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Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
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10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
11
2014
1
Combinatorics
Jeff
Kahn
Rutgers University, PISCATAWAY, UNITED STATES
Angelika
Steger
ETH Zentrum, ZÜRICH, SWITZERLAND
Benjamin
Sudakov
ETH Zürich, ZÜRICH, SWITZERLAND
Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete Geometry, Graph theory, Combinatorial Optimization and Algebraic Combinatorics for a fruitful interaction. New results, methods and developments and future challenges were discussed. This is a report on the meeting containing abstracts of the presentations and a summary of the problem session.
Combinatorics
5
90
10.4171/OWR/2014/01
http://www.ems-ph.org/doi/10.4171/OWR/2014/01
Set Theory
Ilijas
Farah
York University, TORONTO, ONTARIO, CANADA
Sy-David
Friedman
Universität Wien, WIEN, AUSTRIA
Menachem
Magidor
The Hebrew University, JERUSALEM, ISRAEL
W. Hugh
Woodin
University of California, BERKELEY, UNITED STATES
This stimulating workshop featured a broad selection of some of the most important recent developments in combinatorial set theory, the theory and applications of forcing, large cardinal theory and descriptive set theory.
Mathematical logic and foundations
91
144
10.4171/OWR/2014/02
http://www.ems-ph.org/doi/10.4171/OWR/2014/02
Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras
Bernhard
Krötz
Universität Paderborn, PADERBORN, GERMANY
Eric
Opdam
University of Amsterdam, AMSTERDAM, NETHERLANDS
Henrik
Schlichtkrull
University of Copenhagen, COPENHAGEN Ø, DENMARK
Peter
Trapa
University of Utah, SALT LAKE CITY, UNITED STATES
The workshop gave an overview of current research in the representation theory and analysis of reductive Lie groups and its relation to spherical varieties and Hecke algebras. The participants and the speakers represented an international blend of senior researchers and young scientists at the start of their career. Some particular topics covered in the 30 talks related to structure theory of spherical varieties, p-adic symmetric spaces, symmetry breaking operators, automorphic forms, and local Langlands correspondence.
Topological groups, Lie groups
Group theory and generalizations
145
212
10.4171/OWR/2014/03
http://www.ems-ph.org/doi/10.4171/OWR/2014/03
Mixing, Transport and Coherent Structures
Sanjeeva
Balasuriya
University of Adelaide, ADELAIDE, AUSTRALIA
George
Haller
ETH Zürich, ZÜRICH, SWITZERLAND
Nicholas
Ouellette
Yale University, NEW HAVEN, UNITED STATES
Vered
Rom-Kedar
Weizmann Institute of Science, REHOVOT, ISRAEL
The subject of this workshop was coherent structures, which play a significant role in the transport and mixing of passive and active scalars in fluids on a wide range of spatial scales. Participants coming from diverse scientific communities such as experimental fluid flows, dynamical systems theory, computational mathematics and visualisation, reported on recent developments and open problems.
Ordinary differential equations
Partial differential equations
Dynamical systems and ergodic theory
Fluid mechanics
213
286
10.4171/OWR/2014/04
http://www.ems-ph.org/doi/10.4171/OWR/2014/04
Langlands Correspondence and Constructive Galois Theory
Michael
Dettweiler
Universität Bayreuth, BAYREUTH, GERMANY
Jochen
Heinloth
Universität Duisburg-Essen, ESSEN, GERMANY
Zhiwei
Yun
Stanford University, STANFORD, UNITED STATES
Recent progress in the Langlands programm provides a significant step towards the understanding of the arithmetic of global fields. The geometric Langlands program provides a systematic way to construct l-adic sheaves (resp. D-modules) on algebraic curves which subsumes the construction of classical sheaves, like rigid local systems, used in inverse Galois theory (by Belyi, Malle, Matzat, Thompson, Dettweiler, Reiter) for the construction of field extension of the rational function fields $\mathbb F_p(t)$ or $\mathbb Q(t)$ (recent work of Heinloth, Ngo, Yun and Yun). On the other hand, using Langlands correspondence for the field $\mathbb Q$, Khare, Larsen and Savin constructed many new automorphic representations which lead to new Galois realizations for classical and exceptional groups over $\mathbb Q$. It was the aim of the workshop, to bring together the experts working in the fields of Langlands correspondence and constructive Galois theory.
