part B: Representation theory and generalized structures.
Part C: Dynamics.
Part D: The quantum theory.
Part E: Sources.
Parts A, B and D are sequels of parts on the same theme in previous volumes. Part E has
a new character in the series; it contains the translation together with a commentary of
an important paper by Teichmüller which is almost unknown even to specialists. Making
clear the original ideas of and motivations for a theory is crucial for many reasons, and
rendering available this translation together with the commentary that follows will give
a new impulse and will contribute in putting the theory into a broader perspective.
The various volumes in this collection are written by experts who have a broad view on
the subject. In general, the chapters have an expository character, which is the original
purpose of this handbook, while some of them contain new and important results.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/117423cover imageuhttps://www.ems-ph.org/img/books/9783037191170_mini.gif02020nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003000207245010400237260008200341300003400423336002600457337002600483338003600509347002400545490005100569506006600620520076400686650003501450650004801485650004001533856003201573856006501605180-140704CH-001817-320140704234500.0a fot ||| 0|cr nn mmmmamaa140704e20140701sz fot ||| 0|eng d a978303719634270a10.4171/1342doi ach0018173 7aPBKJ2bicssc a58-xxa35-xx2msc1 aHebey, Emmanuel,eauthor.10aCompactness and Stability for Nonlinear Elliptic Equationsh[electronic resource] /cEmmanuel Hebey3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (301 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed
Riemannian manifolds are investigated, a field presently undergoing great development. The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrödinger equation and to its critical formulation.
Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers.07aDifferential equations2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc40uhttps://doi.org/10.4171/134423cover imageuhttps://www.ems-ph.org/img/books/hebey_mini.gif02856nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003100199245009000230260008200320300003400402336002600436337002600462338003600488347002400524490003900548506006600587520167600653650003702329650005302366856003202419856006702451181-140707CH-001817-320140707234500.0a fot ||| 0|cr nn mmmmamaa140707e20140707sz fot ||| 0|eng d a978303719633570a10.4171/1332doi ach0018173 7aPBT2bicssc a60-xx2msc1 aBaudoin, Fabrice,eauthor.10aDiffusion Processes and Stochastic Calculush[electronic resource] /cFabrice Baudoin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (287 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe main purpose of the book is to present at a graduate level and in a self-contained
way the most important aspects of the theory of continuous stochastic
processes in continuous time and to introduce to some of its ramifications like
the theory of semigroups, the Malliavin calculus and the Lyons’ rough paths. It is
intended for students, or even researchers, who wish to learn the basics in a concise
but complete and rigorous manner. Several exercises are distributed throughout
the text to test the understanding of the reader and each chapter ends up
with bibliographic comments aimed to those interested in exploring
further the materials.
The stochastic calculus has been developed in the 1950s and the range of
its applications is huge and still growing today. Besides being a fundamental
component of modern probability theory, domains of applications include but are
not limited to: mathematical finance, biology, physics, and engineering sciences.
The first part of the text is devoted the general theory of stochastic processes,
we focus on existence and regularity results for processes and on the theory of
martingales. This allows to quickly introduce the Brownian motion and to study
its most fundamental properties. The second part deals with the study of Markov
processes, in particular diffusions. Our goal is to stress the connections between
these processes and the theory of evolution semigroups. The third part deals
with stochastic integrals, stochastic differential equations and Malliavin calculus.
Finally, in the fourth and final part we present an introduction to the very new
theory of rough paths by Terry Lyons.07aProbability & statistics2bicssc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/133423cover imageuhttps://www.ems-ph.org/img/books/baudoin_mini.jpg06168nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245012000221260008200341300003400423336002600457337002600483338003600509347002400545490005400569505267500623506006603298520200503364650002705369650003805396650005505434650004005489650002805529700003205557700003705589700003205626856003205658856006805690182-140804CH-001817-320140804234500.0a fot ||| 0|cr nn mmmmamaa140804e20140901sz fot ||| 0|eng d a978303719649670a10.4171/1492doi ach0018173 7aPBFL2bicssc a12-xxa06-xxa13-xxa14-xx2msc10aValuation Theory in Interactionh[electronic resource] /cAntonio Campillo, Franz-Viktor Kuhlmann, Bernard Teissier3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (670 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tA study of irreducible polynomials over henselian valued fields via distinguished pairs /rKamal Aghigh, Anuj Bishnoi, Sudesh K. Khanduja, Sanjeev Kumar --tOn fields of totally $\mathfrak{S}$-adic numbers. With an appendix by Florian Pop /rLior Bary-Soroker, Arno Fehm --tInfinite towers of Artin-Schreier defect extensions of rational function fields /rAnna Blaszczok --tA refinement of Izumi's Theorem /rSébastien Boucksom, Charles Favre, Mattias Jonsson --tMultivariable Hodge theoretical invariants of germs of plane curves. II /rPierrette Cassou-Noguès, Anatoly Libgober --tExistence des diviseurs dicritiques, d’après S.S. Abhyankar /rVincent Cossart, Mickaël Matusinski, Guillermo Moreno-Socías --tInvariants of the graded algebras associated to divisorial valuations dominating a rational surface singularity /rVincent Cossart, Olivier Piltant, Ana J. Reguera --tAn introduction to $C$-minimal structures and their cell decomposition theorem /rPablo Cubides Kovacsics --tValuation semigroups of Noetherian local domains /rSteven Dale Cutkosky --tAdditive polynomials over perfect fields /rSalih Durhan --tOn $\mathbb{R}$-places and related topics /rDanielle Gondard-Cozette --tExtending valuations to formal completions /rFrancisco Javier Herrera Govantes, Miguel Ángel Olalla Acosta, Mark Spivakovsky, Bernard Teissier --tExtending real valuations to skew polynomial rings /rÁngel Granja, M. C. Martínez, C. Rodríguez --tStratifications in valued fields /rImmanuel Halupczok --tImaginaries and definable types in algebraically closed valued fields /rEhud Hrushovski --tDefects of algebraic function fields, completion defects and defect quotients /rFranz-Viktor Kuhlmann, Asim Naseem --tOn generalized series fields and exponential-logarithmic series fields with derivations /rMickaël Matusinski --tJet schemes of rational double point singularities /rHussein Mourtada --tValuations centered at a two-dimensional regular local domain: infima and topologies /rJosnei Novacoski --tReduction of local uniformization to the rank one case /rJosnei Novacoski, Mark Spivakovsky --tLittle survey on large fields - old & new /rFlorian Pop --tQuasi-valuations -- topology and the weak approximation theorem /rShai Sarussi --tOverweight deformations of affine toric varieties and local uniformization /rBernard Teissier --tDetecting valuations using small Galois groups /rAdam Topaz --tTruncation in Hahn fields /rLou van den Dries --tThe ergodicity of 1-Lipschitz transformations on 2-adic spheres /rEkaterina Yurova --tRamification of higher local fields approaches and questions /rLiang Xiao, Igor Zhukov.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHaving its classical roots, since more than a century, in algebraic number theory, algebraic geometry and the theory of ordered fields and groups, valuation theory has seen an amazing expansion into many other areas in recent decades. Moreover, having been dormant for a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities in positive characteristic and to analyse the structure of singularities. Driven by this topic, and by its many new applications in other areas, also the research in valuation theory itself has been intensified, with a particular emphasis on the deep open problems in positive characteristic.
As important examples for the expansion of valuation theory, it has become extremely useful in the theory of complex dynamical systems, and in the study of non-oscillating trajectories of real analytic vector fields in three dimensions. Analogues of the Riemann-Zariski valuation spaces have been found to be the proper framework for questions of intersection theory in algebraic geometry and in the analysis of singularities of complex plurisubharmonic functions. In a different direction, the relation between Berkovich geometry, tropical geometry and valuation spaces, on the one hand, and the geometry of arc spaces and valuation spaces, on the other, have begun to deepen and clarify.
Ever since its beginnings, valuation theory and Galois theory have grown closely together and influenced each other. Arguably, studying and understanding the extensions of valuations in algebraic field extensions is one of the most important questions in valuation theory, whereas using valuation theory is one of he most important tools in studying Galois extensions of fields, as well as constructing field extensions with given properties.
The well established topic of the model theory of valued fields is also being transformed, in particular through the study of valued fields with functions and operators, a...07aFields & rings2bicssc07aField theory and polynomials2msc07aOrder, lattices, ordered algebraic structures2msc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc1 aCampillo, Antonio,eeditor.1 aKuhlmann, Franz-Viktor,eeditor.1 aTeissier, Bernard,eeditor.40uhttps://doi.org/10.4171/149423cover imageuhttps://www.ems-ph.org/img/books/campillo_mini.gif02679nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100002900206245008500235260008200320300003400402336002600436337002600462338003600488347002400524490006100548506006600609520143100675650004502106650004802151650003102199856003202230856006702262183-140812CH-001817-320140812234500.0a fot ||| 0|cr nn mmmmamaa140812e20140812sz fot ||| 0|eng d a978303719641070a10.4171/1412doi ach0018173 7aPBK2bicssc a58-xxa53-xx2msc1 aSergeev, Armen,eauthor.10aLectures on Universal Teichmüller Spaceh[electronic resource] /cArmen Sergeev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (111 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. It is designed for a one semester course for undergraduate students, familiar with basic differential geometry, complex and functional analysis.
The universal Teichmüller space $\mathcal T$ is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Möbius transformations. The first part of the book is devoted to the study of geometric and analytic properties of $\mathcal T$. It is an infinite-dimensional Kähler manifold which contains all classical Teichmüller spaces of compact Riemann surfaces as complex submanifolds which explains
the name “universal Teichmüller space”. Apart from classical Teichmüller spaces, $\mathcal T$ contains the space $\mathcal S$ of diffeomorphisms of the circle modulo Möbius transformations. The latter space plays an important role in the quantization of the theory of smooth strings. The quantization of $\mathcal T$ is presented in the second part of the book. In contrast with the case of diffeomorphism space $\mathcal S$, which can be quantized in frames of the conventional Dirac scheme, the quantization of $\mathcal T$ requires an absolutely different approach based on the noncommutative geometry methods.
The book concludes with a list of 24 problems and exercises which can be used during the examinations.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/141423cover imageuhttps://www.ems-ph.org/img/books/sergeev_mini.gif03381nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245009600221260008200317300003400399336002600433337002600459338003600485347002400521490008300545505120300628506006601831520074001897650004702637650003102684650001802715650003802733650004802771700003702819700002902856856003202885856006602917184-141117CH-001817-320141117234500.0a fot ||| 0|cr nn mmmmamaa141117e20141201sz fot ||| 0|eng d a978303719647270a10.4171/1472doi ach0018173 7aPBMP2bicssc a53-xxa51-xxa52-xxa58-xx2msc10aHandbook of Hilbert Geometryh[electronic resource] /cAthanase Papadopoulos, Marc Troyanov3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (460 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2200tWeak Minkowski spaces /rAthanase Papadopoulos, Marc Troyanov --tFrom Funk to Hilbert geometry /rAthanase Papadopoulos, Marc Troyanov --tFunk and Hilbert geometries from the Finslerian viewpoint /rMarc Troyanov --tOn the Hilbert geometry of convex polytopes /rConstantin Vernicos --tThe horofunction boundary and isometry group of the Hilbert geometry /rCormac Walsh --tCharacterizations of hyperbolic geometry among Hilbert geometries /rRen Guo --tAround groups in Hilbert geometry /rLudovic Marquis --tThe geodesic flow of Finsler and Hilbert geometries /rMickaël Crampon --tDynamics of Hilbert nonexpansive maps /rAnders Karlsson --tBirkhoff’s version of Hilbert’s metric and its applications in analysis /rBas Lemmens, Roger D. Nussbaum --tConvex real projective structures and Hilbert metrics /rInkang Kim, Athanase Papadopoulos --tWeil–Petersson Funk metric on Teichmüller space /rHideki Miyachi, Ken’ichi Ohshika, Sumio Yamada --tFunk and Hilbert geometries in spaces of constant curvature /rAthanase Papadopoulos, Sumio Yamada --tOn the origin of Hilbert geometry /rMarc Troyanov --tHilbert’s fourth problem /rAthanase Papadopoulos --tOpen problems.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron–Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups, Coxeter groups, geometric group theory, Lie groups and discrete group actions.
The Handbook is addressed to both students who want to learn the theory and researchers working in the area.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aGeometry2msc07aConvex and discrete geometry2msc07aGlobal analysis, analysis on manifolds2msc1 aPapadopoulos, Athanase,eeditor.1 aTroyanov, Marc,eeditor.40uhttps://doi.org/10.4171/147423cover imageuhttps://www.ems-ph.org/img/books/irma22_mini.gif02705nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100002800221245010000249260008200349300003400431336002600465337002600491338003600517347002400553490004000577506006600617520138900683650003502072650002902107650004002136650002602176650002802202856003202230856006902262185-150120CH-001817-320150120234500.0a fot ||| 0|cr nn mmmmamaa150120e20150115sz fot ||| 0|eng d a978303719650270a10.4171/1502doi ach0018173 7aPBKJ2bicssc a46-xxa35-xxa42-xxa45-xx2msc1 aTriebel, Hans,eauthor.10aHybrid Function Spaces, Heat and Navier-Stokes Equationsh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (196 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v241 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is the continuation of Local Function Spaces, Heat and Navier–Stokes Equations (Tracts in Mathematics 20, 2013) by the author. A new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder–Zygmund spaces on the one hand and Morrey–Campanato spaces on the other. Morrey–Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play a crucial role in the theory of linear and nonlinear PDEs.
Chapter 1 (Introduction) describes the main motivations and intentions of this book. Chapter 2 is a selfcontained introduction into Morrey spaces.
Chapter 3 deals with hybrid smoothness spaces (which are between local and global spaces) in Euclidean n-space based on the Morrey–Campanato
refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to linear and nonlinear
heat equations in global and hybrid spaces. The obtained assertions about function spaces and nonlinear heat equations are used in the Chapters 5 and
6 to study Navier–Stokes equations in hybrid and global spaces.
This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) function spaces, and who
are interested in applications to nonlinear PDEs with heat and Navier–Stokes equations as prototypes.07aDifferential equations2bicssc07aFunctional analysis2msc07aPartial differential equations2msc07aFourier analysis2msc07aIntegral equations2msc40uhttps://doi.org/10.4171/150423cover imageuhttps://www.ems-ph.org/img/books/triebel24_mini.jpg02830nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100003100220245008500251260008200336300003400418336002600452337002600478338003600504347002400540490003900564506006600603520146500669650004502134650004802179650004002227650002502267650006602292856003202358856006602390186-150225CH-001817-320150225234500.0a fot ||| 0|cr nn mmmmamaa150225e20150218sz fot ||| 0|eng d a978303719651970a10.4171/1512doi ach0018173 7aPBK2bicssc a58-xxa35-xxa47-xxa49-xx2msc1 aLablée, Olivier,eauthor.10aSpectral Theory in Riemannian Geometryh[electronic resource] /cOlivier Lablée3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (197 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSpectral theory is a diverse area of mathematics that derives its motivations, goals and impetus from several sources. In particular, the spectral theory of the Laplacian on a compact Riemannian manifold is a central object in differential geometry. From a physical point a view, the Laplacian on a compact Riemannian manifold is a fundamental linear operator which describes numerous propagation phenomena: heat propagation, wave propagation, quantum dynamics, etc. Moreover, the spectrum of the Laplacian contains vast information about the geometry of the manifold.
This book gives a self-containded introduction to spectral geometry on compact Riemannian manifolds. Starting with an overview of spectral theory on Hilbert spaces, the book proceeds to a description of the basic notions in Riemannian geometry. Then its makes its way to topics of main interests in spectral geometry. The topics presented include direct and inverse problems. Direct problems are concerned with computing or finding properties on the eigenvalues while the main issue in inverse problems is “knowing the spectrum of the Laplacian, can we determine the geometry of the manifold?”
Addressed to students or young researchers, the present book is a first introduction in spectral theory applied to geometry. For readers interested in pursuing the subject further, this book will provide a basis for understanding principles, concepts and developments of spectral geometry.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc07aOperator theory2msc07aCalculus of variations and optimal control; optimization2msc40uhttps://doi.org/10.4171/151423cover imageuhttps://www.ems-ph.org/img/books/lablee_mini.jpg03004nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003000214245009000244260008200334300003400416336002600450337002600476338003600502347002400538490005100562506006600613520168500679650003202364650005202396650005502448650004002503856003202543856006702575187-150313CH-001817-320150313234500.0a fot ||| 0|cr nn mmmmamaa150313e20150320sz fot ||| 0|eng d a978303719652670a10.4171/1522doi ach0018173 7aPHGK2bicssc a82-xxa15-xxa35-xx2msc1 aSerfaty, Sylvia,eauthor.10aCoulomb Gases and Ginzburg–Landau Vorticesh[electronic resource] /cSylvia Serfaty3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (165 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe topic of this book is systems of points in Coulomb interaction, in particular, the classical Coulomb gas, and vortices in the Ginzburg–Landau model of superconductivity. The classical Coulomb and Log gases are classical statistical mechanics models, which have seen important developments in the mathematical literature due to their connection with random matrices and approximation theory. At low temperature, these systems are expected to “cristallize” to so-called Fekete sets, which exhibit microscopically a lattice structure.
The Ginzburg–Landau model, on the other hand, describes superconductors. In superconducting materials subjected to an external magnetic field, densely packed point vortices emerge, forming perfect triangular lattice patterns, so-called Abrikosov lattices.
This book describes these two systems and explores the similarity between them. It presents the mathematical tools developed to analyze the interaction between the Coulomb particles or the vortices, at the microscopic scale, and describes a “renormalized energy” governing the point patterns. This is believed to measure the disorder of a point configuration, and to be minimized by the Abrikosov lattice in dimension 2.
The book gives a self-contained presentation of results on the mean field limit of the Coulomb gas system, with or without temperature, and of the derivation of the renormalized energy. It also provides a streamlined presentation of the similar analysis that can be performed for the Ginzburg–Landau model, including a review of the vortex-specific tools and the derivation of the critical fields, the mean-field limit and the renormalized energy.07aStatistical physics2bicssc07aStatistical mechanics, structure of matter2msc07aLinear and multilinear algebra; matrix theory2msc07aPartial differential equations2msc40uhttps://doi.org/10.4171/152423cover imageuhttps://www.ems-ph.org/img/books/serfaty_mini.jpg03317nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003000206245012700236260008200363300003400445336002600479337002600505338003600531347002400567490005600591506006600647520201900713650003502732650003102767650002302798700003302821856003202854856006902886188-150319CH-001817-320150319234500.0a fot ||| 0|cr nn mmmmamaa150319e20150331sz fot ||| 0|eng d a978303719646570a10.4171/1462doi ach0018173 7aPBX2bicssc a01-xxa11-xx2msc1 aDumbaugh, Della,eauthor.10aEmil Artin and Beyond – Class Field Theory and $L$-Functionsh[electronic resource] /cDella Dumbaugh, Joachim Schwermer3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (245 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book explores the development of number theory, and class field theory in particular, as it passed through the hands of Emil Artin, Claude Chevalley and Robert Langlands in the middle of the twentieth century. Claude Chevalley’s presence in Artin’s 1931 Hamburg lectures on class field theory serves as the starting point for this volume. From there, it is traced how class field theory advanced in the 1930s and how Artin’s contributions influenced other mathematicians at the time and in subsequent years. Given the difficult political climate and his forced emigration as it were, the question of how Artin created a life in America within the existing institutional framework, and especially of how he continued his education of and close connection with graduate students, is considered. In particular, Artin’s collaboration in algebraic number theory with George Whaples and his student Margaret Matchett’s thesis work “On the zeta-function for ideles” in the 1940s are investigated. A (first) study of the influence of Artin on present day work on a non-abelian class field theory finishes the book.
The volume consists of individual essays by the authors and two contributors, James Cogdell and Robert Langlands, and contains relevant archival material. Among these, the letter from Chevalley to Helmut Hasse in 1935 is included, where he introduces the notion of ideles and explores their significance, along with the previously unpublished thesis by Matchett and the seminal letter of Langlands to André Weil of 1967 where he lays out his ideas regarding a non-abelian class field theory. Taken together, these chapters offer a view of both the life of Artin in the 1930s and 1940s and the development of class field theory at that time. They also provide insight into the transmission of mathematical ideas, the careful steps required to preserve a life in mathematics at a difficult moment in history, and the interplay between mathematics and politics (in more ways than one)....07aHistory of mathematics2bicssc07aHistory and biography2msc07aNumber theory2msc1 aSchwermer, Joachim,eauthor.40uhttps://doi.org/10.4171/146423cover imageuhttps://www.ems-ph.org/img/books/schwermer_mini.jpg03401nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001600184084002200200100003700222245014000259260008200399300003400481336002600515337002600541338003600567347002400603490005600627506006600683520202300749650003502772650002602807650003102833650002302864700002702887856003202914856006902946189-150427CH-001817-320150427234500.0a fot ||| 0|cr nn mmmmamaa150427e20150410sz fot ||| 0|eng d a978303719644170a10.4171/1442doi ach0018173 7aPBX2bicssc 7aPBR2bicssc a01-xxa11-xx2msc1 aBečvářová, Martina,eauthor.10aKarl Löwner and His Student Lipman Bers – Pre-war Prague Mathematiciansh[electronic resource] /cMartina Bečvářová, Ivan Netuka3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (310 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis monograph is devoted to two distinguished mathematicians, Karel Löwner (1893–1968) and Lipman Bers (1914–1993), whose lives are dramatically interlinked with key historical events of the 20th century. K. Löwner, Professor of Mathematics at the German University in Prague (Czechoslovakia), was dismissed from his position because he was a Jew, and emigrated to the USA in 1939 (where he changed his name to Charles Loewner). Earlier, he had published several outstanding papers in complex analysis and a masterpiece on matrix functions. In particular, his ground-breaking parametric method in geometric function theory from 1923, which led to Löwner’s celebrated differential equation, brought him world-wide fame and turned out to be a cornerstone in de Branges’ proof of the Bieberbach conjecture. Unexpectedly, Löwner’s differential equation has gained recent prominence with the introduction of a conformally invariant stochastic process called stochastic Loewner evolution (SLE) by O. Schramm in 2000. SLE features in two Fields Medal citations from 2006 and 2010. L. Bers was the final Prague Ph.D. student of K. Löwner. His dissertation on potential theory (1938), completed shortly before his emigration and long thought to be irretrievably lost, was found in 2006. It is here made accessible for the first time, with an extensive commentary, to the mathematical community.
