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Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
7
2010
1
Model Theory: Around Valued Fields and Dependent Theories
Andreas
Baudisch
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Anand
Pillay
University of Leeds, LEEDS, UNITED KINGDOM
Katrin
Tent
Universität Münster, MÜNSTER, GERMANY
Martin
Ziegler
Universität Freiburg, FREIBURG, GERMANY
The general topic of the meeting was “Valued fields and related structures”. It included both applications of model theory, as well as so-called “pure” model theory: the classification of first order structures using new techniques extending those developed in stable theories.
Mathematical logic and foundations
Field theory and polynomials
General
5
53
10.4171/OWR/2010/01
http://www.ems-ph.org/doi/10.4171/OWR/2010/01
Moduli Spaces in Algebraic Geometry
Dan
Abramovich
Brown University, PROVIDENCE, UNITED STATES
Gavril
Farkas
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Stefan
Kebekus
Universität Freiburg, FREIBURG, GERMANY
The workshop on Moduli Spaces in Algebraic Geometry aimed to bring together researchers from all branches of moduli theory, in order to discuss moduli spaces from different points of view, and to give an overview of methods used in their respective fields. Highlights included a complete proof of Göttsche’s conjecture, a proof of rationality of a moduli space constructed via GIT quotient using reduction modulo p, and a proof of a conjecture of Looijenga using the ideas of mirror symmetry.
Algebraic geometry
General
55
107
10.4171/OWR/2010/02
http://www.ems-ph.org/doi/10.4171/OWR/2010/02
Mini-Workshop: History of Mathematics in Germany, 1920-1960
Moritz
Epple
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Volker
Remmert
Fachbereich A - Geschichte, WUPPERTAL, GERMANY
Norbert
Schappacher
Université de Strasbourg et CNRS, STRASBOURG CEDEX, FRANCE
The Mini-Workshop dealt with the history of mathematics in Germany between 1920 and 1960, with a particular focus on the social history of mathematics. For the period under discussion research in the history of mathematics is faced with some fundamental problems, which cannot be addressed by individuals. Consequently the Mini-Workshop’s aim was to develop future perspectives and methods for research and ways to organise new research projects. Among the topics addressed during the Mini-Workshop were the international relations of mathematicians in Germany before, during and after World War II; the prosopography of mathematicians in Germany from before 1933 into the 1950s; the role of mathematics as a key technology in World War II; and the professional policies from the 1920s to the 1950s.
History and biography
General
109
140
10.4171/OWR/2010/03
http://www.ems-ph.org/doi/10.4171/OWR/2010/03
Mini-Workshop: Valuations and Integral Geometry
Semyon
Alesker
Tel Aviv University, TEL AVIV, ISRAEL
Andreas
Bernig
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Peter
Schuster
Universität Wien, WIEN, AUSTRIA
As a generalization of the notion of measure, valuations have long played a central role in the integral geometry of convex sets. In recent years there has been a series of striking developments. Several examples were presented at this meeting, e.g. the work of Bernig and Fu on the integral geometry of groups acting transitively on the unit sphere, that of Hug and Schneider on kinematic and Crofton formulas for tensor valued valuations and a series of results by Ludwig and Reitzner on classifications of affine invariant notions of surface areas and of convex body valued valuations.
Convex and discrete geometry
Differential geometry
General
141
178
10.4171/OWR/2010/04
http://www.ems-ph.org/doi/10.4171/OWR/2010/04
Mini-Workshop: Semiparametric Modelling of Multivariate Economic Time Series With Changing Dynamics
Luc
Bauwens
, LOUVAIN-LA-NEUVE, BELGIUM
Rainer
von Sachs
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Qiwei
Yao
London School of Economics, LONDON, UNITED KINGDOM
Modelling multivariate time series of possibly high dimension calls for appropriate dimension-reduction, e.g. by some factor modelling, additive modelling, or some simplified parametric structure for the dynamics (i.e. the serial dependence) of the time series. This workshop aimed to bring together experts in this field in order to discuss recent methodology for multivariate time series dynamics which are changing over time: by an abrupt switch between two (or more) different regimes or rather smoothly evolving over time. The emphasis has been on mathematical methods for semiparametric modelling and estimation, where ”semiparametric” is to be understood in a rather broad sense: parametric models where the parameters are themselves nonparametric functions (of time), regime-switching nonparametric models with a parametric specification of the transition mechanism, and alike. An ultimate goal of these models to be applied to economic and financial time series is prediction. Another emphasis has been on comparing Bayesian with frequentist approaches, and to cover both theoretical aspects of estimation, such as consistency and efficiency, and computational aspects.
Statistics
General
179
216
10.4171/OWR/2010/05
http://www.ems-ph.org/doi/10.4171/OWR/2010/05
Statistical Issues in Prediction: what can be learned for individualized predictive medicine?
Leonhard
Held
Universität Zürich, ZÜRICH, SWITZERLAND
Robin
Henderson
University of Newcastle, NEWCASTLE UPON TYNE, GREAT BRITAIN
Ulrich
Mansmann
Universität München, MÜNCHEN, GERMANY
Error is unavoidable in prediction. And it is quite common, often sizable, and usually consequential. In a clinical context, especially when dealing with a terminal illness, error in prediction of residual life means that patients and families are misinformed about their illness, that they may take foolish actions as a result, and that they may be given inappropriate or needlesly painful treatments or denied appropriate ones. In meteorology, error in prediction of storm paths or extreme events can have devastating consequences. In finance and economics, major policy decisions are taken on the basis of predictions and forecasts. Rational approaches to reduce and assess error in prediction are presented. Ideas are introduced how to relate these statistical strategies with clinical and medical concepts in particular and how to integrate ideas from apparently different areas.