Algebraic geometry
Number theory
Field theory and polynomials
287
334
10.4171/OWR/2014/05
http://www.ems-ph.org/doi/10.4171/OWR/2014/05
Dirichlet Series and Function Theory in Polydiscs
Andreas
Defant
Carl von Ossietzky Universität Oldenburg, OLDENBURG, GERMANY
Manuel
Maestre
Universitat de Valencia, BURJASSOT (VALENCIA), SPAIN
Eero
Saksmann
University of Helsinki, HELSINKI, FINLAND
Kristian
Seip
University of Trondheim, TRONDHEIM, NORWAY
The interaction between Dirichlet series and function theory in polydiscs dates back to a fundamental insight of Harald Bohr and the subsequent groundbreaking work on multilinear forms and polarization by Bohnenblust and Hille. Since around 1997, there has been a revival of interest in the research area opened up by these early contributions. The workshop reflected the status of the field and led to fruitful discussions on problems of current interest and future research directions.
Functions of a complex variable
Several complex variables and analytic spaces
Functional analysis
Global analysis, analysis on manifolds
335
393
10.4171/OWR/2014/06
http://www.ems-ph.org/doi/10.4171/OWR/2014/06
New Trends in Teichmüller Theory and Mapping Class Groups
Shigeyuki
Morita
University of Tokyo, TOKYO, JAPAN
Athanase
Papadopoulos
Université de Strasbourg et CNRS, STRASBOURG CEDEX, FRANCE
Robert
Penner
Aarhus University, AARHUS C, DENMARK
Anna
Wienhard
Universität Heidelberg, HEIDELBERG, GERMANY
The program “New Trends in Teichmüller Theory and Mapping Class Groups” brought together people working in various aspects of the field and beyond. The focus was on the recent developments that include higher Teichmüller theory, the relation with three-manifolds, mapping class groups, dynamical aspects of the Weil-Petersson geodesic flow, and the relation with physics. The goal of bringing together researchers in these various areas, including young PhDs, and promoting interaction and collaboration between them was attained.
Functions of a complex variable
Several complex variables and analytic spaces
Manifolds and cell complexes
395
452
10.4171/OWR/2014/07
http://www.ems-ph.org/doi/10.4171/OWR/2014/07
Representation Theory of Quivers and Finite Dimensional Algebras
William
Crawley-Boevey
University of Leeds, LEEDS, UNITED KINGDOM
Osamu
Iyama
Nagoya University, NAGOYA, JAPAN
Bernhard
Keller
Université Paris Diderot - Paris 7, PARIS CEDEX 13, FRANCE
Henning
Krause
Universität Bielefeld, BIELEFELD, GERMANY
Methods and results from the representation theory of quivers and finite dimensional algebras have led to many interactions with other areas of mathematics. Such areas include the theory of Lie algebras and quantum groups, commutative algebra, algebraic geometry and topology, and in particular the new theory of cluster algebras. The aim of this workshop was to further develop such interactions and to stimulate progress in the representation theory of algebras.
Associative rings and algebras
Commutative rings and algebras
Linear and multilinear algebra; matrix theory
Category theory; homological algebra
453
529
10.4171/OWR/2014/08
http://www.ems-ph.org/doi/10.4171/OWR/2014/08
Mini-Workshop: Kähler Groups
Dieter
Kotschick
Universität München, MÜNCHEN, GERMANY
Domingo
Toledo
University of Utah, SALT LAKE CITY, UNITED STATES
We reviewed recent advances in the study of fundamental groups of compact Kähler manifolds, involving an interesting mix of complex geometry, harmonic maps and non-Abelian Hodge theory, and geometric group theory. There were also extensive discussions of open problems in the area.