This monograph presents an in-depth account of the lives of both mathematicians, with special emphasis on the pre-war period. Löwner’s teaching activities and professional achievements are presented in the context of the prevailing complex political situation and against the background of the wider development of mathematics in Europe. Each of his publications is accompanied by an extensive commentary, tracing the origin and motivation of the problem studied, and describing the state-of-art at the time of the corresponding mathematical field. Special attention is paid to the impact of the results obta...07aHistory of mathematics2bicssc07aNumber theory2bicssc07aHistory and biography2msc07aNumber theory2msc1 aNetuka, Ivan,eauthor.40uhttps://doi.org/10.4171/144423cover imageuhttps://www.ems-ph.org/img/books/becvarova_mini.jpg03304nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202100003000238245019900268260008200467300003400549336002600583337002600609338003600635347002400671490008300695506006600778520170100844650004702545650003102592650003102623650004002654650004002694650002802734700003202762856003202794856006802826190-150901CH-001817-320150901234501.0a fot ||| 0|cr nn mmmmamaa150901e20150930sz fot ||| 0|eng d a978303719653370a10.4171/1532doi ach0018173 7aPBMP2bicssc 7aPBPD2bicssc a53-xxa13-xxa16-xxa55-xx2msc1 aLatschev, Janko,eauthor.10aFree Loop Spaces in Geometry and Topologyh[electronic resource] :bIncluding the monograph Symplectic cohomology and Viterbo’s theorem by Mohammed Abouzaid /cJanko Latschev, Alexandru Oancea3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (500 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v241 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn the late 1990s two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of string topology, the full scope of which is still not completely understood. A few years earlier, Viterbo had discovered a first deep link between the symplectic topology of cotangent bundles and the topology of their free loop space. In the past 15 years, many exciting connections between these two viewpoints have been found. Still, researchers working on one side of the story often know quite little about the other.
One of the main purposes of this book is to facilitate communication between topologists and symplectic geometers thinking about free loop spaces. It was written by active researchers coming to the topic from both perspectives and provides a concise overview of many of the classical results, while also beginning to explore the new directions of research that have emerged recently. As one highlight, it contains a research monograph by M. Abouzaid which proves a strengthened version of Viterbo’s isomorphism between the homology of the free loop space of a manifold and the symplectic cohomology of its cotangent bundle, following a new strategy.
The book grew out of a learning seminar on free loop spaces held at Strasbourg University in 2008–2009, and should be accessible to a graduate student with a general interest in the topic. It focuses on introducing and explaining the most important aspects rather than offering encyclopedic coverage, while providing the interested reader with a broad basis for further studies and research.07aDifferential & Riemannian geometry2bicssc07aAlgebraic topology2bicssc07aDifferential geometry2msc07aCommutative rings and algebras2msc07aAssociative rings and algebras2msc07aAlgebraic topology2msc1 aOancea, Alexandru,eauthor.40uhttps://doi.org/10.4171/153423cover imageuhttps://www.ems-ph.org/img/books/latschev_mini.jpg03409nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001600184084003600200245015400236260008200390300003400472336002600506337002600532338003600558347002400594490008300618505093700701506006601638520093801704650003502642650002102677650003102698650004002729650001802769650003102787700002502818700003702843856003202880856007502912191-150427CH-001817-320150427234500.0a fot ||| 0|cr nn mmmmamaa150427e20150430sz fot ||| 0|eng d a978303719648970a10.4171/1482doi ach0018173 7aPBX2bicssc 7aPBM2bicssc a01-xxa22-xxa51-xxa53-xx2msc10aSophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physicsh[electronic resource] /cLizhen Ji, Athanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (348 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2300tSophus Lie, a giant in mathematics /rLizhen Ji --tFelix Klein: his life and mathematics /rLizhen Ji --tKlein and the Erlangen Programme /rJeremy J. Gray --tKlein’s “Erlanger Programm”: do traces of it exist in physical theories? /rHubert Goenner --tOn Klein’s So-called Non-Euclidean geometry /rNorbert A’Campo, Athanase Papadopoulos --tWhat are symmetries of PDEs and what are PDEs themselves? /rAlexandre Vinogradov --tTransformation groups in non-Riemannian geometry /rCharles Frances --tTransitional geometry /rNorbert A’Campo, Athanase Papadopoulos --tOn the projective geometry of constant curvature spaces /rAthanase Papadopoulos, Sumio Yamada --tThe Erlangen program and discrete differential geometry /rYuri B. Suris --tThree-dimensional gravity – an application of Felix Klein’s ideas in physics /rCatherine Meusburger --tInvariances in physics and group theory /rJean-Bernard Zuber.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume.
The book is written by well-known experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas.07aHistory of mathematics2bicssc07aGeometry2bicssc07aHistory and biography2msc07aTopological groups, Lie groups2msc07aGeometry2msc07aDifferential geometry2msc1 aJi, Lizhen,eeditor.1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/148423cover imageuhttps://www.ems-ph.org/img/books/ji_papadopoulos_mini.jpg03079nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003200221245013500253260008200388300003400470336002600504337002600530338003600556347002400592490004000616506006600656520155000722650003402272650004202306650002302348650004602371650002602417700003102443700002802474700002802502700002702530856003202557856006802589192-150601CH-001817-320150601234500.0a fot ||| 0|cr nn mmmmamaa150601e20150601sz fot ||| 0|eng d a978303719639770a10.4171/1392doi ach0018173 7aPBFD2bicssc a20-xxa05-xxa18-xxa68-xx2msc1 aDehornoy, Patrick,eauthor.10aFoundations of Garside Theoryh[electronic resource] /cPatrick Dehornoy, François Digne, Eddy Godelle, Daan Krammer, Jean Michel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (710 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v221 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWinner of the 2014 EMS Monograph Award!
This text is a monograph in algebra, with connections toward geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims at providing a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin’s braid groups, this approach turned out to lead to interesting results in a number of cases, the central notion being what the authors call a Garside family. At the moment, the study is far from complete, and the purpose of this book is both to present the current state of the theory and to be an invitation for further research.
There are two parts: the bases of a general theory, including many easy examples, are developed in Part A, whereas various more sophisticated examples are specifically addressed in Part B.
In order to make the content accessible to a wide audience of nonspecialists, exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use the current text as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin–Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, structure groups of set-theoretic solutions of the Yang–Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc07aCombinatorics2msc07aCategory theory; homological algebra2msc07aComputer science2msc1 aDigne, François,eauthor.1 aGodelle, Eddy,eauthor.1 aKrammer, Daan,eauthor.1 aMichel, Jean,eauthor.40uhttps://doi.org/10.4171/139423cover imageuhttps://www.ems-ph.org/img/books/dehornoy_mini.jpg04100nam a22004695a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001700184072001700201072001700218084003600235245015400271260008200425300003400507336002600541337002600567338003600593347002400629490008300653505061000736506006601346520176401412650004103176650002703217650002703244650002703271650002303298650005503321650004003376650003903416700003703455700003303492856003203525856007303557193-150617CH-001817-320150617234500.0a fot ||| 0|cr nn mmmmamaa150617e20150630sz fot ||| 0|eng d a978303719643470a10.4171/1432doi ach0018173 7aPBV2bicssc 7aPBFH2bicssc 7aPBFL2bicssc 7aPBFP2bicssc a05-xxa06-xxa16-xxa41-xx2msc10aFaà di Bruno Hopf Algebras, Dyson–Schwinger Equations, and Lie–Butcher Seriesh[electronic resource] /cKurusch Ebrahimi-Fard, Frédéric Fauvet3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (466 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2100tForeword /rJosé M. Gracia-Bondía --tPre-Lie algebras and systems of Dyson–Schwinger equations /rLoïc Foissy --tFive interpretations of Faà di Bruno’s formula /rAlessandra Frabetti, Dominique Manchon --tA Faà di Bruno Hopf algebra for analytic nonlinear feedback control systems /rW. Steven Gray, Luis A. Duffaut Espinosa --tOn algebraic structures of numerical integration on vector spaces and manifolds /rAlexander Lundervold, Hans Z. Munthe-Kaas --tSimple and contracting arborification /rEmmanuel Vieillard-Baron --tStrong QCD and Dyson–Schwinger equations /rCraig D. Roberts.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSince the early works of G.-C. Rota and his school, Hopf algebras have been instrumental in algebraic combinatorics. In a seminal 1998 paper, A. Connes and D. Kreimer presented a Hopf algebraic approach to renormalization in perturbative Quantum Field Theory (QFT). This work triggered an abundance of new research on applications of Hopf algebraic techniques in QFT as well as other areas of theoretical physics. Furthermore, these new developments were complemented by progress made in other domains of applications, such as control theory, dynamical systems, and numerical integration methods. Especially in the latter context, it became clear that J. Butcher’s work from the early 1970s was well ahead of its time.
The present volume emanated from a conference hosted in June 2011 by IRMA at Strasbourg University in France. Researchers from different scientific communities who share similar techniques and objectives gathered at this meeting to discuss new ideas and results on Faà di Bruno algebras, Dyson–Schwinger equations, and Butcher series.
The purpose of this book is to present a coherent set of lectures reflecting the state of the art of research on combinatorial Hopf algebras relevant to high energy physics, control theory, dynamical systems, and numerical integration methods. More specifically, connections between Dyson–Schwinger equations, Faà di Bruno algebras, and Butcher series are examined in great detail.
This volume is aimed at researchers and graduate students interested in combinatorial and algebraic aspects of QFT, control theory, dynamical systems and numerical analysis of integration methods. It contains introductory lectures on the various constructions that are emerging and developing in these domains.07aCombinatorics & graph theory2bicssc07aLattice theory2bicssc07aFields & rings2bicssc07aLinear algebra2bicssc07aCombinatorics2msc07aOrder, lattices, ordered algebraic structures2msc07aAssociative rings and algebras2msc07aApproximations and expansions2msc1 aEbrahimi-Fard, Kurusch,eeditor.1 aFauvet, Frédéric,eeditor.40uhttps://doi.org/10.4171/143423cover imageuhttps://www.ems-ph.org/img/books/ebrahimi-fard_mini.jpg03303nam a22004455a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202100003900238245018300277260008200460300003400542336002600576337002600602338003600628347002400664490005300688506006600741520158300807650004702390650003502437650003102472650004302503650004102546650004002587700003002627700003502657700003102692700003102723856003202754856007102786194-150629CH-001817-320150629234504.0a fot ||| 0|cr nn mmmmamaa150629e20150629sz fot ||| 0|eng d a978303719636670a10.4171/1362doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc a53-xxa17-xxa34-xxa35-xx2msc1 aBourguignon, Jean-Pierre,eauthor.10aA Spinorial Approach to Riemannian and Conformal Geometryh[electronic resource] /cJean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (462 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental role in differential geometry and mathematical physics.
After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler–Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces.
The special features of the book include a unified treatment of Spin$^\mathrm c$ and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors.
This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aDifferential geometry2msc07aNonassociative rings and algebras2msc07aOrdinary differential equations2msc07aPartial differential equations2msc1 aHijazi, Oussama,eauthor.1 aMilhorat, Jean-Louis,eauthor.1 aMoroianu, Andrei,eauthor.1 aMoroianu, Sergiu,eauthor.40uhttps://doi.org/10.4171/136423cover imageuhttps://www.ems-ph.org/img/books/bourguignon_mini.jpg02608nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003800207245010000245260008200345300003400427336002600461337002600487338003600513347002400549490006100573506006600634520125800700650003401958650003801992650004202030700002902072700002802101856003202129856007302161195-150902CH-001817-320150902234501.0a fot ||| 0|cr nn mmmmamaa150902e20150820sz fot ||| 0|eng d a978303719654070a10.4171/1542doi ach0018173 7aPBFD2bicssc a57-xxa20-xx2msc1 aAschenbrenner, Matthias,eauthor.10a3-Manifold Groupsh[electronic resource] /cMatthias Aschenbrenner, Stefan Friedl, Henry Wilton3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (230 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe field of 3-manifold topology has made great strides forward since 1982, when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari–Gabai, the Surface Subgroup Theorem of Kahn–Markovic, the work of Wise and others on special cube complexes, and finally Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focussing on the consequences for fundamental groups of 3-manifolds.
As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material – although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students.
The book closes with an extensive list of open questions, which will also be of interest to graduate students and established researchers alike.07aGroups & group theory2bicssc07aManifolds and cell complexes2msc07aGroup theory and generalizations2msc1 aFriedl, Stefan,eauthor.1 aWilton, Henry,eauthor.40uhttps://doi.org/10.4171/154423cover imageuhttps://www.ems-ph.org/img/books/aschenbrenner_mini.jpg01935nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002800207245008000235260008200315300003400397336002600431337002600457338003600483347002400519490006100543506006600604520072000670650003201390650002901422650002601451856003201477856007601509196-151029CH-001817-320151029121023.0a fot ||| 0|cr nn mmmmamaa151029e20150930sz fot ||| 0|eng d a978303719655770a10.4171/1552doi ach0018173 7aPBKG2bicssc a46-xxa42-xx2msc1 aTriebel, Hans,eauthor.10aTempered Homogeneous Function Spacesh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (143 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIf one tries to transfer assertions for the inhomogeneous spaces $A^s_{p,q} (\mathbb R^n)$, $A \in \{B,F \}$, appropriately to their homogeneous counterparts ${\overset {\, \ast}{A}}{}^s_{p,q} (\mathbb R^n)$ within the framework of the dual pairing $\big( S(\mathbb R^n), S'(\mathbb R^n) \big)$ then it is hard to make a mistake as long as the parameters $p,q,s$ are restricted by $0 < p,q \le \infty$ and, in particular, $n(\frac {1}{p} – 1) < s < \frac {n}{p}$. It is the main aim of these notes to say what this means.
This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of type $B^s_{p,q}$ and $F^s_{p,q}$.07aFunctional analysis2bicssc07aFunctional analysis2msc07aFourier analysis2msc40uhttps://doi.org/10.4171/155423cover imageuhttps://www.ems-ph.org/img/books/triebel_tempered_mini.jpg02992nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001600183084002200199100003300221245012700254260008200381300003400463336002600497337002600523338003600549347002400585490006100609506006600670520155300736650002402289650002602313650002302339650002602362700002802388700003202416700003302448856003202481856006902513197-151111CH-001817-320151111234500.0a fot ||| 0|cr nn mmmmamaa151111e20151123sz fot ||| 0|eng d a978303719642770a10.4171/1422doi ach0018173 7aPB2bicssc 7aPBR2bicssc a11-xxa68-xx2msc1 aBringmann, Kathrin,eauthor.10aFour Faces of Number Theoryh[electronic resource] /cKathrin Bringmann, Yann Bugeaud, Titus Hilberdink, Jürgen W. Sander3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (198 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book arose from courses given at the International Summer School organized in August 2012 by the number theory group of the Department of Mathematics at the University of Würzburg. It consists of four essentially self-contained chapters and presents recent research results highlighting the strong interplay between number theory and other fields of mathematics, such as combinatorics, functional analysis and graph theory. The book is addressed to (under)graduate students who wish to discover various aspects of number theory. Remarkably, it demonstrates how easily one can approach frontiers of current research in number theory by elementary and basic analytic methods.
Kathrin Bringmann gives an introduction to the theory of modular forms and, in particular, so-called Mock theta-functions, a topic which had been untouched for decades but has obtained much attention in the last years. Yann Bugeaud is concerned with expansions of algebraic numbers. Here combinatorics on words and transcendence theory are combined to derive new information on the sequence of decimals of algebraic numbers and on their continued fraction expansions. Titus Hilberdink reports on a recent and rather unexpected approach to extreme values of the Riemann zeta-function by use of (multiplicative) Toeplitz matrices and functional analysis. Finally, Jürgen Sander gives an introduction to algebraic graph theory and the impact of number theoretical methods on fundamental questions about the spectra of graphs and the analogue of the Riemann hypothesis.07aMathematics2bicssc07aNumber theory2bicssc07aNumber theory2msc07aComputer science2msc1 aBugeaud, Yann,eauthor.1 aHilberdink, Titus,eauthor.1 aSander, Jürgen W.,eauthor.40uhttps://doi.org/10.4171/142423cover imageuhttps://www.ems-ph.org/img/books/bringmann_mini.jpg02852nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100004300206245017900249260008200428300003400510336002600544337002600570338003600596347002400632490005600656506006600712520154200778650003502320650003102355650001702386856003202403856006702435198-151214CH-001817-320151214234500.0a fot ||| 0|cr nn mmmmamaa151214e20160131sz fot ||| 0|eng d a978303719645870a10.4171/1452doi ach0018173 7aPBX2bicssc a01-xxa00-xx2msc1 ade Saint-Gervais, Henri Paul,eauthor.10aUniformization of Riemann Surfacesh[electronic resource] :bRevisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /cHenri Paul de Saint-Gervais3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (512 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn 1907 Paul Koebe and Henri Poincaré almost simultaneously proved the uniformization theorem: Every simply connected Riemann surface is isomorphic to the plane, the open unit disc, or the sphere.
It took a whole century to get to the point of stating this theorem and providing a convincing proof of it, relying as it did on prior work of Gauss, Riemann, Schwarz, Klein, Poincaré, and Koebe, among others. The present
book offers an overview of the maturation process of this theorem.
The evolution of the uniformization theorem took place in parallel with the emergence of modern algebraic geometry, the creation of complex analysis, the first stirrings of functional analysis, and with the flowering of the theory of differential equations and the birth of topology. The uniformization theorem was thus one of the lightning rods of 19th century mathematics. Rather than describe the history of a single theorem, our aim is to return to the original proofs, to look at these through the eyes of modern mathematicians, to enquire as to their correctness, and to attempt to make them rigorous while respecting insofar as possible the state of mathematical knowledge at the time, or, if this should prove impossible, then using modern mathematical tools not available to their authors.
This book will be useful to today's mathematicians wishing to cast a glance back at the history of their discipline. It should also provide graduate students with a non-standard approach to concepts of great importance for modern research.07aHistory of mathematics2bicssc07aHistory and biography2msc07aGeneral2msc40uhttps://doi.org/10.4171/145423cover imageuhttps://www.ems-ph.org/img/books/gervais_mini.jpg02579nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001600185084003600201100003000237245014700267260008200414300003400496336002600530337002600556338003600582347002400618490008300642506006600725520105000791650004701841650003701888650003101925650003301956650004101989650005302030856003202083856006602115199-151214CH-001817-320151214234500.0a fot ||| 0|cr nn mmmmamaa151214e20160105sz fot ||| 0|eng d a978303719658870a10.4171/1582doi ach0018173 7aPBMP2bicssc 7aPBT2bicssc a53-xxa28-xxa30-xxa60-xx2msc1 aShioya, Takashi,eauthor.10aMetric Measure Geometryh[electronic resource] :bGromov’s Theory of Convergence and Concentration of Metrics and Measures /cTakashi Shioya3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (194 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v251 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book studies a new theory of metric geometry on metric measure spaces, originally developed by M. Gromov in his book “Metric Structures for Riemannian and Non-Riemannian Spaces” and based on the idea of the concentration of measure phenomenon due to Lévy and Milman. A central theme in this text is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows to investigate a sequence of Riemannian manifolds with unbounded dimensions. One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.
This book makes advanced material accessible to researchers and graduate students interested in metric measure spaces.07aDifferential & Riemannian geometry2bicssc07aProbability & statistics2bicssc07aDifferential geometry2msc07aMeasure and integration2msc07aFunctions of a complex variable2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/158423cover imageuhttps://www.ems-ph.org/img/books/shioya_mini.jpg03791nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245009400200260008200294300003400376336002600410337002600436338003600462347002400498490008300522505133700605506006601942520121702008650003203225650004103257700003703298856003203335856007403367200-151214CH-001817-320151214234500.0a fot ||| 0|cr nn mmmmamaa151214e20160111sz fot ||| 0|eng d a978303719660170a10.4171/1602doi ach0018173 7aPBKG2bicssc a30-xx2msc10aHandbook of Teichmüller Theory, Volume Vh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (596 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2600tIntroduction to Teichmüller theory, old and new, V /rAthanase Papadopoulos --tIdentities on hyperbolic manifolds /rMartin Bridgeman, Ser Peow Tan --tProblems on the Thurston metric /rWeixu Su --tMeyer functions and the signature of fibered 4-manifolds /rYusuke Kuno --tThe Goldman–Turaev Lie bialgebra and the Johnson homomorphisms /rNariya Kawazumi, Yusuke Kuno --tA survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics /rTakao Satoh --tGeometry and dynamics on character varieties /rInkang Kim --tCompactifications and reduction theory of geometrically finite locally symmetric spaces /rLizhen Ji --tRepresentations of fundamental groups of 2-manifolds /rLisa Jeffrey --tExtremal quasiconformal mappings and quadratic differentials /rOswald Teichmüller --tA commentary on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale /rVincent Alberge, Athanase Papadopoulos, Weixu Su --tDetermination of extremal quasiconformal mappings of closed oriented Riemann surfaces /rOswald Teichmüller --tA commentary on Teichmüller’s paper Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen /rAnnette A’Campo-Neuen, Norbert A’Campo, Vincent Alberge, Athanase Papadopoulos.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is the fifth in a series dedicated to Teichmüller theory in a broad sense, including the study of various deformation spaces and of mapping class group actions. It is divided into four parts:
Part A: The metric and the analytic theory
Part B: The group theory
Part C: Representation theory and generalized structures
Part D: Sources
The topics that are covered include identities for the hyperbolic geodesic length spectrum, Thurston's metric, the cohomology of moduli space and mapping class groups, the Johnson homomorphisms, Higgs bundles, dynamics on character varieties, and there are many others.
Besides surveying important parts of the theory, several chapters contain conjectures and open problems. The last part contains two fundamental papers by Teichmüller, translated into English and accompanied by mathematical commentaries.
The chapters, like those of the other volumes in this collection, are written by experts who have a broad view on the subject. They have an expository character (which fits with the original purpose of this handbook), but some of them also contain original and new material.
The Handbook is addressed to researchers and to graduate students.07aFunctional analysis2bicssc07aFunctions of a complex variable2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/160423cover imageuhttps://www.ems-ph.org/img/books/papadopoulos-v_mini.jpg02208nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003400200245007300234260008200307300003400389336002600423337002600449338003600475347002400511490003900535506006600574520107200640650002601712650003301738856003201771856006701803201-160229CH-001817-320160229234501.0a fot ||| 0|cr nn mmmmamaa160229e20160329sz fot ||| 0|eng d a978303719659570a10.4171/1592doi ach0018173 7aPBKB2bicssc a28-xx2msc1 aSalamon, Dietmar A.,eauthor.10aMeasure and Integrationh[electronic resource] /cDietmar A. Salamon3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (363 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book is intended as a companion to a one semester introductory lecture course on measure and integration. After an introduction to abstract measure theory it proceeds to the construction of the Lebesgue measure
and of Borel measures on locally compact Hausdorff spaces, $L^p$ spaces and their dual spaces and elementary Hilbert space theory. Special features include the formulation of the Riesz Representation Theorem in terms of both inner and outer regularity, the proofs of the Marcinkiewicz Interpolation Theorem and the Calderon–Zygmund inequality as applications of Fubini’s theorem and Lebesgue differentiation, the treatment of the generalized Radon–Nikodym theorem due to Fremlin, and the existence proof for Haar measures. Three appendices deal with Urysohn’s Lemma, product topologies, and the inverse function theorem.