Statistics
Biology and other natural sciences
General
217
251
10.4171/OWR/2010/06
http://www.ems-ph.org/doi/10.4171/OWR/2010/06
New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries
Charles
Elliott
University of Warwick, COVENTRY, UNITED KINGDOM
Yoshikazu
Giga
University of Tokyo, TOKYO, JAPAN
Michael
Hinze
Universität Hamburg, HAMBURG, GERMANY
Vanessa
Styles
University of Sussex, BRIGHTON, UNITED KINGDOM
The field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research. Many such systems arise from mathematical models in material science, fluid dynamics and biology, for example phase separation in alloys, epitaxial growth, dynamics of multiphase fluids, evolution of cell membranes and in industrial processes such as crystal growth. The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force. Here the forcing terms depend on variables that are solutions of additional partial differential equations which hold either on the interface itself or in the surrounding bulk regions. Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified. Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries. Because of the maturity of the field of computational free boundary problems it is now timely to consider such control problems. In order to carry out design, control and simulation of such problems interaction is required between distinct mathematical fields such as analysis, modeling, computation and optimization. By bringing together leading experts and young researchers from these separate fields we intended to develop novel research directions in applied and computational mathematics. The aim of the workshop here was to focus on emerging new themes and developments in these fields and to establish and extend links between them.
Partial differential equations
Calculus of variations and optimal control; optimization
Numerical analysis
General
253
324
10.4171/OWR/2010/07
http://www.ems-ph.org/doi/10.4171/OWR/2010/07
Optimal Constants in the Theory of Sobolev Spaces and PDEs
Andrea
Cianchi
Universita di Firenze, FIRENZE, ITALY
Maria
Esteban
Université de Paris Dauphine, PARIS CEDEX 16, FRANCE
Bernd
Kawohl
Universität Köln, KÖLN, GERMANY
Recent research activities on sharp constants and optimal inequalities have shown their impact on a deeper understanding of geometric, analytical and other phenomena in the context of partial differential equations and mathematical physics. These intrinsic questions have applications not only to a-priori estimates or spectral theory but also to numerics, economics, optimization, etc.
Partial differential equations
Linear and multilinear algebra; matrix theory
Real functions
Measure and integration
325
371
10.4171/OWR/2010/08
http://www.ems-ph.org/doi/10.4171/OWR/2010/08
Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples
Christian
Fleischhack
Universität Paderborn, PADERBORN, GERMANY
Matilde
Marcolli
California Institute of Technology, PASADENA, UNITED STATES
Ryszard
Nest
University of Copenhagen, COPENHAGEN, DENMARK
Spectral triples have recently turned out to be relevant for different approaches that aim at quantizing gravity and the other fundamental forces of nature in a mathematically rigorous way. The purpose of this workshop was to bring together researchers mainly from noncommutative geometry and loop quantum gravity –two major fields that have used spectraltriples independently so far– in order to share their results and open issues.
Global analysis, analysis on manifolds
Functional analysis
Quantum theory
Relativity and gravitational theory
373
413
10.4171/OWR/2010/09
http://www.ems-ph.org/doi/10.4171/OWR/2010/09
Computational Electromagnetism and Acoustics
Ralf
Hiptmair
Eidgenössische Technische Hochschule, ZÜRICH, SWITZERLAND
Ronald
Hoppe
Universität Augsburg, AUGSBURG, GERMANY
Patrick
Joly
Domaine de Voluceau, LE CHESNAY CEDEX, FRANCE
Ulrich
Langer
Johannes Kepler Universität Linz, LINZ, AUSTRIA
The challenge inherent in the accurate and efficient numerical modeling of wave propagation phenomena is the common grand theme in both computational electromagnetics and acoustics. Many excellent contributions at this Oberwolfach workshop were devoted to this theme and a wide range of numerical techniques and algorithms were mustered to tackle this challenge. Among these methods boundary integral equation methods received particular attention, both in frequency and time domain. Combined with phase modulation techniques they pave the way for the construction of frequency robust schemes for wave scattering. This is an exciting recent development, which is complemented by the invention of high-order spectral integral equation methods. In parallel, we also witnessed soaring interest in time-domain integral equation methods. The alternative volume based schemes for wave propagation problems can also boast innovations, most notably in the context of plane wave methods. Though wave propagation is paramount, several other important aspects were addressed during the workshop ranging, among others, from the design of novel Galerkin schemes, asymptotic methods for geometrically singularly perturbed problems, analysis of spectral edge elements, to the design of preconditioners for quasi-static electromagnetics.
Numerical analysis
Optics, electromagnetic theory
General
415
519
10.4171/OWR/2010/10
http://www.ems-ph.org/doi/10.4171/OWR/2010/10
Graph Theory
Reinhard
Diestel
Universität Hamburg, HAMBURG, GERMANY
Alexander
Schrijver
Centrum voor Wiskunde en Informatica, AMSTERDAM, NETHERLANDS
Paul
Seymour
Princeton University, PRINCETON, UNITED STATES
Highlights of this workshop on structural graph theory included new developments on graph and matroid minors, continuous structures arising as limits of finite graphs, and new approaches to higher graph connectivity via tree structures.
Combinatorics
General
521
580
10.4171/OWR/2010/11
http://www.ems-ph.org/doi/10.4171/OWR/2010/11
Disciplines and Styles in Pure Mathematics, 1800-2000
David
Rowe
Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
Klaus
Volkert
Bergische Universität, WUPPERTAL, GERMANY
Pierre-A.
Vuillermot
Université Henri Poincaré, VANDOEUVRE-LÈS-NANCY CEDEX, FRANCE
Volker
Remmert
Fachbereich A - Geschichte, WUPPERTAL, GERMANY
This workshop addressed issues of discipline and style in number theory, algebra, geometry, topology, analysis, and mathematical physics. Most speakers presented case studies, but some offered global surveys of how stylistic shifts informed the transition and transformation of special research fields. Older traditions in established research communities were considered alongside newer trends, including changing views regarding the role of proof.
History and biography
General
581
665
10.4171/OWR/2010/12
http://www.ems-ph.org/doi/10.4171/OWR/2010/12
C*-Algebren
Claire
Anantharaman-Delaroche
Université d'Orléans, ORLÉANS CEDEX 2, FRANCE
Siegfried
Echterhoff
Universität Münster, MÜNSTER, GERMANY
Mikael
Rørdam
Københavns Universitetet, COPENHAGEN, DENMARK
Dan-Virgil
Voiculescu
University of California, BERKELEY, UNITED STATES
The theory of C*-algebras plays a major role in many areas of modern mathematics, like Non-commutative Geometry, Dynamical Systems, Harmonic Analysis, and Topology, to name a few. The aim of the conference “C*-algebras” is to bring together experts from all those areas to provide a present day picture and to initiate new cooperations in this fast growing mathematical field.