Algebraic geometry
Group theory and generalizations
Several complex variables and analytic spaces
531
553
10.4171/OWR/2014/09
http://www.ems-ph.org/doi/10.4171/OWR/2014/09
Mini-Workshop: Negative Curves on Algebraic Surfaces
Sandra
Di Rocco
Royal Institute of Technology, STOCKHOLM, SWEDEN
Alex
Küronya
Budapest University of Technology & Economics, BUDAPEST, HUNGARY
Stefan
Müller-Stach
Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
Tomasz
Szemberg
Krakow Pedagogical Academy, KRAKÓW, POLAND
Negative curves play a prominent role in the geometry of projective surfaces. They occur naturally as the irreducible components of exceptional loci of resolutions of surface singularities, at the same time, they are closely related to the geometry of the effective cone, and thus form an important building block of the Minimal Model Program. In the case of surfaces, classes of negative curves span extremal rays of the Mori cone. Any knowledge about them on a given surface reveals important information on linear series as well.
Algebraic geometry
555
593
10.4171/OWR/2014/10
http://www.ems-ph.org/doi/10.4171/OWR/2014/10
Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids
Vladimir
Dotsenko
Trinity College, DUBLIN, IRELAND
Ulrich
Krähmer
University of Glasgow, GLASGOW, UNITED KINGDOM
This workshop brought together 17 researchers whose work involves Batalin–Vilkovisky algebras, operads, and related structures such as Gerstenhaber algebras and cyclic homology. It featured introductory lectures on some relevant topics followed by talks about recent research results.
Category theory; homological algebra
$K$-theory
Algebraic topology
Relativity and gravitational theory
595
634
10.4171/OWR/2014/11
http://www.ems-ph.org/doi/10.4171/OWR/2014/11
Enumerative Combinatorics
Mireille
Bousquet-Mélou
Université de Bordeaux I, TALENCE CEDEX, FRANCE
Michael
Drmota
Technische Universität Wien, WIEN, AUSTRIA
Christian
Krattenthaler
Universität Wien, WIEN, AUSTRIA
Marc
Noy
Universitat Politècnica de Catalunya, BARCELONA, SPAIN
Enumerative Combinatorics focusses on the exact and asymptotic counting of combinatorial objects. It is strongly connected to the probabilistic analysis of large combinatorial structures and has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, graph theory and computer science. This workshop brought together experts from all these various fields, including also computer algebra, with the goal of promoting cooperation and interaction among researchers with largely varying backgrounds.
Combinatorics
Probability theory and stochastic processes
Computer science
Statistical mechanics, structure of matter
635
720
10.4171/OWR/2014/12
http://www.ems-ph.org/doi/10.4171/OWR/2014/12
Adaptive Statistical Inference
Mark
Low
University of Pennsylvania, PHILADELPHIA, UNITED STATES
Axel
Munk
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
Alexandre
Tsybakov
Timbre J340, MALAKOFF CEDEX, FRANCE
This workshop in mathematical statistics highlights recent advances in adaptive methods for statistical estimation, testing and confidence sets. Related open mathematical problems are discussed with potential impact on the development of computationally efficient algorithms of data processing under prior uncertainty. Parcticular emphasis is on high dimensional models, inverse problems and discrtete structures.
Statistics
Probability theory and stochastic processes
721
779
10.4171/OWR/2014/13
http://www.ems-ph.org/doi/10.4171/OWR/2014/13
Nonlinear Evolution Equations: Analysis and Numerics
Marlis
Hochbruck
Karlsruher Institut für Technologie (KIT), KARLSRUHE, GERMANY
Serge
Nicaise
Université de Valenciennes et du Hainaut Cambrésis, VALENCIENNES CEDEX 9, FRANCE
Alexander
Ostermann
Universität Innsbruck, INNSBRUCK, AUSTRIA
Roland
Schnaubelt
Karlsruher Institut für Technologie (KIT), KARLSRUHE, GERMANY
The workshop was devoted to the analytical and numerical investigation of nonlinear evolution equations. The main aim was to stimulate a closer interaction between experts in analytical and numerical methods for areas such as wave and Schrödinger equations or the Navier–Stokes equations and fluid dynamics.