The book assumes familiarity with first year analysis and linear algebra. It is suitable for second year undergraduate students of mathematics or anyone desiring an introduction to the concepts of measure and integration.07aReal analysis2bicssc07aMeasure and integration2msc40uhttps://doi.org/10.4171/159423cover imageuhttps://www.ems-ph.org/img/books/salamon_mini.jpg04623nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245009500200260008200295300003400377336002600411337002600437338003600463347002400499490008300523505220200606506006602808520118202874650003204056650004104088700003704129856003204166856007504198202-160524CH-001817-320160524234501.0a fot ||| 0|cr nn mmmmamaa160524e20160531sz fot ||| 0|eng d a978303719661870a10.4171/1612doi ach0018173 7aPBKG2bicssc a30-xx2msc10aHandbook of Teichmüller Theory, Volume VIh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (652 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2700tIntroduction to Teichmüller theory, old and new, VI /rAthanase Papadopoulos --tAlexander Grothendieck /rValentin Poénaru --tOn Grothendieck’s construction of Teichmüller space /rNorbert A’Campo, Lizhen Ji, Athanase Papadopoulos --tNull-set compactifications of Teichmüller spaces /rVincent Alberge, Hideki Miyachi, Ken’ichi Ohshika --tMirzakhani’s recursion formula on Weil–Petersson volume and applications /rYi Huang --tRigidity phenomena in the mapping class group /rJavier Aramayona, Juan Souto --tHarmonic volume and its applications /rYuuki Tadokoro --tTorus bundles and 2-forms on the universal family of Riemann surfaces /rRobin de Jong --tCubic Differentials in the Differential Geometry of Surfaces /rJohn Loftin, Ian McIntosh --tTwo-generator groups acting on the complex hyperbolic plane /rPierre Will --tConfiguration spaces of planar linkages /rAlexey Sossinsky --tQuasiconformal mappings on the Heisenberg group: An overview /rIoannis D. Platis --tActions of the absolute Galois group /rNorbert A’Campo, Lizhen Ji, Athanase Papadopoulos --tA primer on dessins /rPierre Guillot --tHypergeometric Galois Actions /rA. Muhammed Uludağ, İsmail Sağlam --tA panaroma of the fundamental group of the modular orbifold /rA. Muhammed Uludağ, Ayberk Zeytin --tOn Grothendieck’s tame topology /rNorbert A’Campo, Lizhen Ji, Athanase Papadopoulos --tSome historical commentaries on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale /rReiner Kühnau --tComplete solution of an extremal problem of the quasiconformal mapping /rOswald Teichmüller --tA Commentary on Teichmüller’s paper Vollständige Lösung einer Extremalaufgabe der quasikonformen Abbildung /rVincent Alberge, Athanase Papadopoulos --tOn extremal problems of conformal geometry /rOswald Teichmüller --tA Commentary on Teichmüller’s paper Über Extremalprobleme der konformen Geometrie /rNorbert A’Campo, Athanase Papadopoulos --tA displacement theorem of quasiconformal mapping /rOswald Teichmüller --tA Commentary on Teichmüller’s paper Ein Verschiebungssatz der quasikonformen Abbildung /rVincent Alberge.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is the sixth in a series dedicated to Teichmüller theory in a broad sense, including various moduli and deformation spaces, and the study of mapping class groups. It is divided into five parts:
Part A: The metric and the analytic theory.
Part B: The group theory.
Part C: Representation theory and generalized structures.
Part D: The Grothendieck–Teichmüller theory.
Part D: Sources.
The topics surveyed include Grothendieck’s construction of the analytic structure of Teichmüller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhani’s application to the computation of Weil–Petersson volumes), moduli spaces of configurations spaces, the Teichmüller tower with the action of the Galois group on dessins d’enfants, and several others actions related to surfaces. The last part contains three papers by Teichmüller, translated into English with mathematical commentaries, and a document that contains H. Grötzsch’s comments on Teichmüller’s famous paper Extremale quasikonforme Abbildungen und quadratische Differentiale.
The handbook is addressed to researchers and to graduate students.07aFunctional analysis2bicssc07aFunctions of a complex variable2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/161423cover imageuhttps://www.ems-ph.org/img/books/papadopoulos-vi_mini.jpg03049nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003500213245015900248260008200407300003400489336002600523337002600549338003600575347002400611490006100635506006600696520160400762650002102366650003802387650004602425650002002471700003602491700003302527856003202560856007102592203-160524CH-001817-320160524234501.0a fot ||| 0|cr nn mmmmamaa160524e20160531sz fot ||| 0|eng d a978303719656470a10.4171/1562doi ach0018173 7aPBP2bicssc a57-xxa18-xxa19-xx2msc1 aCavicchioli, Alberto,eauthor.10aHigher-Dimensional Generalized Manifolds: Surgery and Constructionsh[electronic resource] /cAlberto Cavicchioli, Friedrich Hegenbarth, Dušan D. Repovš3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (154 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aGeneralized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces (this is nowadays called the manifold recognition problem). As such, generalized manifolds have served to understand the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself.
A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful.
Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds.
This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on our graduate courses and seminars, as well as our talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology.07aTopology2bicssc07aManifolds and cell complexes2msc07aCategory theory; homological algebra2msc07a$K$-theory2msc1 aHegenbarth, Friedrich,eauthor.1 aRepovš, Dušan D.,eauthor.40uhttps://doi.org/10.4171/156423cover imageuhttps://www.ems-ph.org/img/books/cavicchioli_mini.jpg03156nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184245008700220260008200307300003400389336002600423337002600449338003600475347002400511505052000535506006601055520138001121650004102501650002302542650002302565650004002588650002802628700002502656856003202681856006902713204-160630CH-001817-320160630234501.0a fot ||| 0|cr nn mmmmamaa160630e20160725sz fot ||| 0|eng d a978303719657170a10.4171/1572doi ach0018173 7aPBV2bicssc a05-xxa11-xxa13-xxa14-xx2msc10aAbsolute Arithmetic and $\mathbb F_1$-Geometryh[electronic resource] /cKoen Thas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (397 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tThe Weyl functor. Introduction to Absolute Arithmetic /rKoen Thas --tBelian categories /rAnton Deitmar --tThe combinatorial-motivic nature of $\mathbb F_1$-schemes /rKoen Thas --tA blueprinted view on $\mathbb F_1$-geometry /rOliver Lorscheid --tAbsolute geometry and the Habiro topology /rLieven Le Bruyn --tWitt vectors, semirings, and total positivity /rJames Borger --tModuli operad over $\mathbb F_1$ /rYuri I. Manin, Matilde Marcolli --tA taste of Weil theory in characteristic one /rKoen Thas.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIt has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, $\mathbb F_1$, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger–Manin program, which aims at solving the classical Riemann Hypothesis.
This book, which is the first of its kind in the $\mathbb F_1$-world, covers several areas in $\mathbb F_1$-theory, and is divided into four main parts – Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic.
Topics treated include the combinatorial theory and geometry behind $\mathbb F_1$, categorical foundations, the blend of different scheme theories over $\mathbb F_1$ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic.
Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way.
The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality.07aCombinatorics & graph theory2bicssc07aCombinatorics2msc07aNumber theory2msc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc1 aThas, Koen,eeditor.40uhttps://doi.org/10.4171/157423cover imageuhttps://www.ems-ph.org/img/books/thas_mini_2016.jpg02721nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245014800221260008200369300003400451336002600485337002600511338003600537347002400573490006100597505030900658506006600967520085001033650004701883650003101930650004001961650006602001650005302067700003102120700002702151700003102178856003202209856007002241205-160613CH-001817-320160613234501.0a fot ||| 0|cr nn mmmmamaa160613e20160630sz fot ||| 0|eng d a978303719662570a10.4171/1622doi ach0018173 7aPBMP2bicssc a53-xxa35-xxa49-xxa60-xx2msc10aGeometry, Analysis and Dynamics on sub-Riemannian Manifoldsh[electronic resource] :bVolume I /cDavide Barilari, Ugo Boscain, Mario Sigalotti3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (332 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-517600tSome topics of geometric measure theory in Carnot groups /rFrancesco Serra Cassano --tHypoelliptic operators and some aspects of analysis and geometry of sub-Riemannian spaces /rNicola Garofalo --tSub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations /rFabrice Baudoin.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds.
In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology.
The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aProbability theory and stochastic processes2msc1 aBarilari, Davide,eeditor.1 aBoscain, Ugo,eeditor.1 aSigalotti, Mario,eeditor.40uhttps://doi.org/10.4171/162423cover imageuhttps://www.ems-ph.org/img/books/barilari_I_mini.jpg02821nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245014900221260008200370300003400452336002600486337002600512338003600538347002400574490006100598505040600659506006601065520085101131650004701982650003102029650004002060650006602100650005302166700003102219700002702250700003102277856003202308856007102340206-161005CH-001817-320161005234502.0a fot ||| 0|cr nn mmmmamaa161005e20161025sz fot ||| 0|eng d a978303719663270a10.4171/1632doi ach0018173 7aPBMP2bicssc a53-xxa35-xxa49-xxa60-xx2msc10aGeometry, Analysis and Dynamics on sub-Riemannian Manifoldsh[electronic resource] :bVolume II /cDavide Barilari, Ugo Boscain, Mario Sigalotti3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (307 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-517600tIntroduction to geodesics in sub-Riemannian geometry /rAndrei Agrachev, Davide Barilari, Ugo Boscain --tGeometry of subelliptic diffusions /rAnton Thalmaier --tGeometric foundations of rough paths /rPeter K. Friz, Paul Gassiat --tSobolev and bounded variation functions on metric measure spaces /rLuigi Ambrosio, Roberta Ghezzi --tSingularities of vector distributions /rMichail Zhitomirskii.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds.
In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology.
The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.07aDifferential & Riemannian geometry2bicssc07aDifferential geometry2msc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aProbability theory and stochastic processes2msc1 aBarilari, Davide,eeditor.1 aBoscain, Ugo,eeditor.1 aSigalotti, Mario,eeditor.40uhttps://doi.org/10.4171/163423cover imageuhttps://www.ems-ph.org/img/books/barilari_II_mini.jpg03109nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168084001500183245007000198260008200268300003400350336002600384337002600410338003600436347002400472505118800496506006601684520085101750650002402601650001702625700003102642856003202673856006602705207-160613CH-001817-320160613234501.0a fot ||| 0|cr nn mmmmamaa160613e20160704sz fot ||| 0|eng d a978303719664970a10.4171/1642doi ach0018173 7aPB2bicssc a00-xx2msc10aMathematics and Societyh[electronic resource] /cWolfgang König3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (314 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tThe truth, the whole truth and nothing but the truth: The challenges of reporting on mathematics /rGeorge G. Szpiro --tExperimental mathematics in the society of the future /rDavid H. Bailey, Jonathan M. Borwein --tWhat is the impact of interactive mathematical experiments? /rAlbrecht Beutelspacher --tMathematics and finance /rWalter Schachermayer --tStatistics in high dimensions /rAad van der Vaart, Wessel van Wieringen --tFiltering theory: Mathematics in engineering, from Gauss to particle filters /rOfer Zeitouni --tMathematical models for population dynamics: Randomness versus determinism /rJean Bertoin --tThe quest for laws and structure /rJürg M. Fröhlich --tGeometry and freeform architecture /rHelmut Pottmann, Johannes Wallner --tSome geometries to describe nature /rChristiane Rousseau --tMathematics in industry /rHelmut Neunzert --tMathematics of signal design for communication systems /rHolger Boche, Ezra Tampubolon --tCryptology: Methods, applications and challenges /rClaus Diem --tA mathematical view on voting and power /rWerner Kirsch --tNumerical methods and scientific computing for climate and geosciences /rJörn Behrens.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe ubiquity and importance of mathematics in our complex society is generally not in doubt. However, even a scientifically interested layman would be hard pressed to point out aspects of our society where contemporary mathematical research is essential. Most popular examples are finance, engineering, wheather and industry, but the way mathematics comes into play is widely unknown in the public. And who thinks of application fields like biology, encryption, architecture, or voting systems?
This volume comprises a number of success stories of mathematics in our society – important areas being shaped by cutting edge mathematical research. The authors are eminent mathematicians with a high sense for public presentation, addressing scientifically interested laymen as well as professionals in mathematics and its application disciplines.07aMathematics2bicssc07aGeneral2msc1 aKönig, Wolfgang,eeditor.40uhttps://doi.org/10.4171/164423cover imageuhttps://www.ems-ph.org/img/books/koenig_mini.jpg03173nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202245012400238260008200362300003400444336002600478337002600504338003600530347002400566490005600590505032800646506006600974520128401040650003202324650003402356650002902390650004202419650002502461650005302486700003702539700003302576700002802609856003202637856007002669208-160711CH-001817-320160711234501.0a fot ||| 0|cr nn mmmmamaa160711e20160731sz fot ||| 0|eng d a978303719665670a10.4171/1652doi ach0018173 7aPBKG2bicssc 7aPBFD2bicssc a46-xxa20-xxa47-xxa60-xx2msc10aFree Probability and Operator Algebrash[electronic resource] /cDan-Virgil Voiculescu, Nicolai Stammeier, Moritz Weber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (142 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aMünster Lectures in Mathematics (MLM) ;x2523-523000tBackground and outlook /rDan-Virgil Voiculescu --tBasics in free probability /rMoritz Weber --tRandom matrices and combinatorics /rRoland Speicher --tFree monotone transport /rDimitri L. Shlyakhtenko --tFree group factors /rKen Dykema --tFree convolution /rHari Bercovici --tEasy quantum groups /rMoritz Weber.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aFree probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices etc). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescu’s attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication.
These lecture notes arose from a masterclass in Münster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). In order to make it more accessible, the exposition features a chapter on basics in free probability, and exercises for each part.
This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras.07aFunctional analysis2bicssc07aGroups & group theory2bicssc07aFunctional analysis2msc07aGroup theory and generalizations2msc07aOperator theory2msc07aProbability theory and stochastic processes2msc1 aVoiculescu, Dan-Virgil,eeditor.1 aStammeier, Nicolai,eeditor.1 aWeber, Moritz,eeditor.40uhttps://doi.org/10.4171/165423cover imageuhttps://www.ems-ph.org/img/books/voiculescu_mini.jpg02585nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003000221245010700251260008200358300003400440336002600474337002600500338003600526347002400562490004000586506006600626520120000692650003401892650004201926650004001968650001802008650003802026700003402064856003202098856006902130209-160920CH-001817-320160920234502.0a fot ||| 0|cr nn mmmmamaa160920e20160930sz fot ||| 0|eng d a978303719666370a10.4171/1662doi ach0018173 7aPBFD2bicssc a20-xxa22-xxa51-xxa57-xx2msc1 aCornulier, Yves,eauthor.10aMetric Geometry of Locally Compact Groupsh[electronic resource] /cYves Cornulier, Pierre de la Harpe3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (243 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v251 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWinner of the 2016 EMS Monograph Award!
The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups, and can favourably be extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where ‘coarse’ refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups.
Basic results in the subject are exposed with complete proofs, others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as p-adic fields, isometry groups of various metric spaces, and, last but not least, discrete group themselves.
The book is aimed at graduate students and advanced undergraduate students, as well as mathematicians who wish some introduction to coarse geometry and locally compact groups.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc07aTopological groups, Lie groups2msc07aGeometry2msc07aManifolds and cell complexes2msc1 ade la Harpe, Pierre,eauthor.40uhttps://doi.org/10.4171/166423cover imageuhttps://www.ems-ph.org/img/books/cornulier_mini.jpg02664nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100002900200245010400229260008200333300003400415336002600449337002600475338003600501347002400537490004000561506006600601520143700667650002902104650005502133700002902188856003202217856006502249210-161219CH-001817-320161219234501.0a fot ||| 0|cr nn mmmmamaa161219e20170112sz fot ||| 0|eng d a978303719667070a10.4171/1672doi ach0018173 7aPBKD2bicssc a32-xx2msc1 aGuedj, Vincent,eauthor.10aDegenerate Complex Monge–Ampère Equationsh[electronic resource] /cVincent Guedj, Ahmed Zeriahi3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (496 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v261 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWinner of the 2016 EMS Monograph Award!
Complex Monge–Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yau’s classical works, culminating in Yau’s solution to the Calabi conjecture. A notable application is the construction of Kähler-Einstein metrics on some compact Kähler manifolds. In recent years degenerate complex Monge–Ampère equations have been intensively studied, requiring more advanced tools.
The main goal of this book is to give a self-contained presentation of the recent developments of pluripotential theory on compact Kähler manifolds and its application to Kähler–Einstein metrics on mildly singular varieties. After reviewing basic properties of plurisubharmonic functions, Bedford–Taylor’s local theory of complex Monge–Ampère measures is developed. In order to solve degenerate complex Monge–Ampère equations on compact Kähler manifolds, fine properties of quasi-plurisubharmonic functions are explored, classes of finite energies defined and various maximum principles established. After proving Yau’s celebrated theorem as well as its recent generalizations, the results are then used to solve the (singular) Calabi conjecture and to construct (singular) Kähler–Einstein metrics on some varieties with mild singularities.
The book is accessible to advanced students and researchers of complex analysis and differential geometry.07aComplex analysis2bicssc07aSeveral complex variables and analytic spaces2msc1 aZeriahi, Ahmed,eauthor.40uhttps://doi.org/10.4171/167423cover imageuhttps://www.ems-ph.org/img/books/guedj_mini.jpg03139nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245020300207260008200410300003400492336002600526337002600552338003600578347002400614490006100638505029800699506006600997520138001063650003502443650004602478650003102524700003502555700003602590700003002626856003202656856006502688211-161121CH-001817-320161121234501.0a fot ||| 0|cr nn mmmmamaa161121e20161130sz fot ||| 0|eng d a978303719668770a10.4171/1682doi ach0018173 7aPBKJ2bicssc a37-xxa53-xx2msc10aDynamics Done with Your Bare Handsh[electronic resource] :bLecture notes by Diana Davis, Bryce Weaver, Roland K. W. Roeder, Pablo Lessa /cFrançoise Dal’Bo, François Ledrappier, Amie Wilkinson3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (214 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-517600tLines in positive genus: An introduction to flat surfaces /rDiana Davis --tIntroduction to complicated behavior and periodic orbits /rBryce Weaver --tAround the boundary of complex dynamics /rRoland K.W. Roeder --tRecurrence vs transience: An introduction to random walks /rPablo Lessa.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book arose from 4 lectures given at the Undergraduate Summer School of the Thematic Program Dynamics and Boundaries held at the University of Notre Dame. It is intended to introduce (under)graduate students to the field of dynamical systems by emphasizing elementary examples, exercises and bare hands constructions.
The lecture of Diana Davis is devoted to billiard flows on polygons, a simple-sounding class of continuous time dynamical system for which many problems remain open.
Bryce Weaver focuses on the dynamics of a 2x2 matrix acting on the flat torus. This example introduced by Vladimir Arnold illustrates the wide class of uniformly hyperbolic dynamical systems, including the geodesic flow for negatively curved, compact manifolds.
Roland Roeder considers a dynamical system on the complex plane governed by a quadratic map with a complex parameter. These maps exhibit complicated dynamics related to the Mandelbrot set defined as the set of parameters for which the orbit remains bounded.
Pablo Lessa deals with a type of non-deterministic dynamical system: a simple walk on an infinite graph, obtained by starting at a vertex and choosing a random neighbor at each step. The central question concerns the recurrence property. When the graph is a Cayley graph of a group, the behavior of the walk is deeply related to algebraic properties of the group.07aDifferential equations2bicssc07aDynamical systems and ergodic theory2msc07aDifferential geometry2msc1 aDal’Bo, Françoise,eeditor.1 aLedrappier, François,eeditor.1 aWilkinson, Amie,eeditor.40uhttps://doi.org/10.4171/168423cover imageuhttps://www.ems-ph.org/img/books/dalbo_mini.jpg02435nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084002900202100003100231245009700262260008200359300003400441336002600475337002600501338003600527347002400563490004000587506006600627520106100693650003501754650003101789650004001820650006601860650002401926856003201950856006701982212-161205CH-001817-320161205234500.0a fot ||| 0|cr nn mmmmamaa161205e20170101sz fot ||| 0|eng d a978303719669470a10.4171/1692doi ach0018173 7aPBKJ2bicssc 7aPBCD2bicssc a35-xxa49-xxa81-xx2msc1 aRaymond, Nicolas,eauthor.10aBound States of the Magnetic Schrödinger Operatorh[electronic resource] /cNicolas Raymond3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (394 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v271 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is a synthesis of recent advances in the spectral theory of the magnetic Schrödinger operator. It can be considered a catalog of concrete examples of magnetic spectral asymptotics.
Since the presentation involves many notions of spectral theory and semiclassical analysis, it begins with a concise account of concepts and methods used in the book and is illustrated by many elementary examples.
Assuming various points of view (power series expansions, Feshbach–Grushin reductions, WKB constructions, coherent states decompositions, normal forms) a theory of Magnetic Harmonic Approximation is then established which allows, in particular, accurate descriptions of the magnetic eigenvalues and eigenfunctions. Some parts of this theory, such as those related to spectral reductions or waveguides, are still accessible to advanced students while others (e.g., the discussion of the Birkhoff normal form and its spectral consequences, or the results related to boundary magnetic wells in dimension three) are intended for seasoned researchers.07aDifferential equations2bicssc07aMathematical logic2bicssc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/169423cover imageuhttps://www.ems-ph.org/img/books/raymond_mini.jpg02239nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084002200202100003100224245009600255260008200351300003400433336002600467337002600493338003600519347002400555490005100579506006600630520091700696650003501613650004701648650004001695650003101735856003201766856006701798213-161205CH-001817-320161205234500.0a fot ||| 0|cr nn mmmmamaa161205e20170101sz fot ||| 0|eng d a978303719670070a10.4171/1702doi ach0018173 7aPBKJ2bicssc 7aPBMP2bicssc a35-xxa53-xx2msc1 aFigalli, Alessio,eauthor.10aThe Monge–Ampère Equation and Its Applicationsh[electronic resource] /cAlessio Figalli3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (210 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Monge–Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry.
This monograph is a comprehensive introduction to the existence and regularity theory of the Monge–Ampère equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation.
The presentation is essentially self-contained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs).
This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for self-study and also as a reference.07aDifferential equations2bicssc07aDifferential & Riemannian geometry2bicssc07aPartial differential equations2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/170423cover imageuhttps://www.ems-ph.org/img/books/figalli_mini.jpg03191nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003200206245015200238260008200390300003400472336002600506337002600532338003600558347002400594490004000618506006600658520191600724650004502640650003302685650002602718856003202744856006502776214-160923CH-001817-320160923234501.0a fot ||| 0|cr nn mmmmamaa160923e20161014sz fot ||| 0|eng d a978303719640370a10.4171/1402doi ach0018173 7aPBK2bicssc a28-xxa31-xx2msc1 aPonce, Augusto C.,eauthor.10aElliptic PDEs, Measures and Capacitiesh[electronic resource] :bFrom the Poisson Equation to Nonlinear Thomas–Fermi Problems /cAugusto C. Ponce3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (463 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v231 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWinner of the 2014 EMS Monograph Award!
Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis whose connections are usually not emphasized in introductory graduate courses. Yet, one cannot dissociate the notions of mass or electric charge, naturally described in terms of measures, from the physical potential they generate. Having such a principle in mind, this book illustrates the beautiful interplay between tools from PDEs and GMT in a simple and elegant way by investigating properties like existence and regularity of solutions of linear and nonlinear elliptic PDEs.
Inspired by a variety of sources, from the pioneer balayage scheme of Poincaré to more recent results related to the Thomas–Fermi and the Chern–Simons models, the problems covered in this book follow an original presentation, intended to emphasize the main ideas in the proofs. Classical techniques like regularity theory, maximum principles and the method of sub- and supersolutions are adapted to the setting where merely integrability or density assumptions on the data are available. The distinguished role played by capacities and precise representatives is also explained.
Other special features are:
• the remarkable equivalence between Sobolev capacities and Hausdorff contents in terms of trace inequalities;
• the strong approximation of measures in terms of capacities or densities, normally absent from GMT books;
• the rescue of the strong maximum principle for the Schrödinger operator involving singular potentials.
This book invites the reader to a trip through modern techniques in the frontier of elliptic PDEs and GMT, and is addressed to graduate students and researchers having some deep interest in analysis. Most of the chapters can be read independently, and only basic knowledge of measure theory, functional analysis and Sobolev spaces is required.07aCalculus & mathematical analysis2bicssc07aMeasure and integration2msc07aPotential theory2msc40uhttps://doi.org/10.4171/140423cover imageuhttps://www.ems-ph.org/img/books/ponce_mini.jpg02365nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003600213245009000249260008200339300003400421336002600455337002600481338003600507347002400543490005100567506006600618520104000684650003701724650002001761650005301781650006401834856003201898856007301930215-170224CH-001817-320170224234501.0a fot ||| 0|cr nn mmmmamaa170224e20170310sz fot ||| 0|eng d a978303719673170a10.4171/1732doi ach0018173 7aPBT2bicssc a62-xxa60-xxa91-xx2msc1 aSchachermayer, Walter,eauthor.10aAsymptotic Theory of Transaction Costsh[electronic resource] /cWalter Schachermayer3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (160 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aA classical topic in Mathematical Finance is the theory of portfolio optimization. Robert Merton's work from the early seventies had enormous impact on academic research as well as on the paradigms guiding practitioners.
One of the ramifications of this topic is the analysis of (small) proportional transaction costs, such as a Tobin tax. The lecture notes present some striking recent results of the asymptotic dependence of the relevant quantities when transaction costs tend to zero.
An appealing feature of the consideration of transaction costs is that it allows for the first time to reconcile the no arbitrage paradigm with the use of non-semimartingale models, such as fractional Brownian motion. This leads to the culminating theorem of the present lectures which roughly reads as follows: for a fractional Brownian motion stock price model we always find a shadow price process for given transaction costs. This process is a semimartingale and can therefore be dealt with using the usual machinery of mathematical finance.07aProbability & statistics2bicssc07aStatistics2msc07aProbability theory and stochastic processes2msc07aGame theory, economics, social and behavioral sciences2msc40uhttps://doi.org/10.4171/173423cover imageuhttps://www.ems-ph.org/img/books/schachermayer_mini.jpg05090nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245017600221260008200397300003400479336002600513337002600539338003600565347002400601490005400625505241300679506006603092520105303158650003104211650002804242650004004270650004304310650004604353700003004399700003204429700002804461700003304489700003604522856003204558856006604590216-161205CH-001817-320161205234500.0a fot ||| 0|cr nn mmmmamaa161205e20170112sz fot ||| 0|eng d a978303719671770a10.4171/1712doi ach0018173 7aPBMW2bicssc a14-xxa16-xxa17-xxa18-xx2msc10aRepresentation Theory – Current Trends and Perspectivesh[electronic resource] /cHenning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb, Christoph Schweigert3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (773 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tSymmetric superspaces: slices, radial parts, and invariant functions /rAlexander Alldridge --tGeometry of quiver Grassmannians of Dynkin type with applications to cluster algebras /rGiovanni Cerulli Irelli --tSpherical varieties and perspectives in representation theory /rStéphanie Cupit-Foutou --tCategorical actions from Lusztig induction and restriction on finite general linear groups /rOlivier Dudas, Michela Varagnolo, Éric Vasserot --tHomological mirror symmetry for singularities /rWolfgang Ebeling --tOn the category of finite-dimensional representations of OSp$(r|2n)$: Part I /rMichael Ehrig, Catharina Stroppel --tOn cubes of Frobenius extensions /rBen Elias, Noah Snyder, Geordie Williamson --tOn toric degenerations of flag varieties /rXin Fang, Ghislain Fourier, Peter Littelmann --tSubquotient categories of the affine category $\mathcal O$ at the critical level /rPeter Fiebig --tLow-dimensional topology, low-dimensional field theory and representation theory /rJürgen Fuchs, Christoph Schweigert --tDerived categories of quasi-hereditary algebras and their derived composition series /rMartin Kalck --tDominant dimension and applications /rSteffen Koenig --tHighest weight categories and strict polynomial functors. With an appendix by Cosima Aquilino /rHenning Krause --tIn the bocs seat: Quasi-hereditary algebras and representation type /rJulian Külshammer --tFrom groups to clusters /rSefi Ladkani --tSemi-infinite combinatorics in representation theory /rMartina Lanini --tLocal-global conjectures in the representation theory of finite groups /rGunter Malle --tBounded and semibounded representations of infinite dimensional Lie groups /rKarl-Hermann Neeb --tOn ideals in $\operatorname{U}(\mathfrak {sl} (\infty)), \operatorname{U}(\mathfrak {o} (\infty)), \operatorname{U}(\mathfrak {sp} (\infty))$ /rIvan Penkov, Alexey Petukhov --tSpherical varieties: applications and generalizations /rGuido Pezzini --tQuiver moduli and small desingularizations of some GIT quotients /rMarkus Reineke --tGeometric invariant theory for principal three-dimensional subgroups acting on flag varieties /rHenrik Seppänen, Valdemar V. Tsanov --tInductive conditions for counting conjectures via character triples /rBritta Späth --tRestricted rational Cherednik algebras /rUlrich Thiel --tOn the existence of regular vectors /rChristoph Zellner.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aFrom April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume.
Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups.
Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aAssociative rings and algebras2msc07aNonassociative rings and algebras2msc07aCategory theory; homological algebra2msc1 aKrause, Henning,eeditor.1 aLittelmann, Peter,eeditor.1 aMalle, Gunter,eeditor.1 aNeeb, Karl-Hermann,eeditor.1 aSchweigert, Christoph,eeditor.40uhttps://doi.org/10.4171/171423cover imageuhttps://www.ems-ph.org/img/books/krause_mini.jpg02104nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100002800200245012000228260008200348300003400430336002600464337002600490338003600516347002400552490006100576506006600637520087800703650003501581650004001616856003201656856007801688217-170224CH-001817-320170224234501.0a fot ||| 0|cr nn mmmmamaa170224e20170323sz fot ||| 0|eng d a978303719672470a10.4171/1722doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aTriebel, Hans,eauthor.10aPDE Models for Chemotaxis and Hydrodynamics in Supercritical Function Spacesh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (140 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book deals with PDE models for chemotaxis (the movement of biological cells or organisms in response of chemical gradients) and hydrodynamics (viscous, homogeneous, and incompressible fluid filling the entire space). The underlying Keller–Segel equations (chemotaxis), Navier–Stokes equations (hydrodynamics), and their numerous modifications and combinations are treated in the context of inhomogeneous spaces of Besov–Sobolev type paying special attention to mapping properties of related nonlinearities. Further models are considered, including (deterministic) Fokker–Planck equations and chemotaxis Navier–Stokes equations.
These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type and interested in mathematical biology and physics.07aDifferential equations2bicssc07aPartial differential equations2msc40uhttps://doi.org/10.4171/172423cover imageuhttps://www.ems-ph.org/img/books/triebel_chemotaxis_mini.jpg05918nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001700184084002200201245017500223260008200398300003400480336002600514337002600540338003600566347002400602490005400626505308700680506006603767520133803833650004805171650003505219650002405254650004005278700003305318700003105351700002605382856003205408856006805440218-170419CH-001817-320170419234501.0a fot ||| 0|cr nn mmmmamaa170419e20170505sz fot ||| 0|eng d a978303719675570a10.4171/1752doi ach0018173 7aPHT2bicssc 7aPBKJ2bicssc a81-xxa35-xx2msc10aFunctional Analysis and Operator Theory for Quantum Physicsh[electronic resource] :bThe Pavel Exner Anniversary Volume /cJaroslav Dittrich, Hynek Kovařík, Ari Laptev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (595 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tRelative partition function of Coulomb plus delta interaction /rSergio Albeverio, Claudio Cacciapuoti, Mauro Spreafico --tInequivalence of quantum Dirac fields of different masses and the underlying general structures involved /rAsao Arai --tOn a class of Schrödinger operators exhibiting spectral transition /rDiana Barseghyan, Olga Rossi --tOn the quantum mechanical three-body problem with zero-range interactions /rGiulia Basti, Alessandro Teta --tOn the index of meromorphic operator-valued functions and some applications /rJussi Behrndt, Fritz Gesztesy, Helge Holden, Roger Nichols --tTrace formulae for Schrödinger operators with singular interactions /rJussi Behrndt, Matthias Langer, Vladimir Lotoreichik --tAn improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ /rRafael D. Benguria, Soledad Benguria --tTwisted waveguide with a Neumann window /rPhilippe Briet, Hiba Hammedi --tExample of a periodic Neumann waveguide with a gap in its spectrum /rGiuseppe Cardone, Andrii Khrabustovskyi --tTwo-dimensional time-dependent point interactions /rRaffaele Carlone, Michele Correggi, Rodolfo Figari --tOn resonant spectral gaps in quantum graphs /rNgoc T. Do, Peter Kuchment, Beng Ong --tAdiabatic theorem for a class of stochastic differential equations on a Hilbert space /rMartin Fraas --tEigenvalues of Schrödinger operators with complex surface potentials /rRupert L. Frank --tA lower bound to the spectral threshold in curved quantum layers /rPedro Freitas, David Krejčiřík --tTo the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions /rYaroslav Granovskyi, Mark M. Malamud, Hagen Neidhardt, Andrea Posilicano --tSpectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator /rAndré Hänel, Timo Weidl --tDirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality /rBernard Helffer, Rola Kiwan --tA mathematical modeling of electron–phonon interaction for small wave numbers close to zero /rMasao Hirokawa --tThe modified unitary Trotter–Kato and Zeno product formulas revisited /rTakashi Ichinose --tSpectral asymptotics induced by approaching and diverging planar circles /rSylwia Kondej --tSpectral estimates for the Heisenberg Laplacian on cylinders /rHynek Kovařík, Bartosch Ruszkowski, Timo Weidl --tVariational proof of the existence of eigenvalues for star graphs /rKonstantin Pankrashkin --tOn the boundedness and compactness of weighted Green operators of second-order elliptic operators /rYehuda Pinchover --tAbstract graph-like spaces and vector-valued metric graphs /rOlaf Post --tA Cayley–Hamiltonian theorem for periodic finite band matrices /rBarry Simon --tPath topology dependence of adiabatic time evolution /rAtushi Tanaka, Taksu Cheon --tOn quantum graph filters with flat passbands /rOndřej Turek --tComments on the Chernoff $\sqrt n$-lemma /rValentin A. Zagrebnov.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrödinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley–Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory.
Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields.07aQuantum physics (quantum mechanics)2bicssc07aDifferential equations2bicssc07aQuantum theory2msc07aPartial differential equations2msc1 aDittrich, Jaroslav,eeditor.1 aKovařík, Hynek,eeditor.1 aLaptev, Ari,eeditor.40uhttps://doi.org/10.4171/175423cover imageuhttps://www.ems-ph.org/img/books/dittrich_mini.jpg02598nam a22004095a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001600183084003600199100003500235245013200270260008200402300003400484336002600518337002600544338003600570347002400606490003900630506006600669520109300735650002401828650002001852650004001872650004001912650005501952650004602007700003002053856003202083856007302115219-170424CH-001817-320170424234500.0a fot ||| 0|cr nn mmmmamaa170424e20170512sz fot ||| 0|eng d a978303719674870a10.4171/1742doi ach0018173 7aPB2bicssc 7aPBF2bicssc a16-xxa13-xxa15-xxa18-xx2msc1 aSkowroński, Andrzej,eauthor.10aFrobenius Algebras IIh[electronic resource] :bTilted and Hochschild Extension Algebras /cAndrzej Skowroński, Kunio Yamagata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (629 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is the second of three volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book is devoted to fundamental results of the representation theory of finite dimensional hereditary algebras and their tilted algebras, which allow to describe the representation theory of prominent classes of Frobenius algebras.
The second part is devoted to basic classical and recent results concerning the Hochschild extensions of finite dimensional algebras by duality bimodules and their module categories. Moreover, the shapes of connected components of the stable Auslander-Reiten quivers of Frobenius algebras are described.
The only prerequisite in this volume is a basic knowledge of linear algebra and some results of the first volume. It includes complete proofs of all results presented and provides a rich supply of examples and exercises.
The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fields.07aMathematics2bicssc07aAlgebra2bicssc07aAssociative rings and algebras2msc07aCommutative rings and algebras2msc07aLinear and multilinear algebra; matrix theory2msc07aCategory theory; homological algebra2msc1 aYamagata, Kunio,eauthor.40uhttps://doi.org/10.4171/174423cover imageuhttps://www.ems-ph.org/img/books/skowronski_II_mini.jpg05879nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168084001500183245012600198260008200324300003400406336002600440337002600466338003600492347002400528505328600552506006603838520142603904650002405330650001705354700003105371700003105402856003205433856006405465220-180813CH-001817-320180813233005.0a fot 1|| 0|cr nn mmmmamaa180813e20180806sz fot 1|| 0|eng d a978303719676270a10.4171/1762doi ach0018173 7aPB2bicssc a00-xx2msc10aEuropean Congress of Mathematicsh[electronic resource] :bBerlin, July 18–22, 2016 /cVolker Mehrmann, Martin Skutella3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (901 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tHow has one, and How could have one approached the diversity of mathematical cultures? /rKarine Chemla --tFlexible polyhedra and their volumes /rAlexander A. Gaifullin --tBoolean Functions: Influence, threshold and noise /rGil Kalai --tQuantum Fields and Probability /rAntti Kupiainen --tExistence of knotted vortex structures in stationary solutions of the Euler equations /rAlberto Enciso, Daniel Peralta-Salas --tSymplectic rigidity and quantum mechanics /rLeonid Polterovich --tThe topology and geometry of automorphism groups of free groups /rKaren Vogtmann --tSpectral synthesis in Hilbert spaces of entire functions /rAnton D. Baranov, Yurii Belov --tPeriodic waves in unsaturated porous media with hysteresis /rBettina Detmann, Pavel Krejčí, Elisabetta Rocca --t2D Ising model: Correlation functions at criticality via Riemann-type boundary value problems /rDmitry Chelkak --tOn perverse equivalences and rationality /rJoseph Chuang, Radha Kessar --tTorsion homology growth in arithmetic groups /rNicolas Bergeron --tPositivity and higher Teichmüller theory /rOlivier Guichard, Anna Wienhard --tDiffusion, optimal transport and Ricci curvature /rGiuseppe Savaré --tNon-discrete simple locally compact groups /rPierre-Emmanuel Caprace --tAn invitation to circle actions /rLeonor Godinho, Silvia Sabatini --tSampling and interpolating sequences in finite dimensional spaces /rJoaquim Ortega-Cerdà --tWeak hyperbolic structures and robust properties of diffeomorphisms and flows /rChristian Bonatti, Adriana da Luz --tFree group rings and derived functors /rRoman Mikhailov, Inder Bir S. Passi --tCongested transport at microscopic and macroscopic scales /rBertrand Maury --tComplex Brunn–Minkowski inequalities and their applications in geometry /rBo Berndtsson --tCounting Steiner Triple Systems /rPeter Keevash --tAmenability versus non amenability: An introduction to von Neumann algebras /rStefaan Vaes --tRecent progress in nonlinear potential theory /rGiuseppe Mingione --tStochastic dynamics for adaptation and evolution of microorganisms /rSylvain Billiard, Pierre Collet, Régis Ferrière, Sylvie Méléard, Viet Chi Tran --tLearning and sparse control of multiagent systems /rMassimo Fornasier --tVariational modeling of dislocations in crystals in the line-tension limit /rPilar Ariza, Sergio Conti, Adriana Garroni, Michael Ortiz --tPhase transitions in discrete structures /rAmin Coja-Oghlan --tTransverse stability issues in Hamiltonian PDE /rNikolay Tzvetkov --tDigits of primes /rJames Maynard --tThe Hodge theory of the Hecke category /rGeordie Williamson --tAdditive combinatorics and graph theory /rEndre Szemerédi --tThe arithmetic and topology of differential equations /rDon B. Zagier --tTwo-scale space-time methods for computational solid mechanics /rPatrice Hauret, Eric Lignon, Nicole Spillane, Benoît Pouliot --tLiving mathematics: Poincaré and Weyl in context /rJeremy J. Gray --tMesoscopic models in biology /rVincent Calvez --tOn the singular part of measures constrained by linear PDEs and applications /rGuido De Philippis --tRecent progress on Bernoulli convolutions /rPéter P. Varjú --tRandom currents expansion of the Ising model /rHugo Duminil-Copin.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe European Congress of Mathematics, held every four years, is a well-established major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004), Amsterdam (2008), and Kraków (2012), the Seventh European Congress of Mathematics (7ECM) took place in Berlin, Germany, July 18–22, 2016, with about 1100 participants from all over the world.
Ten plenary, thirty-three invited and four special lectures formed the core of the program. As at all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: The Felix Klein prize for a remarkable solution of an industrial problem, and – for the second time – the Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by forty-three minisymposia with about 160 talks as well as contributed talks, spread over all areas of mathematics. Several panel discussions and meetings were organized, covering a variety of issues ranging from the future of mathematical publishing to public awareness of mathematics.
These proceedings present extended versions of most of the plenary and invited lectures which were delivered during the congress, providing a permanent record of the best what mathematics offers today.07aMathematics2bicssc07aGeneral2msc1 aMehrmann, Volker,eeditor.1 aSkutella, Martin,eeditor.40uhttps://doi.org/10.4171/176423cover imageuhttps://www.ems-ph.org/img/books/7ecm_mini.jpg03325nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184245011700206260008200323300003400405336002600439337002600465338003600491347002400527505120200551506006601753520089901819650003502718650003102753650001702784700003002801700003302831856003202864856006702896221-170818CH-001817-320170818234504.0a fot ||| 0|cr nn mmmmamaa170818e20170901sz fot ||| 0|eng d a978303719677970a10.4171/1772doi ach0018173 7aPBX2bicssc a01-xxa00-xx2msc10aInterviews with the Abel Prize Laureates 2003–2016h[electronic resource] /cMartin Raussen, Christian F. Skau3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (302 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tAbel Prize 2003: Jean-Pierre Serre /rMartin Raussen, Christian F. Skau --tAbel Prize 2004: Sir Michael Francis Atiyah and Isadore M. Singer /rMartin Raussen, Christian F. Skau --tAbel Prize 2005: Peter D. Lax /rMartin Raussen, Christian F. Skau --tAbel Prize 2006: Lennart Carleson /rMartin Raussen, Christian F. Skau --tAbel Prize 2007: Srinivasa S. R. Varadhan /rMartin Raussen, Christian F. Skau --tAbel Prize 2008: John Griggs Thompson and Jacques Tits /rMartin Raussen, Christian F. Skau --tAbel Prize 2009: Mikhail Gromov /rMartin Raussen, Christian F. Skau --tAbel Prize 2010: John Tate /rMartin Raussen, Christian F. Skau --tAbel Prize 2011: John Milnor /rMartin Raussen, Christian F. Skau --tAbel Prize 2012: Endre Szemerédi /rMartin Raussen, Christian F. Skau --tAbel Prize 2013: Pierre Deligne /rMartin Raussen, Christian F. Skau --tAbel Prize 2014: Yakov G. Sinai /rMartin Raussen, Christian F. Skau --tAbel Prize 2015: John F. Nash, Jr. and Louis Nirenberg /rMartin Raussen, Christian F. Skau --tAbel Prize 2016: Sir Andrew J. Wiles /rMartin Raussen, Christian F. Skau --tAn Imaginary Interview with Niels Henrik Abel /rMartin Raussen, Christian F. Skau.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Abel Prize was established in 2002 by the Norwegian Ministry of Education and Research. It has been awarded annually to mathematicians in recognition of pioneering scientific achievements.
Since the first occasion in 2003, Martin Raussen and Christian Skau have had the opportunity to conduct extensive interviews with the laureates. The interviews were broadcast by Norwegian television; moreover, they have appeared in the membership journals of several mathematical societies.
The interviews from the period 2003 – 2016 have now been collected in this edition. They highlight the mathematical achievements of the laureates in a historical perspective and they try to unravel the way in which the world’s most famous mathematicians conceive and judge their results, how they collaborate with peers and students, and how they perceive the importance of mathematics for society.07aHistory of mathematics2bicssc07aHistory and biography2msc07aGeneral2msc1 aRaussen, Martin,eeditor.1 aSkau, Christian F.,eeditor.40uhttps://doi.org/10.4171/177423cover imageuhttps://www.ems-ph.org/img/books/raussen_mini.jpg02687nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001700184072001700201084003600218100003000254245011900284260008200403300003400485336002600519337002600545338003600571347002400607490004000631506006600671520107700737650004501814650003501859650004701894650006601941650004002007650003102047650004802078700002902126856003202155856006602187222-180207CH-001817-320180207233003.0a fot ||| 0|cr nn mmmmamaa180207e20180215sz fot ||| 0|eng d a978303719678670a10.4171/1782doi ach0018173 7aPBK2bicssc 7aPBKJ2bicssc 7aPBMP2bicssc a49-xxa35-xxa53-xxa58-xx2msc1 aHenrot, Antoine,eauthor.10aShape Variation and Optimizationh[electronic resource] :bA Geometrical Analysis /cAntoine Henrot, Michel Pierre3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (379 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v281 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aOptimizing the shape of an object to make it the most efficient, resistant, streamlined, lightest, noiseless, stealthy or the cheapest is clearly a very old task. But the recent explosion of modeling and scientific computing have given this topic new life. Many new and interesting questions have been asked. A mathematical topic was born – shape optimization (or optimum design).