Functional analysis
$K$-theory
Topological groups, Lie groups
Dynamical systems and ergodic theory
667
732
10.4171/OWR/2010/13
http://www.ems-ph.org/doi/10.4171/OWR/2010/13
Microstructures in Solids: From Quantum Models to Continua
Alexander
Mielke
Angewandte Analysis und Stochastik, BERLIN, GERMANY
Michael
Ortiz
California Institute of Technology, PASADENA, UNITED STATES
The mathematical theory of solids was studied from the modern perspective of materials with microcstructures. The discussed topics ranged from experimental findings, via numerical simulations and mathematical modeling to the analysis of models with microstructures. A special emphasis was given to theories providing rigorous insight into and justification of the limit passage between different scales.
Partial differential equations
Calculus of variations and optimal control; optimization
Mechanics of deformable solids
Statistical mechanics, structure of matter
733
798
10.4171/OWR/2010/14
http://www.ems-ph.org/doi/10.4171/OWR/2010/14
Combinatorial Representation Theory
Christine
Bessenrodt
Leibniz Universität Hannover, HANNOVER, GERMANY
Francesco
Brenti
Università di Roma Tor Vergata, ROMA, ITALY
Alexander
Kleshchev
University of Oregon, EUGENE, UNITED STATES
Arun
Ram
University of Melbourne, PARKVILLE VIC, AUSTRALIA
The workshop brought together researchers from different fields in representation theory and algebraic combinatorics for a fruitful interaction. New results, methods and developments ranging from classical and modular representation theory, the theory of symmetric functions and Lie theory to cluster algebras and connections to physics and geometry were discussed.
Combinatorics
Algebraic geometry
Associative rings and algebras
Nonassociative rings and algebras
799
882
10.4171/OWR/2010/15
http://www.ems-ph.org/doi/10.4171/OWR/2010/15
Modern Nonparametric Statistics: Going Beyond Asymptotic Minimax
Lucien
Birgé
Université Paris VI, PARIS CEDEX 05, FRANCE
Iain
Johnstone
Stanford University, STANFORD, UNITED STATES
Vladimir
Spokoiny
Angewandte Analysis und Stochastik, BERLIN, GERMANY
During the years 1975-1990 a major emphasis in nonparametric estimation was put on computing the asymptotic minimax risk for many classes of functions. Modern statistical practice indicates some serious limitations of the asymptotic minimax approach and calls for some new ideas and methods which can cope with the numerous challenges brought to statisticians by modern sets of data.
Statistics
General
883
939
10.4171/OWR/2010/16
http://www.ems-ph.org/doi/10.4171/OWR/2010/16
2
Arbeitsgemeinschaft: Mathematical Billards
Serge
Tabachnikov
Penn State University, UNIVERSITY PARK, UNITED STATES
Serge
Troubetzkoy
CNRS Luminy, MARSEILLE CEDEX 9, FRANCE
The workshop Mathematical Billiards, organised by Serge Tabachnikov (Penn State) and Serge Troubetzkoy (Marseille) was held April 4th–April 10th, 2010. This meeting was well attended by over 40 participants including a number of master and PhD students, with broad geographic representation. This workshop was a nice blend of researchers with various backgrounds who brought in their various point of views to cover the classics as well as recent advances in mathematical billiards and flat surfaces. The report consists in the abstracts for the 18 lectures, followed by the abstracts for the 4 short talks that took place in the evenings. During the workshop, there was also a demo of the mathematical software Sage.
Functions of a complex variable
Dynamical systems and ergodic theory
General
955
1015
10.4171/OWR/2010/17
http://www.ems-ph.org/doi/10.4171/OWR/2010/17
Mathematics and Algorithms in Tomography
Martin
Burger
Universität Münster, MÜNSTER, GERMANY
Alfred
Louis
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
Eric Todd
Quinto
Tufts University, MEDFORD, UNITED STATES
This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis.
Numerical analysis
Integral transforms, operational calculus
Biology and other natural sciences
General
1017
1099
10.4171/OWR/2010/18
http://www.ems-ph.org/doi/10.4171/OWR/2010/18
Algebraic Groups
Michel
Brion
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Jens Carsten
Jantzen
University of Aarhus, AARHUS, DENMARK
The workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: • classical and quantum cohomology of homogeneous varieties, • representation theory and its connections to orbits and flag varieties.
Algebraic geometry
Nonassociative rings and algebras
Group theory and generalizations
General
1101
1163
10.4171/OWR/2010/19
http://www.ems-ph.org/doi/10.4171/OWR/2010/19
Non-positive Curvature and Geometric Structures in Group Theory
Martin
Bridson
University of Oxford, OXFORD, UNITED KINGDOM
Linus
Kramer
Universität Münster, MÜNSTER, GERMANY
Bertrand
Rémy
Université Claude Bernard Lyon 1, VILLEURBANNE CEDEX, FRANCE
Karen
Vogtmann
Cornell University, ITHACA, UNITED STATES
The focus of this meeting was the use of geometric methods to study infinite discrete groups. Key topics included isometric actions of such groups on spaces of nonpositive curvature, such as CAT(0) cube complexes, buildings, and hyperbolic or symmetric spaces. These actions lead to a rich and fruitful interplay between geometry and group theoretic questions.
Group theory and generalizations
Manifolds and cell complexes
General
1165
1224
10.4171/OWR/2010/20
http://www.ems-ph.org/doi/10.4171/OWR/2010/20
Progress in Surface Theory
Uwe
Abresch
Ruhr-Universität Bochum, BOCHUM, GERMANY
Josef
Dorfmeister
TU München, MÜNCHEN GARCHING, GERMANY
Masaaki
Umehara
Tokyo Institute of Technology, TOKYO, JAPAN
The theory of surfaces is interpreted these days as a prototype of submanifold geometry and is characterized by the substantial application of PDE methods and methods from the theory of integrable systems, in addition to the more classical techniques from real and/or complex analysis. In addition, surfaces with singularities are studied intensively. In this workshop we brought together all the main strands of modern surface theory.