Partial differential equations
Numerical analysis
781
868
10.4171/OWR/2014/14
http://www.ems-ph.org/doi/10.4171/OWR/2014/14
Flat Surfaces and Dynamics on Moduli Space
Howard
Masur
University of Chicago, CHICAGO, UNITED STATES
Martin
Möller
J.W. Goethe-Universität, FRANKFURT A.M., GERMANY
Anton
Zorich
Université Paris 7, PARIS CEDEX 13, FRANCE
Dynamics of the Teichmüller geodesic flow on the moduli space of curves and asymptotic monodromy of the Hodge bundle along this flow have numerous applications to dynamics and geometry of measured foliations, to billiards in polygons, to interval exchange transformations, and to geometry of flat surfaces.
Functions of a complex variable
Several complex variables and analytic spaces
Dynamical systems and ergodic theory
Manifolds and cell complexes
869
941
10.4171/OWR/2014/15
http://www.ems-ph.org/doi/10.4171/OWR/2014/15
2
Arbeitsgemeinschaft: Superrigidity
Uri
Bader
Technion - Israel Institute of Technology, HAIFA, ISRAEL
Alex
Furman
University of Illinois at Chicago, CHICAGO, UNITED STATES
Jesse
Peterson
Vanderbilt University, NASHVILLE, UNITED STATES
The purpose of the Arbeitsgemeinschaft was to review old and new phenomenas of rigidity in mathematics. The broad spectrum of such results was covered, such as Margulis-Zimmer superrigidity, cocyle and character rigidity.
Group theory and generalizations
Topological groups, Lie groups
Measure and integration
Operator theory
957
975
10.4171/OWR/2014/16
http://www.ems-ph.org/doi/10.4171/OWR/2014/16
Real Algebraic Geometry With A View Toward Systems Control and Free Positivity
Didier
Henrion
LAAS-CNRS, TOULOUSE CEDEX 4, FRANCE
Salma
Kuhlmann
Universität Konstanz, KONSTANZ, GERMANY
Victor
Vinnikov
Ben Gurion University of the Negev, BEER SHEVA, ISRAEL
New interactions between real algebraic geometry, convex optimization and free non-commutative geometry have recently emerged, and have been the subject of numerous international meetings. The aim of the workshop was to bring together experts, as well as young researchers, to investigate current key questions at the interface of these fields, and to explore emerging interdisciplinary applications.
Field theory and polynomials
Commutative rings and algebras
Algebraic geometry
Calculus of variations and optimal control; optimization
977
1045
10.4171/OWR/2014/17
http://www.ems-ph.org/doi/10.4171/OWR/2014/17
Mini-Workshop: Mathematical Physics meets Sparse Recovery
David
Gross
Universität Freiburg, FREIBURG I BR, GERMANY
Felix
Krahmer
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
Rachel
Ward
The University of Texas at Austin, AUSTIN, UNITED STATES
Andreas
Winter
Universitat Autònoma de Barcelona, BELLATERRA (BARCELONA), SPAIN
In recent years, there have been several fruitful interchanges of methods between the fields of sparse and low-rank recovery on the one hand and quantum information theory on the other hand. One way to understand this seemingly surprising coincidence is that the analysis of vector- and matrix-valued randomized constructions plays an important role in both fields. An example is the realization that certain matrix-valued large deviation bounds can be employed to substantially simplify and generalize the analysis of low-rank matrix recovery schemes. In this workshop, the participants worked to identify and collaborate on further mathematical problems that are being researched in parallel by the two communities. Topics that have been discussed include • Tools for the analysis of vector- and matrix-valued randomized constructions and their application to phase retrieval problems • Conversely, tools for de-randomizing such protocols, based, e.g., on spherical designs. • Uncertainty relations, e.g., for the task of lower-bounding the number of measurements required for signal identification. • Time-frequency methods (known as phase-space methods in physics). • Matrix- and tensor norms: computational tools, complexity, relaxations and their application to tensor recovery.