This book provides a self-contained introduction to modern mathematical approaches to shape optimization, relying only on undergraduate level prerequisite but allowing to tackle open questions in this vibrant field. The analytical and geometrical tools and methods for the study of shapes are developed. In particular, the text presents a systematic treatment of shape variations and optimization associated with the Laplace operator and the classical capacity. Emphasis is also put on differentiation with respect to domains and a FAQ on the usual topologies of domains is provided. The book ends with geometrical properties of optimal shapes, including the case where they do not exist.07aCalculus & mathematical analysis2bicssc07aDifferential equations2bicssc07aDifferential & Riemannian geometry2bicssc07aCalculus of variations and optimal control; optimization2msc07aPartial differential equations2msc07aDifferential geometry2msc07aGlobal analysis, analysis on manifolds2msc1 aPierre, Michel,eauthor.40uhttps://doi.org/10.4171/178423cover imageuhttps://www.ems-ph.org/img/books/henrot_mini.jpg02777nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001700184084002200201100003000223245011200253260008200365300003400447336002600481337002600507338003600533347002400569490003900593506006600632520140000698650004702098650002702145650004902172650003802221700002802259856003202287856007202319223-170628CH-001817-320170628234501.0a fot ||| 0|cr nn mmmmamaa170628e20170711sz fot ||| 0|eng d a978303719679370a10.4171/1792doi ach0018173 7aUAA2bicssc 7aPBFL2bicssc a94-xxa12-xx2msc1 aJustesen, Jørn,eauthor.10aA Course In Error-Correcting Codesh[electronic resource] :bSecond edition /cJørn Justesen, Tom Høholdt3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (226 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book, updated and enlarged for the second edition, is written as a text for a course aimed at 3rd or 4th year students. Only some familiarity with elementary linear algebra and probability is directly assumed, but some maturity is required. The students may specialize in discrete mathematics, computer science, or communication engineering. The book is also a suitable introduction to coding theory for researchers from related fields or for professionals who want to supplement their theoretical basis. The book gives the coding basics for working on projects in any of the above areas, but material specific to one of these fields has not been included. The chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts. In addition, some problems and suggestions for projects indicate direction for further work. The presentation encourages the use of programming tools for studying codes, implementing decoding methods, and simulating performance. Specific examples of programming exercises are provided on the book's home page.07aMathematical theory of computation2bicssc07aFields & rings2bicssc07aInformation and communication, circuits2msc07aField theory and polynomials2msc1 aHøholdt, Tom,eauthor.40uhttps://doi.org/10.4171/179423cover imageuhttps://www.ems-ph.org/img/books/justesen_2nd_mini.jpg02299nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003300207245011600240260008200356300003400438336002600472337002600498338003600524347002400560490006100584506006600645520097600711650003101687650003801718650005501756700002801811856003201839856006601871224-170711CH-001817-320170711234501.0a fot ||| 0|cr nn mmmmamaa170711e20170725sz fot ||| 0|eng d a978303719680970a10.4171/1802doi ach0018173 7aPBPD2bicssc a57-xxa32-xx2msc1 aMichel, Françoise,eauthor.10aHigher-Dimensional Knots According to Michel Kervaireh[electronic resource] /cFrançoise Michel, Claude Weber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2017 a1 online resource (144 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMichel Kervaire wrote six papers which can be considered fundamental to the development of higher-dimensional knot theory. They are not only of historical interest but naturally introduce to some of the essential techniques in this fascinating theory.
This book is written to provide graduate students with the basic concepts necessary to read texts in higher-dimensional knot theory and its relations with singularities. The first chapters are devoted to a presentation of Pontrjagin’s construction, surgery and the work of Kervaire and Milnor on homotopy spheres. We pursue with Kervaire’s fundamental work on the group of a knot, knot modules and knot cobordism. We add developments due to Levine. Tools (like open books, handlebodies, plumbings, …) often used but hard to find in original articles are presented in appendices. We conclude with a description of the Kervaire invariant and the consequences of the Hill–Hopkins–Ravenel results in knot theory.07aAlgebraic topology2bicssc07aManifolds and cell complexes2msc07aSeveral complex variables and analytic spaces2msc1 aWeber, Claude,eauthor.40uhttps://doi.org/10.4171/180423cover imageuhttps://www.ems-ph.org/img/books/michel_mini.jpg02558nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003500213245013200248260008200380300003400462336002600496337002600522338003600548347002400584490004000608506006600648520123700714650002101951650004001972650003302012650005302045856003202098856006602130225-180504CH-001817-320180504233001.0a fot ||| 0|cr nn mmmmamaa180504e20180525sz fot ||| 0|eng d a978303719681670a10.4171/1812doi ach0018173 7aPBP2bicssc a22-xxa28-xxa60-xx2msc1 aKosyak, Alexander V.,eauthor.10aRegular, Quasi-regular and Induced Representations of Infinite-dimensional Groupsh[electronic resource] /cAlexander V. Kosyak3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (587 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v291 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAlmost all harmonic analysis on locally compact groups is based on the existence (and uniqueness) of a Haar measure. Therefore, it is very natural to attempt a similar construction for non-locally compact groups. The essential idea is to replace the non-existing Haar measure on an infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion of the initial group or on the completion of a homogeneous space.
The aim of the book is a systematic development, by example, of noncommutative harmonic analysis on infinite-dimensional (non-locally compact) matrix groups. We generalize the notion of regular, quasi-regular and induced representations for arbitrary infinite-dimensional groups. The central idea to verify the irreducibility is the Ismagilov conjecture. We also extend the Kirillov orbit method for the group of upper triangular matrices of infinite order.
In order to make the content accessible to a wide audience of nonspecialists, the exposition is essentially self-contained and very few prerequisites are needed. The book is aimed at graduate and advanced undergraduate students, as well as mathematicians who wish an introduction to representations of infinite-dimensional groups.07aTopology2bicssc07aTopological groups, Lie groups2msc07aMeasure and integration2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/181423cover imageuhttps://www.ems-ph.org/img/books/kosyak_mini.jpg03795nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185245017200214260008200386300003400468336002600502337002600528338003600554347002400590490005400614505136600668506006602034520095602100650003003056650002803086650005503114650002803169700003603197700003303233700003203266856003203298856006703330226-180108CH-001817-320180108234002.0a fot ||| 0|cr nn mmmmamaa180108e20180121sz fot ||| 0|eng d a978303719682370a10.4171/1822doi ach0018173 7aPBMS2bicssc a14-xxa32-xxa55-xx2msc10aSchubert Varieties, Equivariant Cohomology and Characteristic Classesh[electronic resource] :bImpanga 15 /cJarosław Buczyński, Mateusz Michałek, Elisa Postinghel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (354 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tIntroduction /rJarosław Buczyński, Mateusz Michałek, Elisa Postinghel --tFriedrich Hirzebruch – a handful of reminiscences /rPiotr Pragacz --tPieri rule for the factorial Schur $P$-functions /rSoojin Cho, Takeshi Ikeda --tRestriction varieties and the rigidity problem /rIzzet Coskun --tOn Plücker equations characterizing Grassmann cones /rLetterio Gatto, Parham Salehyan --tKempf–Laksov Schubert classes for even infinitesimal cohomology theories /rThomas Hudson, Tomoo Matsumura --tOn the multicanonical systems of quasi-elliptic surfaces in characteristic 3 /rToshiyuki Katsura --tCharacteristic classes of mixed Hodge modules and applications /rLaurentiu Maxim, Jörg Schürmann --tOn a certain family of $U(\mathfrak b)$-modules /rPiotr Pragacz --tEquivariant Chern–Schwartz–MacPherson classes in partial flag varieties: interpolation and formulae /rRichárd Rimányi, Alexander Varchenko --tThom polynomials in $\mathcal A$-classification I: counting singular projections of a surface /rTakahisa Sasajima, Toru Ohmoto --tSchubert polynomials and degeneracy locus formulas /rHarry Tamvakis --tHirzebruch $\chi_y$-genera of complex algebraic fiber bundles – the multiplicativity of the signature modulo 4 /rShoji Yokura --tPushing-forward Schur classes using iterated residues at infinity /rMagdalena Zielenkiewicz.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics.
This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010–2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic.07aAnalytic geometry2bicssc07aAlgebraic geometry2msc07aSeveral complex variables and analytic spaces2msc07aAlgebraic topology2msc1 aBuczyński, Jarosław,eeditor.1 aMichałek, Mateusz,eeditor.1 aPostinghel, Elisa,eeditor.40uhttps://doi.org/10.4171/182423cover imageuhttps://www.ems-ph.org/img/books/impanga_mini.jpg02489nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100003300220245009500253260008200348300003400430336002600464337002600490338003600516347002400552490005300576506006600629520110700695650002601802650002301828650005501851650004001906650002801946700002901974856003202003856006802035227-180108CH-001817-320180108234002.0a fot ||| 0|cr nn mmmmamaa180108e20180122sz fot ||| 0|eng d a978303719635970a10.4171/1352doi ach0018173 7aPBR2bicssc a11-xxa06-xxa13-xxa14-xx2msc1 aFujiwara, Kazuhiro,eauthor.10aFoundations of Rigid Geometry Ih[electronic resource] /cKazuhiro Fujiwara, Fumiharu Kato3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (863 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aRigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean
valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries.
In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate‘s original rigid analytic geometry,
V.G. Berkovich‘s analytic geometry and R. Huber‘s adic spaces. As a model example of applications, a proof of Nagata‘s compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost
self-contained.07aNumber theory2bicssc07aNumber theory2msc07aOrder, lattices, ordered algebraic structures2msc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc1 aKato, Fumiharu,eauthor.40uhttps://doi.org/10.4171/135423cover imageuhttps://www.ems-ph.org/img/books/fujiwara_mini.jpg02012nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002800199245008700227260008200314300003400396336002600430337002600456338003600482347002400518490008300542506006600625520083500691650002601526650002301552856003201575856006701607228-180207CH-001817-320180207233003.0a fot ||| 0|cr nn mmmmamaa180207e20180314sz fot ||| 0|eng d a978303719683070a10.4171/1832doi ach0018173 7aPBR2bicssc a11-xx2msc1 aBugeaud, Yann,eauthor.10aLinear Forms in Logarithms and Applicationsh[electronic resource] /cYann Bugeaud3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (240 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v281 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in $p$-adic logarithms) and how this theory applies to many Diophantine problems, including the effective resolution of Diophantine equations, the $abc$-conjecture, and upper bounds for the irrationality measure of some real numbers.
Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.07aNumber theory2bicssc07aNumber theory2msc40uhttps://doi.org/10.4171/183423cover imageuhttps://www.ems-ph.org/img/books/bugeaud_mini.jpg02699nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202245010200238260008200340300003400422336002600456337002600482338003600508347002400544490005600568505040100624506006601025520079101091650003101882650003101913650004401944650002301988650003802011650002802049700003202077700003102109700002702140856003202167856006602199229-180406CH-001817-320180406233001.0a fot ||| 0|cr nn mmmmamaa180406e20180424sz fot ||| 0|eng d a978303719684770a10.4171/1842doi ach0018173 7aPBCD2bicssc 7aPBMW2bicssc a03-xxa05-xxa12-xxa14-xx2msc10aLectures in Model Theoryh[electronic resource] /cFranziska Jahnke, Daniel Palacín, Katrin Tent3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (222 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aMünster Lectures in Mathematics (MLM) ;x2523-523000tAn introduction to stability theory /rDaniel Palacín --tGeometric stability theory /rMartin Bays --tNIP and definably amenable groups /rPierre Simon --tSome model theory of profinite groups /rTim Clausen, Katrin Tent --tAn introduction to valued fields /rFranziska Jahnke --tModel theory of valued fields /rMartin Hils --tAn introduction to motivic integration /rImmanuel Halupczok.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aModel theory is a thriving branch of mathematical logic with strong connections to other fields of mathematics. Its versatility has recently led to spectacular applications in areas ranging from diophantine geometry, algebraic number theory and group theory to combinatorics.
This volume presents lecture notes from a spring school in model theory which took place in Münster, Germany. The notes are aimed at PhD students but should also be accessible to undergraduates with some basic knowledge in model theory. They contain the core of stability theory (Bays, Palacín), two chapters connecting generalized stability theory with group theory (Clausen and Tent, Simon), as well as introductions to the model theory of valued fields (Hils, Jahnke) and motivic integration (Halupczok).07aMathematical logic2bicssc07aAlgebraic geometry2bicssc07aMathematical logic and foundations2msc07aCombinatorics2msc07aField theory and polynomials2msc07aAlgebraic geometry2msc1 aJahnke, Franziska,eeditor.1 aPalacín, Daniel,eeditor.1 aTent, Katrin,eeditor.40uhttps://doi.org/10.4171/184423cover imageuhttps://www.ems-ph.org/img/books/jahnke_mini.jpg02643nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245012000200260008200320300003400402336002600436337002600462338003600488347002400524490006100548505052000609506006601129520081301195650003402008650004202042700002802084700002802112700003102140856003202171856006602203230-180411CH-001817-320180411233001.0a fot ||| 0|cr nn mmmmamaa180411e20180430sz fot ||| 0|eng d a978303719685470a10.4171/1852doi ach0018173 7aPBFD2bicssc a20-xx2msc10aLocal Representation Theory and Simple Groupsh[electronic resource] /cRadha Kessar, Gunter Malle, Donna Testerman3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (369 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-517600tBasic local representation theory /rBurkhard Külshammer --tReduction theorems for some global–local conjectures /rBritta Späth --tA first guide to the character theory of finite groups of Lie type /rMeinolf Geck --tLectures on modular Deligne–Lusztig theory /rOlivier Dudas --tLocal methods for blocks of finite simple groups /rMarc Cabanes --tSimple groups, fixed point ratios and applications /rTimothy C. Burness --tApplications of character theory of finite simple groups /rMartin W. Liebeck.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe book contains extended versions of seven short lecture courses given during a semester programme on "Local Representation Theory and Simple Groups" held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These focussed on modular representation theory of finite groups, modern Clifford theoretic methods, the representation theory of finite reductive groups, as well as on various applications of character theory and representation theory, for example to base sizes and to random walks.
These lectures are intended to form a good starting point for graduate students and researchers who wish to familiarize themselves with the foundations of the topics covered here. Furthermore they give an introduction to current research directions, including the state of some open problems in the field.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc1 aKessar, Radha,eeditor.1 aMalle, Gunter,eeditor.1 aTesterman, Donna,eeditor.40uhttps://doi.org/10.4171/185423cover imageuhttps://www.ems-ph.org/img/books/kessar_mini.jpg05214nam a22004455a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245027000221260008200491300003400573336002600607337002600633338003600659347002400695490005400719505231700773506006603090520111303156650003504269650004004304650005504344650004604399650002604445700003004471700003504501700003304536700003504569700003504604700002904639856003204668856006804700231-180504CH-001817-320180504233001.0a fot ||| 0|cr nn mmmmamaa180504e20180530sz fot ||| 0|eng d a978303719686170a10.4171/1862doi ach0018173 7aPBKJ2bicssc a35-xxa15-xxa37-xxa42-xx2msc10aNon-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysish[electronic resource] :bThe Helge Holden Anniversary Volume /cFritz Gesztesy, Harald Hanche-Olsen, Espen R. Jakobsen, Yurii I. Lyubarskii, Nils Henrik Risebro, Kristian Seip3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (502 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tOptimal control of forward-backward stochastic Volterra equations /rNacira Agram, Bernt Øksendal, Samia Yakhlef --tA unified approach to infinite dimensional integrals of probabilistic and oscillatory type with applications to Feynman path integrals /rSergio Albeverio, Sonia Mazzucchi --tThe numbers lead a dance. Mathematics of the Sestina /rAlan R. Champneys, Poul G. Hjorth, Harry Man --tCompensated compactness in Banach spaces and weak rigidity of isometric immersions of manifolds /rGui-Qiang G. Chen, Siran Li --tThe initial-boundary-value problem for an Ostrovsky–Hunter type equation /rGiuseppe Maria Coclite, Lorenzo di Ruvo, Kenneth Hvistendahl Karlsen --tModeling crowd dynamics through hyperbolic – elliptic equations /rRinaldo M. Colombo, Maria Gokieli, Massimiliano D. Rosini --tOn the well-posedness of solutions with finite energy for nonlocal equations of porous medium type /rFélix del Teso, Jørgen Endal, Espen R. Jakobsen --tOn the spectrum of leaky surfaces with a potential bias /rPavel Exner --tOn the decay of almost periodic solutions of anisotropic degenerate parabolic-hyperbolic equations /rHermano Frid --tFactorizations and Hardy–Rellich-type inequalities /rFritz Gesztesy, Lance Littlejohn --tSymmetries and multipeakon solutions for the modified two-component Camassa–Holm system /rKatrin Grunert, Xavier Raynaud --tVanishing viscosity solutions of Riemann problems for models of polymer flooding /rGraziano Guerra, Wen Shen --tEfficient computation of all speed flows using an entropy stable shock-capturing space-time discontinuous Galerkin method /rAndreas Hiltebrand, Siddhartha Mishra --tDispersion estimates for spherical Schrödinger equations with critical angular momentum /rMarkus Holzleitner, Aleksey Kostenko, Gerald Teschl --tSixty years of moments for random matrices /rWerner Kirsch, Thomas Kriecherbauer --tBound states of Schrödinger type operators with Heisenberg sub-Laplacian /rAri Laptev, Andrei Velicu --tOn Holden’s seven guidelines for scientific computing and development of open-source community software /rKnut-Andreas Lie --tSharp uniqueness results for discrete evolutions /rYurii I. Lyubarskii, Eugenia Malinnikova --tSpatial analyticity of solutions to nonlinear dispersive PDE /rSigmund Selberg.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in non-linear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holden’s longstanding research interests. Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinite-dimensional analysis, linear and nonlinear PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference Non-linear PDEs, Mathematical Physics and Stochastic Analysis, held at NTNU, Trondheim, July 4–7, 2016 (https://wiki.math.ntnu.no/holden60).
The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory.
This collection of research papers will be of interest to any active scientist working in one of the above mentioned areas.07aDifferential equations2bicssc07aPartial differential equations2msc07aLinear and multilinear algebra; matrix theory2msc07aDynamical systems and ergodic theory2msc07aFourier analysis2msc1 aGesztesy, Fritz,eeditor.1 aHanche-Olsen, Harald,eeditor.1 aJakobsen, Espen R.,eeditor.1 aLyubarskii, Yurii I.,eeditor.1 aRisebro, Nils Henrik,eeditor.1 aSeip, Kristian,eeditor.40uhttps://doi.org/10.4171/186423cover imageuhttps://www.ems-ph.org/img/books/gesztesy_mini.jpg02352nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003300200245009800233260008200331300003400413336002600447337002600473338003600499347002400535490003900559506006600598520117500664650003401839650004201873856003201915856006701947232-180719CH-001817-320180719233001.0a fot ||| 0|cr nn mmmmamaa180719e20180615sz fot ||| 0|eng d a978303719687870a10.4171/1872doi ach0018173 7aPBFD2bicssc a20-xx2msc1 aMarquis, Timothée,eauthor.10aAn Introduction to Kac–Moody Groups over Fieldsh[electronic resource] /cTimothée Marquis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (343 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe interest for Kac–Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic.
The aims of this book are twofold:
- to offer an accessible, reader-friendly and self-contained introduction to Kac–Moody algebras and groups;
- to clean the foundations and to provide a unified treatment of the theory.
The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac–Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac–Moody groups. It is complemented by two appendices, respectively offering introductions to affine group schemes and to the theory of buildings. Many
exercises are included, accompanying the readers throughout their journey.
The book assumes only a minimal background in linear algebra and basic topology, and is addressed to anyone interested in learning about Kac–Moody algebras and/or groups, from graduate (master) students to specialists.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc40uhttps://doi.org/10.4171/187423cover imageuhttps://www.ems-ph.org/img/books/marquis_mini.jpg02380nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002700213245008800240260008200328300003400410336002600444337002600470338003600496347002400532490003900556506006600595520111900661650004101780650002301821650002301844650005501867856003201922856006401954233-180518CH-001817-320180518233001.0a fot ||| 0|cr nn mmmmamaa180518e20180530sz fot ||| 0|eng d a978303719688570a10.4171/1882doi ach0018173 7aPBV2bicssc a05-xxa11-xxa15-xx2msc1 aNica, Bogdan,eauthor.10aA Brief Introduction to Spectral Graph Theoryh[electronic resource] /cBogdan Nica3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (168 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSpectral graph theory starts by associating matrices to graphs – notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial.
This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions.
The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained.07aCombinatorics & graph theory2bicssc07aCombinatorics2msc07aNumber theory2msc07aLinear and multilinear algebra; matrix theory2msc40uhttps://doi.org/10.4171/188423cover imageuhttps://www.ems-ph.org/img/books/nica_mini.jpg02184nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100002700200245010800227260008200335300003400417336002600451337002600477338003600503347002400539490005100563506006600614520099200680650003401672650004201706856003201748856006601780234-180509CH-001817-320180509233001.0a fot ||| 0|cr nn mmmmamaa180509e20180525sz fot ||| 0|eng d a978303719689270a10.4171/1892doi ach0018173 7aPBFD2bicssc a20-xx2msc1 aThomas, Anne,eauthor.10aGeometric and Topological Aspects of Coxeter Groups and Buildingsh[electronic resource] /cAnne Thomas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (160 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aCoxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them.
These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings.
This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.07aGroups & group theory2bicssc07aGroup theory and generalizations2msc40uhttps://doi.org/10.4171/189423cover imageuhttps://www.ems-ph.org/img/books/thomas_mini.jpg03176nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184245016400206260008200370300003400452336002600486337002600512338003600538347002400574490005400598505078000652506006601432520097401498650002602472650002302498650004002521700003102561700002602592700002502618700003802643856003202681856006502713235-200417CH-001817-320200417233004.0a fot ||| 0|cr nn mmmmamaa200417e20200520sz fot ||| 0|eng d a978303719698470a10.4171/1982doi ach0018173 7aPBR2bicssc a11-xxa13-xx2msc10a$t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspectsh[electronic resource] /cGebhard Böckle, David Goss, Urs Hartl, Matthew A. Papanikolas3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (473 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tA rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives /rW. Dale Brownawell, Matthew A. Papanikolas --tPink’s theory of Hodge structures and the Hodge conjecture over function fields /rUrs Hartl, Ann-Kristin Juschka --tLocal shtukas, Hodge–Pink structures and Galois representations /rUrs Hartl, Wansu Kim --tFrobenius difference equations and difference Galois groups /rChieh-Yu Chang --tAn introduction to Mahler’s method for transcendence and algebraic independence /rFederico Pellarin --tAutomata methods in transcendence /rDinesh S. Thakur --tAspects of Iwasawa theory over function fields /rAndrea Bandini, Francesc Bars, Ignazio Longhi --t1-$t$-Motifs /rLenny Taelman --tMultizeta in function field arithmetic /rDinesh S. Thakur.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume contains research and survey articles on Drinfeld modules, Anderson $t$-modules and $t$-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pink’s theory of Hodge structures attached to Drinfeld modules and $t$-motives. Also included are survey articles on the function field analogue of Fontaine’s theory of $p$-adic crystalline Galois representations and on transcendence methods over function fields, encompassing the theories of Frobenius difference equations, automata theory, and Mahler’s method. In addition, this volume contains a small number of research articles on function field Iwasawa theory, 1-$t$-motifs, and multizeta values.