Nonassociative rings and algebras
Functions of a complex variable
Partial differential equations
Dynamical systems and ergodic theory
1225
1318
10.4171/OWR/2010/21
http://www.ems-ph.org/doi/10.4171/OWR/2010/21
Interactions between Algebraic Geometry and Noncommutative Algebra
Dieter
Happel
Technische Universität Chemnitz, CHEMNITZ, GERMANY
Lance
Small
University of California, San Diego, LA JOLLA, UNITED STATES
J. Toby
Stafford
The University of Manchester, MANCHESTER, UNITED KINGDOM
Michel
Van den Bergh
Hasselt University, HASSELT, BELGIUM
The aim of this workshop was to communicate the most current developments in the field of noncommutative algebra and its interactions with algebraic geometry and representation theory.
Associative rings and algebras
General
1319
1381
10.4171/OWR/2010/22
http://www.ems-ph.org/doi/10.4171/OWR/2010/22
Motives and Homotopy Theory of Schemes
Bruno
Kahn
Université Paris 7, PARIS CEDEX 05, FRANCE
Marc
Levine
Universität Duisburg-Essen, ESSEN, GERMANY
Michael
Spiess
Universität Bielefeld, BIELEFELD, GERMANY
The 2010 program on Motives and Homotopy Theory of Schemes consisted of a lively and varied series of 19 one-hour lectures on the latest developments in the field, presenting a wide range of aspects of this multifaceted subject. Besides the lectures, we were happy to welcome a wide range of nationalities and age groups to the conference.
Algebraic geometry
$K$-theory
General
1383
1429
10.4171/OWR/2010/23
http://www.ems-ph.org/doi/10.4171/OWR/2010/23
Phase Transitions
Kaushik
Bhattacharya
California Institute of Technology, PASADENA, UNITED STATES
Dmitry
Ioffe
Technion - Israel Institute of Technology, HAIFA, ISRAEL
Stephan
Luckhaus
Universität Leipzig, LEIPZIG, GERMANY
Felix
Otto
für Mathematik in den Naturwissenschaften, LEIPZIG, GERMANY
Phase transitions are common phenomena which occur in many fields of material sciences. Models of phase transitions in diverse physical systems often lead to ill-posed mathematical problems whose solutions are characterized by oscillations, bifurcations and singularities. Random fluctuations and stochastic events also play an important role in determining the nature of the solutions.
Mechanics of particles and systems
Partial differential equations
Mechanics of deformable solids
Statistical mechanics, structure of matter
1431
1484
10.4171/OWR/2010/24
http://www.ems-ph.org/doi/10.4171/OWR/2010/24
Geometry, Quantum Fields, and Strings: Categorial Aspects
Peter
Bouwknegt
Australian National University, CANBERRA, AUSTRALIA
Daniel
Freed
University of Texas at Austin, AUSTIN, UNITED STATES
Christoph
Schweigert
Universität Hamburg, HAMBURG, GERMANY
Currently, in the interaction between string theory, quantum field theory and topology, there is an increased use of category-theoretic methods. Independent developments (e.g. the categorificiation of knot invariants, bundle gerbes and topological field theories on extended cobordism categories) have put higher categories in the focus. The workshop has brought together researchers working on diverse problems in which categorical ideas play a significant role.
Quantum theory
General
1485
1533
10.4171/OWR/2010/25
http://www.ems-ph.org/doi/10.4171/OWR/2010/25
Geometrie
John
Lott
University of California, BERKELEY, UNITED STATES
Iskander
Taimanov
Siberian Branch of the Russian Academy of Sciences, NOVOSIBIRSK, RUSSIAN FEDERATION
Burkhard
Wilking
Universität Münster, MÜNSTER, GERMANY
The program of this meeting covered a wide range of recent developements in geometry such as geometric flows and connections to transport problems, metric and Alexandrov geometry, positively curved manifolds and the positive energy theorem.
Differential geometry
General
1535
1572
10.4171/OWR/2010/26
http://www.ems-ph.org/doi/10.4171/OWR/2010/26
Classical Algebraic Geometry
David
Eisenbud
Mathematical Sciences Research Institute, BERKELEY, UNITED STATES
Frank-Olaf
Schreyer
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
Ravi
Vakil
Stanford University, STANFORD, UNITED STATES
Claire
Voisin
Institut de Mathématiques de Jussieu, PARIS, FRANCE
Algebraic geometry studies properties of specific algebraic varieties, on the one hand, and moduli spaces of all varieties of fixed topological type on the other hand. Of special importance is the moduli space of curves, whose properties are subject of ongoing research. The rationality versus general type question of these and related spaces is of classical and also very modern interest with recent progress presented in the conference. Certain different birational models of the moduli space of curves and maps have an interpretation as moduli spaces of singular curves and maps. For specific varieties a wide range of questions was addressed, including extrinsic questions (syzygies, the k-secant lemma) and intrinsic ones (generalization of notions of positivity of line bundles, closure operations on ideals and sheaves).
Algebraic geometry
General
1573
1623
10.4171/OWR/2010/27
http://www.ems-ph.org/doi/10.4171/OWR/2010/27
Analysis and Geometric Singularities
Jochen
Brüning
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Rafe
Mazzeo
Stanford University, STANFORD, UNITED STATES
Paolo
Piazza
Università di Roma La Sapienza, ROMA, ITALY
The Conference on “Analysis and Geometric Singularities” took place from June 27 to July 3, 2010 and had 53 participants. The organization of the meeting followed the well-established scheme, providing plenty of discussion time which was intensely used, especially by the young participants. The four survey talks were given by Gilles Carron, Jean-Michel Bismut, Ulrich Bunke and Xiaonan Ma.
Global analysis, analysis on manifolds
Partial differential equations
General
1625
1690
10.4171/OWR/2010/28
http://www.ems-ph.org/doi/10.4171/OWR/2010/28
3
Homogeneous Dynamics and Number Theory
Manfred
Einsiedler
ETH Zürich, HG G 64.2, ZÜRICH, SWITZERLAND
Dmitry
Kleinbock
Brandeis University, WALTHAM, UNITED STATES
Elon
Lindenstrauss
The Hebrew University of Jerusalem, JERUSALEM, ISRAEL
Hee
Oh
Yale University, NEW HAVEN, UNITED STATES
The theory of flows on homogeneous spaces of Lie groups has emerged as a distinct, rapidly advancing subject over the last few decades incorporating ergodic theory, geometry and number theory. The workshop showcased the latest advances in the subject as well as a wide range of applications.