This book is a useful source for learning important techniques and an effective reference for all researchers working in or interested in the area of function field arithmetic, from graduate students to established experts.07aNumber theory2bicssc07aNumber theory2msc07aCommutative rings and algebras2msc1 aBöckle, Gebhard,eeditor.1 aGoss, David,eeditor.1 aHartl, Urs,eeditor.1 aPapanikolas, Matthew A.,eeditor.40uhttps://doi.org/10.4171/198423cover imageuhttps://www.ems-ph.org/img/books/hartl_mini.jpg02322nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003400207245012100241260008200362300003400444336002600478337002600504338003600530347002400566490004000590506006600630520107800696650003501774650004001809650002601849856003201875856006501907236-180910CH-001817-320180910233004.0a fot ||| 0|cr nn mmmmamaa180910e20180930sz fot ||| 0|eng d a978303719690870a10.4171/1902doi ach0018173 7aPBKJ2bicssc a35-xxa31-xx2msc1 aMaz'ya, Vladimir G.,eauthor.10aBoundary Behavior of Solutions to Elliptic Equations in General Domainsh[electronic resource] /cVladimir G. Maz'ya3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (441 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v301 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present book is a detailed exposition of the author and his collaborators’ work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as “piecewise smoothness” or being a “Lipschitz graph”. The description of the boundary behavior of such solutions is one of the most difficult problems in the theory of partial differential equations. After the famous Wiener test, the main contributions to this area were made by the author. In particular, necessary and sufficient conditions for the validity of imbedding theorems are given, which provide criteria for the unique solvability of boundary value problems of second and higher order elliptic equations. Another striking result is a test for the regularity of a boundary point for polyharmonic equations.
The book will be interesting and useful for a wide audience. It is intended for specialists and graduate students working in the theory of partial differential equations.07aDifferential equations2bicssc07aPartial differential equations2msc07aPotential theory2msc40uhttps://doi.org/10.4171/190423cover imageuhttps://www.ems-ph.org/img/books/mazya_mini.jpg02800nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003100200245017000231260008200401300003400483336002600517337002600543338003600569347002400605490004000629506006600669520150800735650003502243650004002278700003402318856003202352856006602384237-190109CH-001817-320190109233003.0a fot ||| 0|cr nn mmmmamaa190109e20190131sz fot ||| 0|eng d a978303719691570a10.4171/1912doi ach0018173 7aPBKJ2bicssc a35-xx2msc1 aGel'man, Igor W.,eauthor.10aEstimates for Differential Operators in Half-spaceh[electronic resource] :bTranslated from the German by Darya Apushkinskaya /cIgor W. Gel'man, Vladimir G. Maz'ya3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (264 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v311 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aInequalities for differential operators play a fundamental role in the modern theory of partial differential equations. Among the numerous applications of such inequalities are existence and uniqueness theorems, error estimates for numerical approximations of solutions and for residual terms in asymptotic formulas, as well as results on the structure of the spectrum. The inequalities cover a wide range of differential operators, boundary conditions and norms of the corresponding function spaces.
The book focuses on estimates up to the boundary of a domain. It contains a great variety of inequalities for differential and pseudodifferential operators with constant coefficients. Results of final character are obtained, without any restrictions on the type of differential operators. Algebraic necessary and sufficient conditions for the validity of the corresponding a priori estimates are presented. General criteria are systematically applied to particular types of operators found in classical equations and systems of mathematical physics (such as Lame’s system of static elasticity theory or the linearized Navier–Stokes system), Cauchy–Riemann’s operators, Schrödinger operators, among others. The well-known results of Aronszajn, Agmon–Douglis–Nirenberg and Schechter fall into the general scheme, and sometimes are strengthened.
The book will be interesting and useful to a wide audience, including graduate students and specialists in the theory of differential equations.07aDifferential equations2bicssc07aPartial differential equations2msc1 aMaz'ya, Vladimir G.,eauthor.40uhttps://doi.org/10.4171/191423cover imageuhttps://www.ems-ph.org/img/books/gelman_mini.jpg02939nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003900207245008400246260008200330300003400412336002600446337002600472338003600498347002400534490005300558506006600611520170100677650003502378650004002413650002502453856003202478856007902510238-181122CH-001817-320181122233002.0a fot ||| 0|cr nn mmmmamaa181122e20190107sz fot ||| 0|eng d a978303719692270a10.4171/1922doi ach0018173 7aPBKJ2bicssc a35-xxa76-xx2msc1 aChristodoulou, Demetrios,eauthor.10aThe Shock Development Problemh[electronic resource] /cDemetrios Christodoulou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (932 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis monograph addresses the problem of the development of shocks in the context of the Eulerian equations of the mechanics of compressible fluids. The mathematical problem is that of an initial-boundary value problem for a nonlinear hyperbolic system of partial differential equations with a free boundary and singular initial conditions.
The free boundary is the shock hypersurface and the boundary conditions are jump conditions relative to a prior solution, conditions following from the integral form of the mass, momentum and energy conservation laws. The prior solution is provided by the author‘s previous work which studies the maximal classical development of smooth initial data. New geometric and analytic methods are introduced to solve the problem. Geometry enters as the acoustical structure, a Lorentzian metric structure defined on the spacetime manifold by the fluid. This acoustical structure interacts with the background spacetime structure. Reformulating the equations as two coupled first order systems, the characteristic system, which is fully nonlinear, and the wave system, which is quasilinear, a complete regularization of the problem is achieved.
Geometric methods also arise from the need to treat the free boundary. These methods involve the concepts of bi-variational stress and of variation fields. The main new analytic method arises from the need to handle the singular integrals appearing in the energy identities. Shocks being an ubiquitous phenomenon, occuring also in magnetohydrodynamics, nonlinear elasticity, and the electrodynamics of noninear media, the methods developed in this monograph are likely to be found relevant in these fields as well.07aDifferential equations2bicssc07aPartial differential equations2msc07aFluid mechanics2msc40uhttps://doi.org/10.4171/192423cover imageuhttps://www.ems-ph.org/img/books/christodoulou_shock_mini.jpg03198nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003000214245017900244260008200423300003400505336002600539337002600565338003600591347002400627490005300651506006600704520177500770650002802545650002502573650004002598650005202638700003502690856003202725856006702757239-190314CH-001817-320190314233005.0a fot ||| 0|cr nn mmmmamaa190314e20190408sz fot ||| 0|eng d a978303719693970a10.4171/1932doi ach0018173 7aPHDF2bicssc a76-xxa35-xxa82-xx2msc1 aArsénio, Diogo,eauthor.10aFrom the Vlasov–Maxwell–Boltzmann System to Incompressible Viscous Electro-magneto-hydrodynamicsh[electronic resource] :bVolume 1 /cDiogo Arsénio, Laure Saint-Raymond3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (418 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Vlasov–Maxwell–Boltzmann system is a microscopic model to describe the dynamics of charged particles subject to self-induced electromagnetic forces. At the macroscopic scale, in the incompressible viscous fluid limit the evolution of the plasma is governed by equations of Navier–Stokes–Fourier type, with some electromagnetic forcing that may take on various forms depending on the number of species and on the strength of the interactions.
From the mathematical point of view, these models have very different behaviors. Their analysis therefore requires various mathematical methods which this book aims to present in a systematic, painstaking, and exhaustive way.
The first part of this work is devoted to the systematic formal analysis of viscous hydrodynamic limits of the Vlasov–Maxwell–Boltzmann system, leading to a precise classification of physically relevant models for viscous incompressible plasmas, some of which have not previously been described in the literature.
In the second part, the convergence results are made precise and rigorous, assuming the existence of renormalized solutions for the Vlasov–Maxwell–Boltzmann system. The analysis is based essentially on the scaled entropy inequality. Important mathematical tools are introduced, with new developments used to prove these convergence results (Chapman–Enskog-type decomposition and regularity in the $v$ variable, hypoelliptic transfer of compactness, analysis of high frequency time oscillations, and more).
The third and fourth parts (which will be published in a second volume) show how to adapt the arguments presented in the conditional case to deal with a weaker notion of solutions to the Vlasov–Maxwell–Boltzmann system, the existence of which is known.07aFluid mechanics2bicssc07aFluid mechanics2msc07aPartial differential equations2msc07aStatistical mechanics, structure of matter2msc1 aSaint-Raymond, Laure,eauthor.40uhttps://doi.org/10.4171/193423cover imageuhttps://www.ems-ph.org/img/books/arsenio_mini.jpg01984nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002800207245009200235260008200327300003400409336002600443337002600469338003600495347002400531490006100555506006600616520075500682650003201437650002901469650002601498856003201524856007801556241-181122CH-001817-320181122233002.0a fot ||| 0|cr nn mmmmamaa181122e20190131sz fot ||| 0|eng d a978303719695370a10.4171/1952doi ach0018173 7aPBKG2bicssc a46-xxa42-xx2msc1 aTriebel, Hans,eauthor.10aFunction Spaces with Dominating Mixed Smoothnessh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (210 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe first part of this book is devoted to function spaces in Euclidean $n$-space with dominating mixed smoothness. Some new properties are derived and applied in the second part where weighted spaces with dominating mixed smoothness in arbitrary bounded domains in Euclidean $n$-space are introduced and studied. This includes wavelet frames, numerical integration and discrepancy, measuring the deviation of sets of points from uniformity.
These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov–Sobolev type. In particular, it will be of interest for researchers dealing with approximation theory, numerical integration and discrepancy.07aFunctional analysis2bicssc07aFunctional analysis2msc07aFourier analysis2msc40uhttps://doi.org/10.4171/195423cover imageuhttps://www.ems-ph.org/img/books/triebel_smoothness_mini.jpg03826nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001700183084003600200245011100236260008200347300003400429336002600463337002600489338003600515347002400551490008300575505156700658506006602225520076002291650002403051650003103075650004403106650001803150650003803168650003103206700003103237700003703268856003203305856006703337243-190219CH-001817-320190219233004.0a fot ||| 0|cr nn mmmmamaa190219e20190227sz fot ||| 0|eng d a978303719696070a10.4171/1962doi ach0018173 7aPB2bicssc 7aPBCD2bicssc a03-xxa51-xxa52-xxa53-xx2msc10aEighteen Essays in Non-Euclidean Geometryh[electronic resource] /cVincent Alberge, Athanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (475 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v2900tArea in non-Euclidean geometry /rNorbert A’Campo, Athanase Papadopoulos --tThe area formula for hyperbolic triangles /rElena Frenkel, Weixu Su --tOn a problem of Schubert in hyperbolic geometry /rVincent Alberge, Elena Frenkel --tOn a theorem of Lambert: medians in spherical and hyperbolic geometries /rHimalaya Senapati --tInscribing a triangle in a circle in spherical geometry /rHimalaya Senapati --tMonotonicity in spherical and hyperbolic triangles /rHimalaya Senapati --tDe Tilly’s mechanical view on hyperbolic and spherical geometries /rDmitriy Slutskiy --tThe Gauss–Bonnet theorem and the geometry of surfaces /rSon Lam Ho --tOn the non-existence of a perfect map from the 2-sphere to the Euclidean plane /rCharalampos Charitos, Ioannis Papadoperakis --tArea preserving maps from the sphere to the Euclidean plane /rCharalampos Charitos --tArea and volume in non-Euclidean geometry /rNikolay Abrosimov, Alexander Mednykh --tStatics and kinematics of frameworks in Euclidean and non-Euclidean geometry /rIvan Izmestiev --tContributions to non-Euclidean geometry I /rEduard Study --tNotes on Eduard Study’s paper “Contributions to non-Euclidean geometry I” /rAnnette A’Campo-Neuen, Athanase Papadopoulos --tSpherical and hyperbolic conics /rIvan Izmestiev --tSpherical, hyperbolic, and other projective geometries: convexity, duality, transitions /rFrançois Fillastre, Andrea Seppi --tHermitian trigonometry /rBoumediene Et-Taoui --tA theorem on equiareal triangles with a fixed base /rVictor Pambuccian.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book consists of a series of self-contained essays in non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and some axiomatically defined geometries. Some of these essays deal with very classical questions and others address problems that are at the heart of present day research, but all of them are concerned with fundamental topics.
All the essays are self-contained and most of them can be understood by the general educated mathematician. They should be useful to researchers and to students of non-Euclidean geometry, and they are intended to be references for the various topics they present.07aMathematics2bicssc07aMathematical logic2bicssc07aMathematical logic and foundations2msc07aGeometry2msc07aConvex and discrete geometry2msc07aDifferential geometry2msc1 aAlberge, Vincent,eeditor.1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/196423cover imageuhttps://www.ems-ph.org/img/books/alberge_mini.jpg04125nam a22004335a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001400168072001600182084003600198245013800234260008200372300003400454336002600488337002600514338003600540347002400576490005400600505153800654506006602192520101202258650003603270650004503306650004803351650002303399650004203422650003803464700002903502700003203531700003103563856003203594856006503626244-190619CH-001817-320190619233003.0a fot ||| 0|cr nn mmmmamaa190619e20190705sz fot ||| 0|eng d a978303719697770a10.4171/1972doi ach0018173 7aP2bicssc 7aPBK2bicssc a58-xxa11-xxa20-xxa52-xx2msc10aSpectral Structures and Topological Methods in Mathematicsh[electronic resource] /cMichael Baake, Friedrich Götze, Werner Hoffmann3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (433 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tConvergence and asymptotic approximations to universal distributions in probability /rFriedrich Götze, Holger Kösters --tKolmogorov operators and SPDEs /rMichael Röckner --tAnalysis and stochastic processes on metric measure spaces /rAlexander Grigor'yan --tMarkov evolutions in spatial ecology: From microscopic dynamics to kinetics /rYuri Kondratiev, Oleksandr Kutoviy, Pavlo Tkachov --tMetastability in randomly perturbed dynamical systems: Beyond large-deviation theory /rBarbara Gentz --tComputation and stability of waves in equivariant evolution equations /rWolf-Jürgen Beyn, Denny Otten --tInitial value problems for nonlinear dispersive equations at critical regularity /rSebastian Herr --tVariational solutions to nonlocal problems /rMoritz Kassmann --tSpectral and arithmetic structures in aperiodic order /rMichael Baake, Franz Gähler, Christian Huck, Peter Zeiner --tAffine special Kähler structures in real dimension two /rMartin Callies, Andriy Haydys --tNon-crossing partitions /rBarbara Baumeister, Kai-Uwe Bux, Friedrich Götze, Dawid Kielak, Henning Krause --tThe derived category of the projective line /rHenning Krause, Greg Stevenson --tHigher finiteness properties of braided groups /rKai-Uwe Bux --tZeta functions and the trace formula /rWerner Hoffmann --tZeta functions of groups and rings – functional equations and analytic uniformity /rChristopher Voll --tConjectures of Brumer, Gross and Stark /rAndreas Nickel --tDisplays and $p$-divisible groups /rThomas Zink.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied. The topics are based on work done in the Collaborative Research Centre (SFB) 701.
Notable examples are non-crossing partitions, which connect representation theory, braid groups, non-commutative probability as well as spectral distributions of random matrices. The local distributions of such spectra are universal, also representing the local distribution of zeros of $L$-functions in number theory.
An overarching method is the use of zeta functions in the asymptotic counting of sublattices, group representations etc. Further examples connecting probability, analysis, dynamical systems and geometry are generating operators of deterministic or stochastic processes, stochastic differential equations, and fractals, relating them to the local geometry of such spaces and the convergence to stable and semi-stable states.07aMathematics and science2bicssc07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aNumber theory2msc07aGroup theory and generalizations2msc07aConvex and discrete geometry2msc1 aBaake, Michael,eeditor.1 aGötze, Friedrich,eeditor.1 aHoffmann, Werner,eeditor.40uhttps://doi.org/10.4171/197423cover imageuhttps://www.ems-ph.org/img/books/baake_mini.jpg02569nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100003300213245010700246260008200353300003400435336002600469337002600495338003600521347002400557490005000581506006600631520125200697650004801949650002401997650004002021650004802061856003202109856006602141245-191015CH-001817-320191015233004.0a fot ||| 0|cr nn mmmmamaa191015e20191115sz fot ||| 0|eng d a978303719594970a10.4171/0942doi ach0018173 7aPHT2bicssc a81-xxa35-xxa58-xx2msc1 aGérard, Christian,eauthor.10aMicrolocal Analysis of Quantum Fields on Curved Spacetimesh[electronic resource] /cChristian Gérard3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (228 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aESI Lectures in Mathematics and Physics (ESI)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aWe focus on free fields and the corresponding quasi-free states and more precisely on Klein–Gordon fields and Dirac fields. The first chapters are devoted to preliminary material on CCR*-algebras, quasi-free states, wave equations on Lorentzian manifolds, microlocal analysis and to the important Hadamard condition, characterizing physically acceptable quantum states on curved spacetimes. In the later chapters more advanced tools of microlocal analysis, like the global pseudo-differential calculus on non-compact manifolds, are used to construct and study Hadamard states for Klein–Gordon fields by various methods, in particular by scattering theory and by Wick rotation arguments. In the last chapter the fermionic theory of free Dirac quantum fields on Lorentzian manifolds is described in some detail.
This monograph is addressed to both mathematicians and mathematical physicists. The first will be able to use it as a rigorous exposition of free quantum fields on curved spacetimes and as an introduction to some interesting and physically important problems arising in this domain. The second may find this text a useful introduction and motivation to the use of more advanced tools of microlocal analysis in this area of research.07aQuantum physics (quantum mechanics)2bicssc07aQuantum theory2msc07aPartial differential equations2msc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/094423cover imageuhttps://www.ems-ph.org/img/books/gerard_mini.jpg03410nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001400168084001500182100003300197245017700230260008200407300003400489336002600523337002600549338003600575347002400611490005600635506006600691520201200757650003602769650003102805700003102836700004002867700003202907856003202939856006502971246-191022CH-001817-320191022233003.0a fot ||| 0|cr nn mmmmamaa191022e20191108sz fot ||| 0|eng d a978303719699170a10.4171/1992doi ach0018173 7aP2bicssc a01-xx2msc1 aJaëck, Frédéric,eauthor.10aGösta Mittag-Leffler and Vito Volterra. 40 Years of Correspondenceh[electronic resource] /cFrédéric Jaëck, Laurent Mazliak, Emma Sallent Del Colombo, Rossana Tazzioli3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (438 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present book contains the voluminous correspondence exchanged between the Swedish mathematician Gösta Mittag-Leffler and his younger Italian colleague Vito Volterra spanning a period of almost forty years at the end of the 19th and beginning of the 20th centuries. The relationship between the two men is remarkable for both personal and scientific reasons. Mittag-Leffler met Volterra for the first time as a brilliant young student of Ulisse Dini in Pisa. He was soon captivated by the creativity and the skills of the young man, and eventually became his mentor. Being himself at the center of a major scientific network, Mittag-Leffler introduced Volterra to the major mathematicians of the time, especially the Germans (Weierstrass, Klein, Cantor…) and French (Darboux, Jordan…). In a few years, Volterra became the most prominent Italian mathematician and forged his own network of scientists all over Europe, and even in the United States which he was one of the first major European mathematicians to visit. Despite their difference in age, both men developed a deep and faithful friendship and their letters reflect the variety of themes of their exchanges. Of course, mathematics was the most prominent, and both men often used the letters as a first draft of their ideas and the addressee as a first judge of their soundness. Besides mathematics, they also touched upon many aspects of both private and public life: matrimony, children, holidays, politics and so on. This vast set of letters affords the reader a general overview of mathematical life at the turn of the 19th century and an appreciation of the European intellectual spirit which came to an end, or at least suffered a drastic turn, when the Great War broke out. Volterra and Mittag-Leffler’s exchanges illustrate how general analysis, especially functional analysis, gained a dramatic momentum during those years, and how Volterra became one of the major leaders of the topic, opening the path for several fundamenta...07aMathematics and science2bicssc07aHistory and biography2msc1 aMazliak, Laurent,eauthor.1 aSallent Del Colombo, Emma,eauthor.1 aTazzioli, Rossana,eauthor.40uhttps://doi.org/10.4171/199423cover imageuhttps://www.ems-ph.org/img/books/jaeck_mini.jpg02501nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100002700200245007800227260008200305300003400387336002600421337002600447338003600473347002400509490005100533506006600584520128900650650003501939650004601974700003302020856003202053856006602085247-191101CH-001817-320191101233002.0a fot ||| 0|cr nn mmmmamaa191101e20191210sz fot ||| 0|eng d a978303719700470a10.4171/2002doi ach0018173 7aPBKJ2bicssc a37-xx2msc1 aFisher, Todd,eauthor.10aHyperbolic Flowsh[electronic resource] /cTodd Fisher, Boris Hasselblatt3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (737 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consultation with experts is often needed to find them.
This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. Therefore, the book can be used both as a textbook – for either courses or self-study – and as a reference for students and researchers.
There are a number of new results in the book, and many more are hard to locate elsewhere, often having appeared only in the original research literature. This book makes them all easily accessible and does so in the context of a comprehensive and coherent presentation of the theory of hyperbolic flows.07aDifferential equations2bicssc07aDynamical systems and ergodic theory2msc1 aHasselblatt, Boris,eauthor.40uhttps://doi.org/10.4171/200423cover imageuhttps://www.ems-ph.org/img/books/fisher_mini.jpg05377nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002600133040001400159072001400173084001500187245017100202260008200373300003500455336002600490337002600516338003600542347002400578505258300602506006603185520159103251650003604842650002604878700003004904856003704934856006804971248-210806CH-001817-320210806234503.0a fot ||| 0|cr nn mmmmamaa210806e20210913sz fot ||| 0|eng d a978398547506370a10.4171/Automata2doi ach0018173 7aP2bicssc a68-xx2msc10aHandbook of Automata Theoryh[electronic resource] :bVolume I. Theoretical Foundations Volume II. Automata in Mathematics and Selected Applications /cJean-Éric Pin3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (1608 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda00tFinite automata /rJean-Éric Pin --tAutomata and rational expressions /rJacques Sakarovitch --tFinite transducers and rational transductions /rTero Harju, Juhani Karhumäki --tWeighted automata /rManfred Droste, Dietrich Kuske --tMax-plus automata /rSylvain Lombardy, Jean Mairesse --tω-Automata /rThomas Wilke, Sven Schewe --tAutomata on finite trees /rChristof Löding, Wolfgang Thomas --tAutomata on infinite trees /rChristof Löding --tTwo-dimensional models /rStefano Crespi Reghizzi, Dora Giammarresi, Violetta Lonati --tMinimisation of automata /rJean Berstel, Luc Boasson, Olivier Carton, Isabelle Fagnot --tLearning algorithms /rHenrik Björklund, Johanna Björklund, Wim Martens --tDescriptional complexity of regular languages /rHermann Gruber, Markus Holzer, Martin Kutrib --tEnumerating regular expressions and their languages /rHermann Gruber, Jonathan Lee, Jeffrey Shallit --tCircuit complexity of regular languages /rMichal Koucký --tČerný’s conjecture and the road colouring problem /rJarkko Kari, Mikhail V. Volkov --tVarieties /rHoward Straubing, Pascal Weil --tProfinite topologies /rJorge Almeida, Alfredo Costa --tThe factorisation forest theorem /rThomas Colcombet --tWadge–Wagner hierarchies /rJacques Duparc --tEquational theories for automata /rZoltán Ésik --tLanguage equations /rMichal Kunc, Alexander Okhotin --tAlgebra for trees /rMikołaj Bojańczyk --tRational subsets of groups /rLaurent Bartholdi, Pedro Silva --tGroups defined by automata /rLaurent Bartholdi, Pedro Silva --tAutomata in number theory /rBoris Adamczewski, Jason Bell --tOn Cobham’s theorem /rFabien Durand, Michel Rigo --tSymbolic dynamics /rMarie-Pierre Béal, Jean Berstel, Søren Eilers, Dominique Perrin --tAutomatic structures /rSasha Rubin --tAutomata and finite model theory /rWouter Gelade, Thomas Schwentick --tFinite automata, image manipulation, and automatic real functions /rJuhani Karhumäki, Jarkko Kari --tCommunicating automata /rDietrich Kuske, Anca Muscholl --tSymbolic methods and automata /rBernard Boigelot --tSynthesis with finite automata /rIgor Walukiewicz --tTimed automata /rPatricia Bouyer --tHigher-order recursion schemes and their automata models /rArnaud Carayol, Olivier Serre --tAnalysis of probabilistic processes and automata theory /rKousha Etessami --tNatural language parsing /rMark-Jan Nederhof, Giorgio Satta --tVerification /rJavier Esparza, Orna Kupferman, Moshe Y. Vardi --tAutomata and quantum computing /rAndris Ambainis, Abuzer Yakaryılmaz.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAutomata theory is a subject of study at the crossroads of mathematics, theoretical
computer science, and applications. In its core it deals with abstract models of systems whose behaviour is
based on transitions between states, and it develops methods for the description, classification, analysis, and
design of such systems.
The Handbook of Automata Theory gives a comprehensive overview of current research in automata theory,
and is aimed at a broad readership of researchers and graduate students in mathematics and computer
science.
Volume I is divided into three parts. The first part presents various types of automata: automata on words,
on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional
models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata
theory are covered in the third part.
Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group
theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further
applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed
automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing,
formal verification of programs and quantum computing.
The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of
contents for each one, as well as a detailed subject index.07aMathematics and science2bicssc07aComputer science2msc1 aPin, Jean-Éric,eeditor.40uhttps://doi.org/10.4171/Automata423cover imageuhttps://www.ems-ph.org/img/books/Pin-Vol1_mini.jpg05232nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185245009600221260008200317300003400399336002600433337002600459338003600485347002400521490008300545505247200628506006603100520133303166650003204499650004104531650002804572650005504600650004604655700003704701856003204738856007604770250-200117CH-001817-320200117233001.0a fot ||| 0|cr nn mmmmamaa200117e20200215sz fot ||| 0|eng d a978303719703570a10.4171/2032doi ach0018173 7aPBKG2bicssc a30-xxa14-xxa32-xxa37-xx2msc10aHandbook of Teichmüller Theory, Volume VIIh[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (626 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v3000tIntroduction to Teichmüller theory, old and new, VII /rAthanase Papadopoulos --tThe Deligne–Mumford compactification and crystallographic groups /rYukio Matsumoto --tComplex geometry of Teichmüller domains /rSubhojoy Gupta, Harish Seshadri --tHolomorphic quadratic differentials in Teichmüller theory /rSubhojoy Gupta --tMostow strong rigidity of locally symmetric spaces revisited /rLizhen Ji --tModels of ends of hyperbolic 3-manifolds. A survey /rMahan Mj --tUniversal Teichmüller space as a non-trivial example of infinite-dimensional complex manifolds /rArmen Sergeev --tGeneralized conformal barycentric extensions of circle maps /rJun Hu --tHiggs bundles and higher Teichmüller spaces /rÓscar García Prada --tA note on Nicolas-Auguste Tissot: at the origin of quasiconformal mappings /rAthanase Papadopoulos --tMemories of Herbert Grötzsch /rReiner Kühnau --tA note about Mikhaïl Lavrentieff and his world of analysis in the Soviet Union /rAthanase Papadopoulos, Galina Sinkevich --tA letter /rOswald Teichmüller --tOn some extremal problems of the conformal mapping /rHerbert Grötzsch --tOn some extremal problems of the conformal mapping II /rHerbert Grötzsch --tOn the distortion of schlicht non-conformal mappings and on a related extension of Picard’s theorem /rHerbert Grötzsch --tOn the distortion of non-conformal schlicht mappings of multiply-connected schlicht regions /rHerbert Grötzsch --tOn closest-to-conformal mappings /rHerbert Grötzsch --tOn five papers by Herbert Grötzsch /rVincent Alberge, Athanase Papadopoulos --tOn a class of continuous representations /rMikhaïl Lavrentieff --tA commentary on Lavrentieff’s paper "Sur une classe de représentations continues" /rVincent Alberge, Athanase Papadopoulos --tAn application of quasiconformal mappings to the type problem /rOswald Teichmüller --tInvestigations on conformal and quasiconformal mappings /rOswald Teichmüller --tSimple examples for value distribution /rOswald Teichmüller --tTeichmüller’s work on the type problem /rVincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos --tA Commentary on Teichmüller’s paper "Untersuchungen über konforme und quasikonforme Abbildungen" /rVincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos --tValue distribution theory and Teichmüller’s paper "Einfache Beispiele zur Wertverteilungslehre" /rAthanase Papadopoulos.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present volume of the Handbook of Teichmüller theory is divided into three parts.
The first part contains surveys on various topics in Teichmüller theory, including the complex structure of Teichmüller space, the Deligne–Mumford compactification of the moduli space, holomorphic quadratic differentials, Kleinian groups, hyperbolic 3-manifolds and the ending lamination theorem, the universal Teichmüller space, barycentric extensions of maps of the circle, and the theory of Higgs bundles.
The second part consists of three historico-geometrical articles on Tissot (a precursor of the theory of quasiconfomal mappings), Grötzsch and Lavrentieff, the two main founders of the modern theory of quasiconformal mappings.
The third part comprises English translations of five papers by Grötzsch, a paper by Lavrentieff, and three papers by Teichmüller. These nine papers are foundational essays on the theories of conformal invariants and quasiconformal mappings, with applications to conformal geometry, to the type problem and to Nevanlinna's theory. The papers are followed by commentaries that highlight the relations between them and between later works on the subject. These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory.07aFunctional analysis2bicssc07aFunctions of a complex variable2msc07aAlgebraic geometry2msc07aSeveral complex variables and analytic spaces2msc07aDynamical systems and ergodic theory2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/203423cover imageuhttps://www.ems-ph.org/img/books/papadopoulos-vii_mini.jpg03187nam a22004455a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001500168072001700183084003600200245018700236260008200423300003400505336002600539337002600565338003600591347002400627490008300651505067600734506006601410520083701476650002402313650003502337650002402372650002302396650004102419650004602460700003502506700003302541700003302574700003202607856003202639856007002671251-200122CH-001817-320200122233001.0a fot ||| 0|cr nn mmmmamaa200122e20200228sz fot ||| 0|eng d a978303719704270a10.4171/2042doi ach0018173 7aPB2bicssc 7aPBKJ2bicssc a81-xxa05-xxa34-xxa37-xx2msc10aAlgebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)h[electronic resource] :bVolume 1 /cFrédéric Chapoton, Frédéric Fauvet, Claudia Malvenuto, Jean-Yves Thibon3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (354 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v3100tShuffle quadri-algebras and concatenation /rMohamed Belhaj Mohamed, Dominique Manchon --tStructure theorems for dendriform and tridendriform algebras /rEmily Burgunder, Bérénice Delcroix-Oger --tA group-theoretical approach to conditionally free cumulants /rKurusch Ebrahimi-Fard, Frédéric Patras --tThe Natural Growth Scale /rJean Ecalle --tRealizations of Hopf algebras of graphs by alphabets /rLoïc Foissy --tDuplicial algebras, parking functions, and Lagrange inversion /rJean-Christophe Novelli, Jean-Yves Thibon --tThe triduplicial operad is Koszul /rAnthony Mansuy --tThe Hopf algebra of integer binary relations /rVincent Pilaud, Viviane Pons.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is volume 1 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications),
held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017.
The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota–Baxter algebras, operads, Ecalle’s mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths.
The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus.07aMathematics2bicssc07aDifferential equations2bicssc07aQuantum theory2msc07aCombinatorics2msc07aOrdinary differential equations2msc07aDynamical systems and ergodic theory2msc1 aChapoton, Frédéric,eeditor.1 aFauvet, Frédéric,eeditor.1 aMalvenuto, Claudia,eeditor.1 aThibon, Jean-Yves,eeditor.40uhttps://doi.org/10.4171/204423cover imageuhttps://www.ems-ph.org/img/books/chapoton_1_mini.jpg03079nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184245018700220260008200407300003400489336002600523337002600549338003600575347002400611490008300635505062000718506006601338520083601404650004802240650002402288650002302312650004102335650004602376700003502422700003302457700003302490700003202523856003202555856007002587252-200122CH-001817-320200122233001.0a fot ||| 0|cr nn mmmmamaa200122e20200228sz fot ||| 0|eng d a978303719705970a10.4171/2052doi ach0018173 7aPHT2bicssc a81-xxa05-xxa34-xxa37-xx2msc10aAlgebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)h[electronic resource] :bVolume 2 /cFrédéric Chapoton, Frédéric Fauvet, Claudia Malvenuto, Jean-Yves Thibon3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (396 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v3200tSpecial values of finite multiple harmonic $q$-series at roots of unity /rHenrik Bachmann, Yoshihiro Takeyama, Koji Tasaka --tMould calculus: from primary to secondary mould symmetries /rOlivier Bouillot --tRenormalisation and locality: branched zeta values /rPierre Clavier, Li Guo, Sylvie Paycha, Bin Zhang --tThe scrambling operators applied to multizeta algebra and singular perturbation analysis /rJean Ecalle --tQuasi-shuffle algebras and applications /rMichael E. Hoffman --tPlanar binary trees in scattering amplitudes /rCarlos R. Mafra --tA study on prefixes of $c_2$ invariants /rKaren Yeats.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis is volume 2 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017.
The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota–Baxter algebras, operads, Ecalle’s mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths.
The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus.07aQuantum physics (quantum mechanics)2bicssc07aQuantum theory2msc07aCombinatorics2msc07aOrdinary differential equations2msc07aDynamical systems and ergodic theory2msc1 aChapoton, Frédéric,eeditor.1 aFauvet, Frédéric,eeditor.1 aMalvenuto, Claudia,eeditor.1 aThibon, Jean-Yves,eeditor.40uhttps://doi.org/10.4171/205423cover imageuhttps://www.ems-ph.org/img/books/chapoton_2_mini.jpg02455nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245015500252260008200407300003400489336002600523337002600549338003600575347002400611490004000635506006600675520099000741650003501731650004001766650006601806650002801872650004001900700003201940856003201972856006502004253-200706CH-001817-320200706233004.0a fot ||| 0|cr nn mmmmamaa200706e20200806sz fot ||| 0|eng d a978303719706670a10.4171/2062doi ach0018173 7aPBKJ2bicssc a35-xxa49-xxa65-xxa74-xx2msc1 aRepin, Sergey I.,eauthor.10aAccuracy of Mathematical Modelsh[electronic resource] :bDimension Reduction, Homogenization, and Simplification /cSergey I. Repin, Stefan A. Sauter3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (333 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v331 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control.
This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates.07aDifferential equations2bicssc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aNumerical analysis2msc07aMechanics of deformable solids2msc1 aSauter, Stefan A.,eauthor.40uhttps://doi.org/10.4171/206423cover imageuhttps://www.ems-ph.org/img/books/repin_mini.jpg04332nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168072001400184084003600198245021100234260008200445300003400527336002600561337002600587338003600613347002400649490007900673505118900752506006601941520152402007650003203531650004903563650002603612650002503638650005503663650003303718700003103751700002903782856003203811856006703843254-200421CH-001817-320200421233002.0a fot ||| 0|cr nn mmmmamaa200421e20200605sz fot ||| 0|eng d a978303719707370a10.4171/2072doi ach0018173 7aPBW2bicssc 7aU2bicssc a68-xxa76-xxa90-xxa93-xx2msc10aDecision Support Systems for Water Supply Systemsh[electronic resource] :bSmart Water System to Improve the Operation of Water Supply Systems by Using Applied Mathematics /cAndreas Pirsing, Antonio Morsi3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (243 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series in Industrial and Applied Mathematics (ESIAM) ;x2523-5087 ;v200tRole of ICT in water supply systems: requirements, current status and challenges /rAndreas Pirsing, Moritz Allmaras, Roland Rosen, Tim Schenk, Annelie Sohr --tEWave energy management system /rConstantin Blanck, Stefan Fischer, Michael Plath, Moritz Allmaras, Andreas Pirsing, Tim Schenk, Annelie Sohr --tDemand forecast /rPatrick Hausmann --tHydraulic modeling and energy view /rGerd Steinebach, Oliver Kolb --tOptimization /rBjörn Geißler, Alexander Martin, Antonio Morsi, Maximilian Walther, Oliver Kolb, Jens Lang, Lisa Wagner --tNetwork aggregation /rTim Jax --tSetup of simulation model and calibration /rGerd Steinebach, David Dreistadt, Patrick Hausmann, Tim Jax --tField data, automation, instrumentation and communication /rConstantin Blanck, Stefan Fischer, Michael Plath --tNew ICT architecture /rTim Schenk, Moritz Allmaras, Andreas Pirsing, Annelie Sohr --tWater cockpit: dashboards for decision support systems /rMichael Plath, Constantin Blanck, Stefan Fischer, Moritz Allmaras, Andreas Pirsing, Tim Schenk, Annelie Sohr --tField test /rAnnelie Sohr, Constantin Blanck, Stefan Fischer, Michael Plath, Moritz Allmaras, Tim Schenk, Andreas Pirsing.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aOperating water supply systems is complex. Engineers must ensure that consumers are reliably supplied with a sufficient quantity and quality of water, as well as a sufficient water pressure at all times – all while maintaining reasonable prices. This book summarizes the results of the German BMBF (Federal Ministry of Education and Research) funded joint research project, EWave (Project ID: 02WER1323F), that was initiated to develop an innovative Decision Support System (DSS) for water supply companies. For decision making and operational support, the EWave system uses newly developed integrated optimization modules. As a result, the user receives operating schedules on a 15 minute scale. To achieve this, mixed-integer linear and nonlinear mathematical optimization methods are combined. First, a mixed-integer optimization model is solved in order to derive all discrete decisions (primarily pump schedules). The aim is to approximate the physics by piecewise linear relaxations sufficiently to optimize decisions. EWave then uses nonlinear optimization and simulation methods to verify the physics. The process is iterated as necessary. This approach enables globally optimal solutions within an a priori given quality tolerance.
Optimization results obtained in real time yield a potential of energy savings of up to 4–6% daily for the waterworks in the pilot area.
This book was written for automation experts in water supply companies as well as mathematicians who work for infrastructure companies.07aApplied mathematics2bicssc07aComputing and information technology2bicssc07aComputer science2msc07aFluid mechanics2msc07aOperations research, mathematical programming2msc07aSystems theory; control2msc1 aPirsing, Andreas,eeditor.1 aMorsi, Antonio,eeditor.40uhttps://doi.org/10.4171/207423cover imageuhttps://www.ems-ph.org/img/books/pirsing_mini.jpg02767nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003200207245006100239260008200300300003400382336002600416337002600442338003600468347002400504490004000528506006600568520157300634650003002207650002802237650005502265856003202320856006502352255-200213CH-001817-320200213233004.0a fot ||| 0|cr nn mmmmamaa200213e20200331sz fot ||| 0|eng d a978303719708070a10.4171/2082doi ach0018173 7aPBMS2bicssc a14-xxa32-xx2msc1 aKondō, Shigeyuki,eauthor.10a$K3$ Surfacesh[electronic resource] /cShigeyuki Kondō3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (250 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v321 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php a$K3$ surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 – a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century.
$K3$ surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods – called the Torelli-type theorem for $K3$ surfaces – was established around 1970. Since then, several pieces of research on $K3$ surfaces have been undertaken and more recently $K3$ surfaces have even become of interest in theoretical physics.
The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic $K3$ surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study $K3$ surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of $K3$ surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice.
The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry.07aAnalytic geometry2bicssc07aAlgebraic geometry2msc07aSeveral complex variables and analytic spaces2msc40uhttps://doi.org/10.4171/208423cover imageuhttps://www.ems-ph.org/img/books/kondo_mini.jpg02889nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001400168084003600182100002700218245010000245260008200345300003400427336002600461337002600487338003600513347002400549490005300573506006600626520150800692650003602200650004202236650004602278650002002324650002802344700003302372856003202405856006602437256-200706CH-001817-320200706233004.0a fot ||| 0|cr nn mmmmamaa200706e20200804sz fot ||| 0|eng d a978303719709770a10.4171/2092doi ach0018173 7aP2bicssc a20-xxa18-xxa19-xxa55-xx2msc1 aBalmer, Paul,eauthor.10aMackey 2-Functors and Mackey 2-Motivesh[electronic resource] /cPaul Balmer, Ivo Dell'Ambrogio3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (235 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists.
The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples and the separable monadicity theorem explains how the value of a Mackey 2-functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology. The second part of the book provides a motivic approach to Mackey 2-functors, 2-categorifying the well-known span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida’s crossed Burnside ring are the universal source of block decompositions.
The book is self-contained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested
in category theory, representation theory and topology.07aMathematics and science2bicssc07aGroup theory and generalizations2msc07aCategory theory; homological algebra2msc07a$K$-theory2msc07aAlgebraic topology2msc1 aDell'Ambrogio, Ivo,eauthor.40uhttps://doi.org/10.4171/209423cover imageuhttps://www.ems-ph.org/img/books/balmer_mini.jpg02137nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185100003000200245009000230260008200320300003400402336002600436337002600462338003600488347002400524490006100548506006600609520096400675650003101639650002801670856003201698856006901730257-200527CH-001817-320200527233006.0a fot ||| 0|cr nn mmmmamaa200527e20200630sz fot ||| 0|eng d a978303719710370a10.4171/2102doi ach0018173 7aPBMW2bicssc a14-xx2msc1 aCiliberto, Ciro,eauthor.10aClassification of Complex Algebraic Surfacesh[electronic resource] /cCiro Ciliberto3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (143 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aΤhe classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the classification of algebraic varieties. The text includes the $P_{12}$ theorem, the Sarkisov programme in the surface case and the Noether–Castelnuovo theorem in its classical version.
This book serves as a relatively quick and handy introduction to the theory of algebraic surfaces and is intended for readers with a good knowledge of basic algebraic geometry. Although an acquaintance with the basic parts of books like Principles of Algebraic Geometry by Griffiths and Harris or Algebraic Geometry by Hartshorne should be sufficient, the author strove to make the text as self-contained as possible and, for this reason, a first chapter is devoted to a quick exposition of some preliminaries.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc40uhttps://doi.org/10.4171/210423cover imageuhttps://www.ems-ph.org/img/books/ciliberto_mini.jpg02929nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100003400206245014700240260008200387300003400469336002600503337002600529338003600555347002400591490005300615506006600668520157500734650004502309650004602354650004002400700003002440856003202470856006502502258-200908CH-001817-320200908234501.0a fot ||| 0|cr nn mmmmamaa200908e20201009sz fot ||| 0|eng d a978303719711070a10.4171/2112doi ach0018173 7aPBK2bicssc a37-xxa35-xx2msc1 aBerti, Massimiliano,eauthor.10aQuasi-Periodic Solutions of Nonlinear Wave Equations on the $d$-Dimensional Torush[electronic resource] /cMassimiliano Berti, Philippe Bolle3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (374 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aMany partial differential equations (PDEs) arising in physics, such as the nonlinear wave equation and the Schrödinger equation, can be viewed as infinite-dimensional Hamiltonian systems. In the last thirty years, several existence results of time quasi-periodic solutions have been proved adopting a "dynamical systems" point of view. Most of them deal with equations in one space dimension, whereas for multidimensional PDEs a satisfactory picture is still under construction.
An updated introduction to the now rich subject of KAM theory for PDEs is provided in the first part of this research monograph. We then focus on the nonlinear wave equation, endowed with periodic boundary conditions. The main result of the monograph proves the bifurcation of small amplitude finite-dimensional invariant tori for this equation, in any space dimension. This is a difficult small divisor problem due to complex resonance phenomena between the normal mode frequencies of oscillations. The proof requires various mathematical methods, ranging from Nash–Moser and KAM theory to reduction techniques in Hamiltonian dynamics and multiscale analysis for quasi-periodic linear operators, which are presented in a systematic and self-contained way. Some of the techniques introduced in this monograph have deep connections with those used in Anderson localization theory.
This book will be useful to researchers who are interested in small divisor problems, particularly in the setting of Hamiltonian PDEs, and who wish to get acquainted with recent developments in the field.07aCalculus & mathematical analysis2bicssc07aDynamical systems and ergodic theory2msc07aPartial differential equations2msc1 aBolle, Philippe,eauthor.40uhttps://doi.org/10.4171/211423cover imageuhttps://www.ems-ph.org/img/books/berti_mini.jpg01684nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002500133040001400158072001400172072001500186084001500201100003200216245008100248260008200329300003300411336002600444337002600470338003600496347002400532490005100556506006600607520044900673650003601122650002401158650003801182856003601220856006601256261-210304CH-001817-320210304234502.0a fot ||| 0|cr nn mmmmamaa210304e20210331sz fot ||| 0|eng d a978398547500170a10.4171/ZLAM/262doi ach0018173 7aP2bicssc 7aPB2bicssc a57-xx2msc1 aBaader, Sebastian,eauthor.10aGeometry and Topology of Surfacesh[electronic resource] /cSebastian Baader3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (86 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThese lecture notes cover the classification of hyperbolic structures and measured foliations on surfaces in a minimalist way. While the inspiration is obviously taken from the excellent books Primer on mapping class groups and Travaux de Thurston sur les surfaces, the author aimed at including a little bit more of hyperbolic trigonometry, including a proof of Basmajian's identity on the orthogeodesic spectrum, while keeping the rest short.07aMathematics and science2bicssc07aMathematics2bicssc07aManifolds and cell complexes2msc40uhttps://doi.org/10.4171/ZLAM/26423cover imageuhttps://www.ems-ph.org/img/books/baader_mini.jpg02226nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001700171084001500188100002600203245009300229260008200322300003400404336002600438337002600464338003600490347002400526490006100550506006600611520105100677650003201728650002901760856003501789856006401824262-210305CH-001817-320210305234504.0a fot ||| 0|cr nn mmmmamaa210305e20210401sz fot ||| 0|eng d a978398547504970a10.4171/ELM/322doi ach0018173 7aPBKG2bicssc a46-xx2msc1 aHiai, Fumio,eauthor.10aLectures on Selected Topics in von Neumann Algebrash[electronic resource] /cFumio Hiai3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (250 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe theory of von Neumann algebras, originating with the work of F. J. Murray and J. von Neumann in the late 1930s, has grown into a rich discipline with connections to different branches of mathematics and physics. Following the breakthrough of Tomita–Takesaki theory, many great advances were made throughout the 1970s by H. Araki,
A. Connes, U. Haagerup, M. Takesaki and others.
These lecture notes aim to present a fast-track study of some important topics in classical parts of von Neumann algebra theory that were developed in the 1970s. Starting with Tomita–Takesaki theory, this book covers topics such as the standard form, Connes’ cocycle derivatives, operator-valued weights, type III structure theory and non-commutative integration theory.