Dynamical systems and ergodic theory
Number theory
Topological groups, Lie groups
General
1703
1759
10.4171/OWR/2010/29
http://www.ems-ph.org/doi/10.4171/OWR/2010/29
Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry
Gerhard
Knieper
Ruhr-Universität Bochum, BOCHUM, GERMANY
Leonid
Polterovich
Tel-Aviv University, TEL-AVIV, ISRAEL
Leonid
Potyagailo
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
The main theme of the workshop is the interaction between the speedily developing fields of mathematics mentioned in the title. One of the purposes of the workshop is to highlight new exciting developments which are happening right now on the borderline between hyperbolic dynamics, geometric group theory and symplectic geometry.
Group theory and generalizations
Topological groups, Lie groups
Dynamical systems and ergodic theory
General
1761
1825
10.4171/OWR/2010/30
http://www.ems-ph.org/doi/10.4171/OWR/2010/30
Calculus of Variations
Camillo
De Lellis
Universität Zürich, ZÜRICH, SWITZERLAND
Gerhard
Huisken
Albert-Einstein-Institut, POTSDAM, GERMANY
Robert
McCann
University of Toronto, TORONTO, ONTARIO, CANADA
Since its invention by Newton, the calculus of variations has formed one of the central techniques for studying problems in geometry, physics, and partial differential equations. This trend continues even today. On the one hand, slow but steady progress is made on long-standing questions concerning minimal surfaces, curvature flows, and related geometric objects. Basic questions also remain in such areas as mathematical physics and general relativity. On the other hand, new types of question emerge, driven by applications from economics and engineering to materials science, whose solution will depend on developing ideas and techniques in this classical branch of analysis. The July 2010 Oberwolfach workshop on the Calculus of Variations showcased a blend of continued progress in traditional areas with surprising developments which emerged from the exploration of new lines of research.
Calculus of variations and optimal control; optimization
Partial differential equations
Differential geometry
Global analysis, analysis on manifolds
1827
1884
10.4171/OWR/2010/31
http://www.ems-ph.org/doi/10.4171/OWR/2010/31
Cohomology of Finite Groups: Interactions and Applications
Alejandro
Adem
The University of British Columbia, VANCOUVER, CANADA
Jon
Carlson
University of Georgia, ATHENS, UNITED STATES
Henning
Krause
Universität Bielefeld, BIELEFELD, GERMANY
The cohomology of finite groups is an important tool in many subjects including representation theory and algebraic topology. This meeting was the third in a series that has emphasized the interactions of group cohomology with other areas.
Group theory and generalizations
Algebraic topology
Manifolds and cell complexes
General
1885
1952
10.4171/OWR/2010/32
http://www.ems-ph.org/doi/10.4171/OWR/2010/32
Wavelet and Multiscale Methods
Albert
Cohen
Université Pierre et Marie Curie, PARIS, FRANCE
Wolfgang
Dahmen
Technische Hochschule Aachen, AACHEN, GERMANY
Ronald
DeVore
Texas A&M University, COLLEGE STATION, UNITED STATES
Angela
Kunoth
Universität Paderborn, PADERBORN, GERMANY
Various scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers. These have advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines. A special emphasis was placed on high dimensional problems since these amplify even further the need for novel theory and computation.
Associative rings and algebras
General
1953
2025
10.4171/OWR/2010/33
http://www.ems-ph.org/doi/10.4171/OWR/2010/33
Mathematical Theory and Modelling in Atmosphere-Ocean-Science
Andrew
Majda
New York University, NEW YORK, UNITED STATES
Bjorn
Stevens
Max Planck Institute for Meteorology, HAMBURG, GERMANY
Rupert
Klein
Freie Universität Berlin, BERLIN, GERMANY
Participants from around the world gathered to review application and development of mathematics in relation to problems in the atmospheric, oceanic and climate sciences.
Geophysics
Probability theory and stochastic processes
Numerical analysis
Fluid mechanics
2027
2099
10.4171/OWR/2010/34
http://www.ems-ph.org/doi/10.4171/OWR/2010/34
Low-Dimensional Topology and Number Theory
Paul
Gunnells
University of Massachusetts, AMHERST, UNITED STATES
Walter
Neumann
Barnard College, Columbia University, NEW YORK, UNITED STATES
Adam
Sikora
University at Buffalo SUNY, BUFFALO, UNITED STATES
Don
Zagier
, BONN, GERMANY
The workshop on Low-Dimensional Topology and Number Theory brought together researchers in these areas with the intent of exploring the many tantalizing connections between Low-Dimensional Topology and Number Theory. Some of the most actively discussed topics were the appearances of modularity in quantum invariants and mutual relations between hyperbolic volume, K-theory, and asymptotics of quantum invariants.
Manifolds and cell complexes
Number theory
General
2101
2163
10.4171/OWR/2010/35
http://www.ems-ph.org/doi/10.4171/OWR/2010/35
Mini-Workshop: Mechanics of Cell Motion
Wolfgang
Alt
Rheinische Friedrich-Wilhelms-Universität Bonn, BONN, GERMANY
Davide
Ambrosi
Politecnico di Milano, MILANO, ITALY
This mini-workshop brought together established researchers and newer entrants in the field of cell motility, a challenging research area located at the crossroads of biology, mathematics and physics. Cell locomotion occurs through complex interactions that involve, among others, actin polymerization, matrix degradation, chemical signaling, adhesion and pulling on the substrate and fibers. In recent years the spatial resolution of experiments at a cellular and sub-cellular level have revealed a landscape of unexpected behaviors that demand for the application of physics and classical mathematical methods to reveal the principles that are at the basis of cell motion in terms of adhesion, directionality, internal engines. The focus of the mini-workshop was on the fundamental research in mathematical methods for biophysics of the cell, especially on the mathematical framework for the mechanics of the actin network, the encadrement of cellular traction as an inverse problem and the relation between cell-to-cell communication and morphogenesis.