The self-contained presentation of the material makes this book useful not only to graduate students and researchers who want to know the fundamentals of von Neumann algebras, but also to interested undergraduates who have a basic knowledge of functional analysis and measure theory.07aFunctional analysis2bicssc07aFunctional analysis2msc40uhttps://doi.org/10.4171/ELM/32423cover imageuhttps://www.ems-ph.org/img/books/hiai_mini.jpg05038nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001400171084002200185245009900207260008200306300003400388336002600422337002600448338003600474347002400510490005400534505211000588506006602698520159502764650003604359650004404395650005304439700002704492700003304519856003504552856007704587264-210428CH-001817-320210428234504.0a fot ||| 0|cr nn mmmmamaa210428e20210531sz fot ||| 0|eng d a978398547505670a10.4171/ECR/172doi ach0018173 7aP2bicssc a92-xxa60-xx2msc10aProbabilistic Structures in Evolutionh[electronic resource] /cEllen Baake, Anton Wakolbinger3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (502 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tAccessibility percolation in random fitness landscapes /rJoachim Krug --tBranching random walks in random environment /rWolfgang König --tMicrobial populations under selection /rEllen Baake, Anton Wakolbinger --tThe population genetics of the CRISPR-Cas system in bacteria /rRolf Backofen, Peter Pfaffelhuber --tEvolution of altruistic defence traits in structured populations /rMartin Hutzenthaler, Dirk Metzler --tStochastic processes and host-parasite coevolution: Linking coevolutionary dynamics and DNA polymorphism data /rWolfgang Stephan, Aurélien Tellier --tStochastic models for adaptive dynamics: Scaling limits and diversity /rAnton Bovier --tGenealogies and inference for populations with highly skewed offspring distributions /rMatthias Birkner, Jochen Blath --tMultiple-merger genealogies: Models, consequences, inference /rFabian Freund --tDiploid populations and their genealogies /rAnja Sturm --tProbabilistic aspects of Λ-coalescents in equilibrium and in evolution /rGötz Kersting, Anton Wakolbinger --tPopulation genetic models of dormancy /rJochen Blath, Noemi Kurt --tFrom high to low volatility: Spatial Cannings with block resampling and spatial Fleming–Viot with seed-bank /rAndreas Greven, Frank den Hollander --tAncestral lineages in spatial population models with local regulation /rMatthias Birkner, Nina Gantert --tThe symbiotic branching model: Duality and interfaces /rJochen Blath, Marcel Ortgiese --tMultitype branching models with state-dependent mutation and competition in the context of phylodynamic patterns /rAnja Sturm, Anita Winter --tAncestral lines under recombination /rEllen Baake, Michael Baake --tTowards more realistic models of genomes in populations: The Markov-modulated sequentially Markov coalescent /rJulien Y. Dutheil --tDiffusion limits of genealogies under various modes of selection /rMartin Hutzenthaler, Peter Pfaffelhuber --tCounting, grafting and evolving binary trees /rThomas Wiehe --tAlgebraic measure trees: Statistics based on sample subtree shapes and sample subtree masses /rAnita Winter.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present volume collects twenty-one survey articles about probabilistic aspects of biological evolution. They cover a large variety of topics from the research done within the German Priority Programme SPP 1590.
Evolution is a complex phenomenon driven by various processes, such as mutation and recombination of genetic material, reproduction of individuals, and selection of favourable types. These processes all have intrinsically random elements, which give rise to a wealth of phenomena that cannot be explained by deterministic models. Examples of such effects are the loss of genetic variability due to random reproduction and the emergence of random genealogies.
The collection is centred around the stochastic processes in population genetics and population dynamics. On the one hand, these are individual-based models of predator-prey and of coevolution type, of adaptive dynamics, or of experimental evolution, considered in the usual forward direction of time. They lead to processes describing the evolution of type frequencies, which may then be analysed via suitable limit theorems. On the other hand, one traces the ancestral lines of individuals back into the past; this leads to random genealogies. Beyond the classical concept of Kingman's coalescent, emphasis is on genealogies with multiple mergers and on ancestral structures that take into account selection, recombination, or migration.
The contributions in this volume will be valuable to researchers interested in stochastic processes and their biological applications, or in mathematical population biology.07aMathematics and science2bicssc07aBiology and other natural sciences2msc07aProbability theory and stochastic processes2msc1 aBaake, Ellen,eeditor.1 aWakolbinger, Anton,eeditor.40uhttps://doi.org/10.4171/ECR/17423cover imageuhttps://www.ems-ph.org/img/books/baake-wakolbinger_mini.jpg05753nam a22004215a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001400171084002900185245021200214260008200426300003400508336002600542337002600568338003600594347002400630490005400654505311200708506006603820520105603886650003604942650004104978650004005019650002505059700002705084700003105111700003005142700002805172700002605200856003505226856007005261265-210518CH-001817-320210518234502.0a fot ||| 0|cr nn mmmmamaa210518e20210615sz fot ||| 0|eng d a978398547507070a10.4171/ECR/182doi ach0018173 7aP2bicssc a34-xxa35-xxa47-xx2msc10aPartial Differential Equations, Spectral Theory, and Mathematical Physicsh[electronic resource] :bThe Ari Laptev Anniversary Volume /cPavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (494 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tA non-existence result for a generalized radial Brezis–Nirenberg problem /rRafael D. Benguria, Soledad Benguria --tFriedrichs-type inequalities in arbitrary domains /rAndrea Cianchi, Vladimir G. Maz'ya --tAri Laptev and the Journal of Spectral Theory /rE. Brian Davies --tCritical magnetic field for 2D magnetic Dirac–Coulomb operators and Hardy inequalities /rJean Dolbeault, Maria J. Esteban, Michael Loss --tThe Feshbach–Schur map and perturbation theory /rGeneviève Dusson, Israel Michael Sigal, Benjamin Stamm --tAdiabatic and non-adiabatic evolution of wave packets and applications to initial value representations /rClotilde Fermanian Kammerer, Caroline Lasser, Didier Robert --tLength scales for BEC in the dilute Bose gas /rSøren Fournais --tThe periodic Lieb–Thirring inequality /rRupert L. Frank, David Gontier, Mathieu Lewin --tSemiclassical asymptotics for a class of singular Schrödinger operators /rRupert L. Frank, Simon Larson --tOn the spectral properties of the Bloch–Torrey equation in infinite periodically perforated domains /rDenis S. Grebenkov, Bernard Helffer, Nicolas Moutal --tCounting bound states with maximal Fourier multipliers /rDirk Hundertmark, Peer Christian Kunstmann, Tobias Ried, Semjon Vugalter --tSharp dimension estimates of the attractor of the damped 2D Euler–Bardina equations /rAlexei A. Ilyin, Sergey Zelik --tUpper estimates for the electronic density in heavy atoms and molecules /rVictor Ivrii --tNon-linear Schrödinger equation in a uniform magnetic field /rThomas F. Kieffer, Michael Loss --tLarge $|k|$ behavior of d-bar problems for domains with a smooth boundary /rChristian Klein, Johannes Sjöstrand, Nikola Stoilov --tHeat kernel estimates for two-dimensional relativistic Hamiltonians with magnetic field /rHynek Kovařík --tA version of Watson lemma for Laplace integrals and some applications /rStanislas Kupin, Sergey Naboko --tWehrl-type coherent state entropy inequalities for SU(1,1) and its $AX+B$ subgroup /rElliott H. Lieb, Jan Philip Solovej --tBlow-ups for the Horn–Kapranov parametrization of the classical discriminant /rEvgeny Mikhalkin, Vitaly Stepanenko, Avgust Tsikh --tEigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case /rGrigori Rozenblum, Eugene Shargorodsky --tRelations between two parts of the spectrum of a Schrödinger operator and other remarks on the absolute continuity of the spectrum in a typical case /rOleg Safronov --tBogoliubov theory for many-body quantum systems /rBenjamin Schlein --tA statistical theory of heavy atoms: Asymptotic behavior of the energy and stability of matter /rHeinz Siedentop --tHomogenization of the higher-order Schrödinger-type equations with periodic coefficients /rTatiana A. Suslina --tTrace formulas for the modified Mathieu equation /rLeon A. Takhtajan --tEigenvalue accumulation and bounds for non-selfadjoint matrix differential operators related to NLS /rChristiane Tretter --tScattering theory for Laguerre operators /rDmitri Yafaev.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects
contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory.
In brief, the topics covered include Friedrichs, Hardy, and Lieb–Thirring inequalities, eigenvalue bounds and
asymptotics, Feshbach–Schur maps and perturbation theory, scattering theory and orthogonal polynomials,
stability of matter, electron density estimates, Bose–Einstein condensation, Wehrl-type entropy inequalities,
Bogoliubov theory, wave packet evolution, heat kernel estimates, homogenization, d-bar problems,
Brezis–Nirenberg problems, the nonlinear Schrödinger equation in magnetic fields, classical discriminants,
and the two-dimensional Euler–Bardina equations. In addition, Ari’s multifaceted service to the mathematical
community is also touched upon.
Altogether the volume presents a collection of research articles which will be of interest to any active scientist
working in one of the above mentioned fields.07aMathematics and science2bicssc07aOrdinary differential equations2msc07aPartial differential equations2msc07aOperator theory2msc1 aExner, Pavel,eeditor.1 aFrank, Rupert L.,eeditor.1 aGesztesy, Fritz,eeditor.1 aHolden, Helge,eeditor.1 aWeidl, Timo,eeditor.40uhttps://doi.org/10.4171/ECR/18423cover imageuhttps://www.ems-ph.org/img/books/exner-etal_mini.jpg04746nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002500133040001400158072001400172084003600186245013200222260008200354300003400436336002600470337002600496338003600522347002400558490008300582505242500665506006603090520087903156650003604035650003104071650002304102650004004125650004304165700003704208856003604245856007904281266-210621CH-001817-320210621234507.0a fot ||| 0|cr nn mmmmamaa210621e20210715sz fot ||| 0|eng d a978398547501870a10.4171/IRMA/332doi ach0018173 7aP2bicssc a01-xxa05-xxa16-xxa17-xx2msc10aTopology and Geometryh[electronic resource] :bA Collection of Essays Dedicated to Vladimir G. Turaev /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (698 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v3300tVladimir Turaev, friend and colleague /rAthanase Papadopoulos --tTriangles on planar Jordan $C^1$-curves and differential topology /rJean-Claude Hausmann --tNull-homologous unknottings /rCharles Livingston --tA question of Turaev about triple higher Milnor linking numbers of divide links /rNorbert A’Campo --tFundamental groups in projective knot theory /rJulia Viro, Oleg Viro --tThe Affine Index Polynomial and the Sawollek Polynomial /rLouis H. Kauffman --tIntroduction to quantum representations of mapping class groups /rJulien Marché --tOn symmetric matrices associated with oriented link diagrams /rRinat Kashaev --tOn Chen–Yang’s volume conjecture for various quantum invariants /rJun Murakami --tNon-semisimple invariants and Habiro’s series /rAnna Beliakova, Kazuhiro Hikami --tModular categories and TQFTs beyond semisimplicity /rChristian Blanchet, Marco De Renzi --tState sums for some super quantum link invariants /rLouis-Hadrien Robert, Emmanuel Wagner --tBrane Topological Field Theory and Hurwitz numbers for CW-complexes /rSergey M. Natanzon --tResurgence of Faddeev’s quantum dilogarithm /rStavros Garoufalidis, Rinat Kashaev --tOn mapping class group quotients by powers of Dehn twists and their representations /rLouis Funar --tHigher holonomy and iterated integrals /rToshitake Kohno --tSome algebraic aspects of the Turaev cobracket /rNariya Kawazumi --tGeneralized Dehn twists in low-dimensional topology /rYusuke Kuno, Gwénaël Massuyeau, Shunsuke Tsuji --tOn geometric group theory /rValentin Poénaru --tGeometry of knots and links /rNikolay Abrosimov, Alexander Mednykh --tEssential closed surfaces and finite coverings of negatively curved cusped 3-manifolds /rCharalampos Charitos --tContinuous and discontinuous functions on deformation spaces of Kleinian groups /rKen’ichi Ohshika --tA generalization of King’s equation via noncommutative geometry /rGourab Bhattacharya, Maxim Kontsevich --tDessins for modular operads and the Grothendieck–Teichmüller group /rNoémie C. Combe, Yuri I. Manin, Matilde Marcolli --tOn the involution Jimm /rA. Muhammed Uludağ --tWhat is a black hole? – A geometric introduction /rSumio Yamada --tThe paradoxical nature of mathematics /rVassiliki Farmaki, Stelios Negrepontis --tReturns of geometry: From the Pythagoreans to mathematical modernism and beyond /rArkady Plotnitsky.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe present volume consists of a collection of essays dedicated to Vladimir Turaev.
The essays cover the large spectrum of topics in which Turaev has been interested, including knot and link invariants, quantum representations, TQFTs, state sum constructions, geometric structures on knot complements, Kleinian groups, geometric group theory and its relationship with 3-manifolds, mapping class groups, operads, mathematical physics, Grothendieck’s program, the philosophy of mathematics, and several other topics.
At the same time, this volume will give an overview of topics that are at the forefront of current research in topology and geometry. Some of the essays are research articles and contain new results, sometimes answering questions that were raised by Turaev. The rest of the essays are surveys that will introduce the reader to some key ideas in the field.07aMathematics and science2bicssc07aHistory and biography2msc07aCombinatorics2msc07aAssociative rings and algebras2msc07aNonassociative rings and algebras2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/IRMA/33423cover imageuhttps://www.ems-ph.org/img/books/papadopoulos-turaev_mini.jpg02120nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001400171084003600185100003100221245014100252260008200393300003400475336002600509337002600535338003600561347002400597490003900621506006600660520064000726650003601366650006601402650003301468650004001501650005301541700003101594856003501625856007401660267-210629CH-001817-320210629234504.0a fot ||| 0|cr nn mmmmamaa210629e20210802sz fot ||| 0|eng d a978398547510070a10.4171/ETB/222doi ach0018173 7aP2bicssc a49-xxa28-xxa35-xxa60-xx2msc1 aFigalli, Alessio,eauthor.10aAn Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flowsh[electronic resource] /cAlessio Figalli, Federico Glaudo3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (144 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject.
The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto’s calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given.
The book is suitable for a course at the graduate level, and also includes an appendix with a series of exercises along with their solutions.07aMathematics and science2bicssc07aCalculus of variations and optimal control; optimization2msc07aMeasure and integration2msc07aPartial differential equations2msc07aProbability theory and stochastic processes2msc1 aGlaudo, Federico,eauthor.40uhttps://doi.org/10.4171/ETB/22423cover imageuhttps://www.ems-ph.org/img/books/figalli-glaudo_mini.jpg02376nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001400171084003600185100004200221245018700263260008200450300003400532336002600566337002600592338003600618347002400654490006100678506006600739520080500805650003601610650002701646650005501673650004101728650002601769700003601795700003401831856003501865856007801900268-210705CH-001817-320210705234503.0a fot ||| 0|cr nn mmmmamaa210705e20210802sz fot ||| 0|eng d a978398547508770a10.4171/ELM/332doi ach0018173 7aP2bicssc a33-xxa15-xxa34-xxa42-xx2msc1 aGarcía-Ardila, Juan Carlos,eauthor.10aOrthogonal Polynomials and Linear Functionalsh[electronic resource] :bAn Algebraic Approach and Applications /cJuan Carlos García-Ardila, Francisco Marcellán, Misael E. Marriaga3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (128 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book presents an introduction to orthogonal polynomials, with an algebraic flavor,
based on linear functionals defining the orthogonality and the Jacobi matrices associated with them. Basic
properties of their zeros as well as quadrature rules are discussed. A key point is the analysis of those functionals
satisfying Pearson equations (semiclassical case) and the hierarchy based on their class.
The book's structure reflects the fact that its content is based on a set of lectures delivered by one of the
authors at the first Orthonet Summer School in Seville, Spain in 2016. The presentation of the material is
self-contained and will be valuable to students and researchers interested in a novel approach to the study
of orthogonal polynomials, focusing on their analytic properties.07aMathematics and science2bicssc07aSpecial functions2msc07aLinear and multilinear algebra; matrix theory2msc07aOrdinary differential equations2msc07aFourier analysis2msc1 aMarcellán, Francisco,eauthor.1 aMarriaga, Misael E.,eauthor.40uhttps://doi.org/10.4171/ELM/33423cover imageuhttps://www.ems-ph.org/img/books/garcia-ardila-etal_mini.jpg02607nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001700171072001600188084002200204100003400226245014000260260008200400300003400482336002600516337002600542338003600568347002400604490003900628506006600667520116500733650003501898650002501933650006601958650005502024700003102079856003502110856007602145269-210913CH-001817-320210913234504.0a fot ||| 0|cr nn mmmmamaa210913e20211011sz fot ||| 0|eng d a978398547512470a10.4171/ETB/232doi ach0018173 7aPBKQ2bicssc 7aPBU2bicssc a49-xxa90-xx2msc1 aCannarsa, Piermarco,eauthor.10aDynamic Optimization for Beginnersh[electronic resource] :bWith Prerequisites and Applications /cPiermarco Cannarsa, Filippo Gazzola3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (360 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aNowadays, optimization problems for dynamical systems enter more and more the
basic knowledge required to approach applied sciences, engineering, and social
sciences. On the other hand, even the results of most common use in this field,
known as dynamic optimization, assume familiarity with an advanced mathematical
background which may at times be perceived as discouraging.
The main purpose of this book is to give interested readers a friendly introduction to
this subject, providing them with the essential notions needed to handle most of the
concrete situations they will be faced with. The main topics covered are calculus of
variations, optimal control theory, and dynamic programming. As explained above,
the book aims to be of interest both to mathematics students and to students or
researchers in other disciplines such as economics and data science, who wish to use
dynamic optimization in a conscientious way.
The contents are self-contained and all the prerequisites may be found in the first
chapters. Many applications are discussed and a large number of examples and
exercises, both proposed and solved, complements the theory.07aCalculus of variations2bicssc07aOptimization2bicssc07aCalculus of variations and optimal control; optimization2msc07aOperations research, mathematical programming2msc1 aGazzola, Filippo,eauthor.40uhttps://doi.org/10.4171/ETB/23423cover imageuhttps://www.ems-ph.org/img/books/Cannarsa-Gazzola_mini.jpg02460nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001400171084002200185100003400207245009100241260008200332300003400414336002600448337002600474338003600500347002400536490004000560506006600600520124000666650003601906650004001942650002501982856003502007856006802042270-211011CH-001817-320211011234505.0a fot ||| 0|cr nn mmmmamaa211011e20211122sz fot ||| 0|eng d a978398547509470a10.4171/ETM/342doi ach0018173 7aP2bicssc a35-xxa76-xx2msc1 aKhruslov, Evgen Ya.,eauthor.10aHomogenized Models of Suspension Dynamicsh[electronic resource] /cEvgen Ya. Khruslov3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2021 a1 online resource (288 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v341 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book studies the motion of suspensions, that is, of mixtures of a viscous incompressible fluid with small solid particles that can interact with each other through forces of
non-hydrodynamic origin. In view of the complexity of the original (microscopic) system of equations that describe such phenomena, which appear both in nature and in engineering processes, the problem is reduced to a macroscopic description of the motion of mixtures as an effective continuous medium.
The focus is on developing mathematical methods for constructing such homogenized models for the motion of suspensions with an arbitrary distribution of solid particles in a fluid. In particular, the results presented establish that depending on the concentration of the solid phase of the mixture, the motion of suspensions can occur in two qualitatively different modes: that of frozen or of filtering particles.
Being one of the first mathematically rigorous treatises on suspensions from the viewpoint of homogenization theory, this book will be useful to graduate students and researchers in applied analysis and partial differential equations as well as to physicists and engineers interested in the theory of complex fluids with microstructure.07aMathematics and science2bicssc07aPartial differential equations2msc07aFluid mechanics2msc40uhttps://doi.org/10.4171/ETM/34423cover imageuhttps://www.ems-ph.org/img/books/Khruslov_mini.jpg02906nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001500171072001700186084002900203100002900232245015600261260008200417300003400499336002600533337002600559338003600585347002400621490006100645506006600706520147100772650002402243650002402267650005302291650004002344650002402384856003502408856007702443271-220422CH-001817-320220422114427.0a fot ||| 0|cr nn mmmmamaa220422e20220419sz fot ||| 0|eng d a978398547514870a10.4171/ELM/342doi ach0018173 7aPB2bicssc 7aPBWL2bicssc a60-xxa35-xxa81-xx2msc1 aBerglund, Nils,eauthor.10aAn Introduction to Singular Stochastic PDEsh[electronic resource] :bAllen–Cahn Equations, Metastability, and Regularity Structures /cNils Berglund3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2022 a1 online resource (230 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aStochastic partial differential equations (SPDEs) model the evolution in time of spatially
extended systems subject to a random driving. Recent years have witnessed tremendous progress in the
theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a
typical example being spacetime white noise, which makes them ill-posed as such. In many cases, it is
however possible to make sense of these equations by applying a so-called renormalisation procedure,
initially introduced in quantum field theory.
This book gives a largely self-contained exposition of the subject of regular and singular SPDEs in the
particular case of the Allen–Cahn equation, which models phase separation. Properties of the equation are
discussed successively in one, two and three spatial dimensions, allowing to introduce new difficulties of the
theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of long-time
dynamics such as invariant measures and metastability are discussed. A large part of the last chapter, about
the three-dimensional case, is dedicated to the theory of regularity structures, which has been developed by
Martin Hairer and co-authors in the last years, and allows to describe a large class of singular SPDEs.
The book is intended for graduate students and researchers in mathematics and physics with prior knowledge in stochastic processes or stochastic calculus.07aMathematics2bicssc07aStochastics2bicssc07aProbability theory and stochastic processes2msc07aPartial differential equations2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/ELM/34423cover imageuhttps://www.ems-ph.org/img/books/9783985470143_Berglund.jpg