Biology and other natural sciences
General
2165
2193
10.4171/OWR/2010/36
http://www.ems-ph.org/doi/10.4171/OWR/2010/36
Mini-Workshop: Combinatorics on Words
Valerie
Berthe
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Juhani
Karhumäki
University of Turku, TURKU, FINLAND
Dirk
Nowotka
Universität Stuttgart, STUTTGART, GERMANY
Jeffrey
Shallit
University of Waterloo, WATERLOO, ONTARIO, CANADA
The area of combinatorics on words is concerned with properties of sequences of symbols. It is characteristic to the field that questions arise from various mathematical problems, and hence, many fundamental results on words have been established in different areas. Over the last two decades the theory has developed into a quickly growing topic of its own. This work-shop was dedicated to reflect on the current status of the field, discuss the impact of recent results, and provide new research challenges. This is a report on the meeting and presentation of extended abstracts of the lectures.
Computer science
General
2195
2244
10.4171/OWR/2010/37
http://www.ems-ph.org/doi/10.4171/OWR/2010/37
Mini-Workshop: Exploiting Symmetry in Optimization
Volker
Kaibel
Otto-von-Guericke-Universität, MAGDEBURG, GERMANY
Leo
Liberti
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Achill
Schürmann
Universität Rostock, ROSTOCK, GERMANY
Renata
Sotirov
Tilburg University, TILBURG, NETHERLANDS
The feasible regions of mathematical optimization models quite often exhibit a high degree of symmetry. In recent years, several groups of researchers have independently worked on algorithmic approaches to exploit such symmetries in a variety of contexts. Many of the techniques that have been developed are related or rely on similar computational tools. The workshop brought together researchers working on symmetry aspects in different areas of optimization. The exchange of state-of-the-art knowledge between these areas lead to identification of important directions for future research activities.
Operations research, mathematical programming
Combinatorics
Group theory and generalizations
Convex and discrete geometry
2245
2281
10.4171/OWR/2010/38
http://www.ems-ph.org/doi/10.4171/OWR/2010/38
Komplexe Analysis
Jean-Pierre
Demailly
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Klaus
Hulek
Universität Hannover, HANNOVER, GERMANY
Thomas
Peternell
Universität Bayreuth, BAYREUTH, GERMANY
The aim of this workshop was to discuss recent developments in several complex variables and complex geometry. Special emphasis was put on the interaction between model theory and the classification theory of complex manifolds. Other topics included Kähler geometry, foliations, complex symplectic manifolds and moduli theory.
Several complex variables and analytic spaces
Algebraic geometry
General
2283
2333
10.4171/OWR/2010/39
http://www.ems-ph.org/doi/10.4171/OWR/2010/39
Actions and Invariants of Residually Finite Groups: Asymptotic Methods
George
Glauberman
University of Chicago, CHICAGO, UNITED STATES
Damien
Gaboriau
École Normale Supérieure de Lyon, LYON CEDEX 07, FRANCE
Fritz
Grunewald
Heinrich-Heine-Universität, DÜSSELDORF, GERMANY
The workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.
Group theory and generalizations
Topological groups, Lie groups
Ordinary differential equations
Dynamical systems and ergodic theory
2335
2391
10.4171/OWR/2010/40
http://www.ems-ph.org/doi/10.4171/OWR/2010/40
Nonlinear Waves and Dispersive Equations
Carlos
Kenig
University of Chicago, CHICAGO, UNITED STATES
Herbert
Koch
Universität Bonn, BONN, GERMANY
Daniel
Tataru
University of California, BERKELEY, UNITED STATES
The aim of the workshop was to discuss current developments in nonlinear waves and dispersive equations from a PDE based view. The talks centered around rough initial data, long time and global existence, perturbations of special solutions, and applications.
Partial differential equations
General
2393
2463
10.4171/OWR/2010/41
http://www.ems-ph.org/doi/10.4171/OWR/2010/41
Topologie
Thomas
Schick
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
Peter
Teichner
University of California, BERKELEY, UNITED STATES
Nathalie
Wahl
University of Copenhagen, COPENHAGEN, DENMARK
Michael
Weiss
University of Aberdeen, ABERDEEN, UNITED KINGDOM
This conference is one of the few occasions where researchers from many different areas in algebraic and geometric topology are able to meet and exchange ideas. Accordingly, the program covered a wide range of new developments in such fields as geometric group theory, rigidity of group actions, knot theory, and stable and unstable homotopy theory. More specifically, we discussed progress on problems such as the Farrell-Jones conjecture, the Levine conjecture in grope cobordism of knots and Rosenberg’s conjecture about homotopy invariance of negative algebraic K-theory, to mention just a few subjects with a name attached. One of the highlights was a series of four talks on the solution of Arf-Kervaire invariant problem by Mike Hill and Doug Ravenel, reporting on their joint work with Mike Hopkins.
Algebraic topology
Manifolds and cell complexes
General
2465
2502
10.4171/OWR/2010/42
http://www.ems-ph.org/doi/10.4171/OWR/2010/42
Deformation Methods in Mathematics and Physics
Alice
Fialowski
ELTE TTK, BUDAPEST, HUNGARY
Jürg
Fröhlich
ETH Zürich, ZÜRICH, SWITZERLAND
Martin
Schlichenmaier
Université du Luxembourg, LUXEMBOURG, LUXEMBOURG
Deformations of mathematical structures play an important role in most parts of mathematics but also in theoretical physics. In this interdisciplinary workshop, different aspects of deformations and their applications were discussed. The workshop was attended by experts in the fields, but also by quite a number of young post-docs and PhD students. One of the goals was to foster interactions between different communities.
Associative rings and algebras
Nonassociative rings and algebras
Differential geometry
Mechanics of particles and systems
2503
2560
10.4171/OWR/2010/43
http://www.ems-ph.org/doi/10.4171/OWR/2010/43
4
Mini-Workshop: Shearlets
Gitta
Kutyniok
Technische Universität Berlin, BERLIN, GERMANY
Demetrio
Labate
University of Houston, HOUSTON, UNITED STATES
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means for encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multivariate signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both the continuum and digital setting. By now, shearlet analysis has reached maturity as a research field, with deep mathematical results, efficient numerical methods, and a variety of high-impact applications. The main goal of the Mini-Workshop Shearlets was to gather the world’s experts in this field in order to foster closer interaction, attack challenging open problems, and identify future research directions.
Fourier analysis
General
2573
2611
10.4171/OWR/2010/44
http://www.ems-ph.org/doi/10.4171/OWR/2010/44
Mini-Workshop: Linear Series on Algebraic Varieties
Thomas
Bauer
Philipps-Universität, MARBURG, GERMANY
Sandra
Di Rocco
Royal Institute of Technology, STOCKHOLM, SWEDEN
Brian
Harbourne
University of Nebraska-Lincoln, LINCOLN, UNITED STATES
Tomasz
Szemberg
Krakow Pedagogical Academy, KRAKÓW, POLAND
Linear series have long played a central role in algebraic geometry. In recent years, starting with seminal papers by Demailly and Ein-Lazarsfeld, local properties of linear series – in particular local positivity, as measured by Seshadri constants – have come into focus. Interestingly, in their multi-point version they are closely related to the famous Nagata conjecture on plane curves. While a number of important basic results are available by now, there are still a large number of open questions and even completely open lines of research.
Algebraic geometry
General
2613
2650
10.4171/OWR/2010/45
http://www.ems-ph.org/doi/10.4171/OWR/2010/45
Mini-Workshop: Higher Dimensional Elliptic Fibrations
Gavin
Brown
Loughborough University, LOUGHBOROUGH, UNITED KINGDOM
Anda
Degeratu
Universität Freiburg, FREIBURG I. BR., GERMANY
Katrin
Wendland
Universität Freiburg, FREIBURG, GERMANY
Elliptic fibrations play a central role in the geometry of complex surfaces, and there is a comprehensive array of theory and examples. They arise also as a tool in many applications, such as the construction of rational points in arithmetic, metrics in differential geometry and certain string dualities in physics. In higher dimensional geometry, the foundational results of the past 30 years have not yet developed into a practical collection of everyday tools, as they have in the surface case. Nevertheless, the applications already work in higher dimensions – a glance at the literature shows the extent to which practical calculations in physics alone now far outpace the existing theory. This workshop brings together geometers, physicists and others to compare applications of elliptic fibrations and the state of the general theory.
Algebraic geometry
Differential geometry
Quantum theory
General
2651
2680
10.4171/OWR/2010/46
http://www.ems-ph.org/doi/10.4171/OWR/2010/46
Arbeitsgemeinschaft: Topological Robotics
Michael
Farber
Queen Mary University of London, LONDON, UNITED KINGDOM
Jesus
Gonzalez Espino Barros
CINVESTAV–I.P.N., MEXICO, D.F., MEXICO
Dirk
Schütz
University of Durham, DURHAM, UNITED KINGDOM
The purpose of the Arbeitsgemeinschaft was to enable PhD students and researchers to study Topological Robotics, a new field investigating topological problems motivated by robotics and engineering as well as problems of practical robotics requiring topological tools. The topics broadly fell into the areas of Topology of configuration spaces, Topological complexity of robot motion planning algorithms and Stochastic topology.
Combinatorics
Convex and discrete geometry
Algebraic topology
General
2681
2744
10.4171/OWR/2010/47
http://www.ems-ph.org/doi/10.4171/OWR/2010/47
Mathematical Challenges in Stochastic Networks
Serguei
Foss
Heriot-Watt University, EDINBURGH, UNITED KINGDOM
Günter
Last
Universität Karlsruhe, KARLSRUHE, GERMANY
Michel
Mandjes
University of Amsterdam, AMSTERDAM, NETHERLANDS
Balaji
Prabhakar
Stanford University, STANFORD, UNITED STATES
The workshop was devoted to the discussion of recent progress in modern stochastic network theory and to the exploration of open mathematical challenging problems in the field. The workshop covered a wide range of mathematical topics; while being centered around applied probability, it also included a substantial amount of graph theory and (combinatorial) optimization.
Probability theory and stochastic processes
General
2745
2812
10.4171/OWR/2010/48
http://www.ems-ph.org/doi/10.4171/OWR/2010/48
Operator Theory and Harmonic Analysis
Alexander
Borichev
Aix Marseille Université, MARSEILLE CEDEX 13, FRANCE
Raymond
Mortini
Université de Lorraine, METZ, FRANCE
Nicolai
Nikolski
Université de Bordeaux I, TALENCE CEDEX, FRANCE
Kristian
Seip
University of Trondheim, TRONDHEIM, NORWAY
The major topics discussed in this workshop were the Feichtinger conjecture and related questions of harmonic analysis, the corona problem for the ball Bn, the weighted approximation problem, and questions related to the model spaces, to multipliers, (hyper-)cyclicity, differentiability, Bezout and Fermat equations, traces and Toeplitz operators in different function spaces. A list of open problems raised at this workshop is also included.
Real functions
Functions of a complex variable
Potential theory
General
2813
2875
10.4171/OWR/2010/49
http://www.ems-ph.org/doi/10.4171/OWR/2010/49
Large Scale Stochastic Dynamics
Claudio
Landim
Estrada Dona Castorina 110, RIO DE JANEIRO RJ, BRAZIL
Stefano
Olla
Université de Paris Dauphine, PARIS CEDEX 16, FRANCE
Herbert
Spohn
TU München, GARCHING BEI MÜNCHEN, GERMANY
In focus are interacting stochastic systems with many components, ranging from stochastic partial differential equations to discrete systems as interacting particles on a lattice moving through random jumps. More specifically one wants to understand the large scale behavior, large in spatial extent but also over long time spans, as entailed by the characterization of stationary measures, effective macroscopic evolution laws, transport of conserved fields, homogenization, self-similar structure and scaling, critical dynamics, aging, dynamical phase transitions, large deviations, to mention only a few key items.
Probability theory and stochastic processes
Partial differential equations
Statistical mechanics, structure of matter
General
2877
2975
10.4171/OWR/2010/50
http://www.ems-ph.org/doi/10.4171/OWR/2010/50
Infinite Dimensional Lie Theory
Karl-Hermann
Neeb
FAU Erlangen-Nürnberg, ERLANGEN, GERMANY
Arturo
Pianzola
University of Alberta, EDMONTON, CANADA
Tudor
Ratiu
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
The workshop focussed on recent developments in infinite-dimensional Lie theory. The talks covered a broad range of topics, such as structure and classification theory of infinite-dimensional Lie algebras, geometry of infinite-dimensional Lie groups and homogeneous spaces and representations theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras.
Topological groups, Lie groups
Nonassociative rings and algebras
Group theory and generalizations
General
2977
3042
10.4171/OWR/2010/51
http://www.ems-ph.org/doi/10.4171/OWR/2010/51
Representation Theory and Harmonic Analysis
Toshiyuki
Kobayashi
University of Tokyo, TOKYO, JAPAN
Bernhard
Krötz
Universität Paderborn, PADERBORN, GERMANY
The workshop gave an overview of current research in the representation theory and harmonic analysis of reductive Lie groups and its relation to algebraic number theory. Some particular topics covered in the 17 talks related to unitarity questions and globalizations for Harish–Chandra modules, Fourier transformation on symmetric spaces and p–adic groups, affine Hecke algebras or the spectral theory of automorphic forms and trace formulas.
Topological groups, Lie groups
Abstract harmonic analysis
General
3043
3083
10.4171/OWR/2010/52
http://www.ems-ph.org/doi/10.4171/OWR/2010/52
Teichmüller Theory
Shigeyuki
Morita
University of Tokyo, TOKYO, JAPAN
Athanase
Papadopoulos
Université de Strasbourg et CNRS, STRASBOURG CEDEX, FRANCE
Robert
Penner
Aarhus University, AARHUS C, DENMARK
This is a report on the workshop on Teichmüller theory held in Oberwolfach, from November 28 to December 4, 2010. The workshop brought together people working in various aspects of the field, with a focus on recent developments. The topics discussed included higher Teichmüller theory, moduli spaces of flat connections, cluster algebras, quantization of Teichmüller spaces, the dynamical aspects of the Teichmüller and Weil-Petersson geodesic flows, the metric and the boundary theory of Teichmüller space including the new developments on Thurston’s asymmetric metric, string topology, geometric analysis on moduli spaces, and relations with three-manifold topology and with minimal surface theory were also highlighted. The mapping class group was also discussed in detail, from various points of view, including its actions on simplicial complexes and on infinite-dimensional Teichmüller spaces, its asymptotic dimension, the relation with the arc operad, the generalizations of the Johnson homomorphisms to the monoid of homology cylinders, making contact with knot theory and with the Casson invariant and other 3-manifolds invariants. There was an open problem session, which is also reported on here.
Manifolds and cell complexes
General
3085
3157
10.4171/OWR/2010/53
http://www.ems-ph.org/doi/10.4171/OWR/2010/53
Classical and Quantum Mechanical Models of Many-Particle Systems
Anton
Arnold
Technische Universität Wien, WIEN, AUSTRIA
Eric
Carlen
Rutgers University, PISCATAWAY, UNITED STATES
Laurent
Desvillettes
, CACHAN CEDEX, FRANCE
The topic of this meeting were non-linear partial differential and integro-differential equations (in particular kinetic equations and their macroscopic/fluid-dynamical limits) modeling the dynamics of many-particle systems with applications in physics, engineering, and mathematical biology. Typical questions of interest were the derivation of macro-models from micro-models, the mathematical analysis (well-posedness, stability, asymptotic behavior of solutions), and “to a lesser extent” numerical aspects of such equations. A highlight of this meeting was a mini-course on the recent mathematical theory of Landau damping.
Partial differential equations
Quantum theory
Statistical mechanics, structure of matter
General
3159
3236
10.4171/OWR/2010/54
http://www.ems-ph.org/doi/10.4171/OWR/2010/54
Mini-Workshop: 1-Motives
Luca
Barbieri-Viale
Università di Milano, MILANO, ITALY
Hélène
Esnault
FU Berlin, BERLIN, GERMANY
David
Harari
Université Paris-Sud, ORSAY CEDEX, FRANCE
One-motives were introduced by Deligne in 1974 [10], as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives [31], it can be understood as motives of level ≤ 1. While Voevosdky’s more general theory of mixed motives contains deep conjectures which at present seem to be out of reach, one-motives are much more accessible. In this mini-workshop, recent progresses were discussed: various aspects of one-motives and their realizations were explained, some applications in arithmetic algebraic geometry were given.
Number theory
Algebraic geometry
General
3237
3267
10.4171/OWR/2010/55
http://www.ems-ph.org/doi/10.4171/OWR/2010/55
Mini-Workshop: Wellposedness and Controllability of Evolution Equations
Birgit
Jacob
Universität Wuppertal, WUPPERTAL, GERMANY
Jonathan
Partington
University of Leeds, LEEDS, UNITED KINGDOM
Sandra
Pott
Lund University, LUND, SWEDEN
Hans
Zwart
Universiteit Twente, ENSCHEDE, NETHERLANDS
This mini-workshop brought together mathematicians engaged in partial differential equations, operator theory, functional analysis and harmonic analysis in order to address a number of current problems in the wellposedness and controllability of infinite-dimensional systems.
Operator theory
Systems theory; control
General
3269
3309
10.4171/OWR/2010/56
http://www.ems-ph.org/doi/10.4171/OWR/2010/56
Mini-Workshop: Algebraic and Analytic Techniques for Polynomial Vector Fields
Armengol
Gasull
Universitat Autònoma de Barcelona, BELLATERRA, SPAIN
Julia
Hartmann
RWTH Aachen, AACHEN, GERMANY
Jaume
Llibre
Universitat Autònoma de Barcelona, BELLATERRA, SPAIN
Sebastian
Walcher
RWTH Aachen, AACHEN, GERMANY
Polynomial vector fields are in the focus of research in various areas of mathematics and its applications. As a consequence, researchers from rather different disciplines work with polynomial vector fields. The main goal of this mini workshop was to create new and consolidate existing interdisciplinary exchange on the subject.
Ordinary differential equations
Dynamical systems and ergodic theory
General
3311
3348
10.4171/OWR/2010/57
http://www.ems-ph.org/doi/10.4171/OWR/2010/57