Linear and multilinear algebra; matrix theory
Functional analysis
Operator theory
1047
1073
10.4171/OWR/2014/18
http://www.ems-ph.org/doi/10.4171/OWR/2014/18
Mini-Workshop: Mathematical Models for Cancer Cell Migration
Andreas
Deutsch
Technische Universität Dresden, DRESDEN, GERMANY
Thomas
Hillen
University of Alberta, EDMONTON, CANADA
Christina
Surulescu
Technische Universität Kaiserslautern, KAISERSLAUTERN, GERMANY
Michael
Winkler
Universität Paderborn, PADERBORN, GERMANY
Tumour cell invasion is an essential hallmark in the progression of malignant cancer. Thereby, cancer cells migrate through the surrounding tissue (normal cells, extracellular matrix, interstitial fluid) towards blood or lymph vessels which they penetrate and thus access the blood flow. They are carried by blood circulation to distant locations where they extravasate and develop new tumours, a phenomenon known as metastasis. The invasive spread of cancer cells is highly complex – it involves several mechanisms, like diffusion, chemotaxis and haptotaxis; these in turn are conditioned by and influence the subcellular dynamics. Mathematical models offer a powerful tool to gain insight into the complicated biological processess connected to tumour invasion and have also stimulated advanced mathematical research. Some of the new developments in the field of biomedical oncology were inspired by such models. A significant challenge arises due to the interactions of cancer cells with a complicated and structured microenvironment of healthy tissue. Many of the models of cancer cell migration are based on partial differential equations (PDEs) including spatial heterogeneity, orientational tissue structure, tissue stiffness and deformability. Specific settings relate to reaction-diffusion equations, transport equations, continuum equations, and to their multi-scale analysis, to local and global existence and uniqueness, to pattern formation, blow-ups and invasions. A further approach involves agent-based models providing a characterisation of cell migration by way of simulating the (inter)actions of autonomous agents (individual cells, collective dynamics) and aiming for assessing their effects on the entire system. In this meeting we covered the full spectrum between macroscopic PDE models and microscopic individual based models with the common goal of modelling cancer cell migration. Of particular interest was the derivation of macroscopic properties from microscopic details. Similar multiscale models have been used in other contexts (such as chemotaxis for example), and we gained some significant insight from the collaborations in this workshop. In this one week meeting we posted nine open ended problems (outlined below), which will form the seed for new collaborations going far beyond this workshop.
Biology and other natural sciences
Partial differential equations
1075
1109
10.4171/OWR/2014/19
http://www.ems-ph.org/doi/10.4171/OWR/2014/19
Mini-Workshop: Infinite Dimensional Hopf Algebras
Ken
Brown
University of Glasgow, GLASGOW, UNITED KINGDOM
Kenneth
Goodearl
University of California, SANTA BARBARA, UNITED STATES
Thomas
Lenagan
University of Edinburgh, EDINBURGH, UNITED KINGDOM
James
Zhang
University of Washington, SEATTLE, UNITED STATES
This is a report of the above mini-workshop. It contains brief accounts of all 17 talks given at the meeting, with commentary on their interconnections. A selection of the numerous open questions discussed at and generated by the meeting is provided in a separate section. The cumulative references listed for each of the talks together provide an up-to-date guide to the fast-growing literature on the topics covered.
Associative rings and algebras
1111
1137
10.4171/OWR/2014/20
http://www.ems-ph.org/doi/10.4171/OWR/2014/20
Hilbert Modules and Complex Geometry
Kenneth
Davidson
University of Waterloo, WATERLOO, ONTARIO, CANADA
Ronald
Douglas
Texas A&M University, COLLEGE STATION, UNITED STATES
Jörg
Eschmeier
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
Harald
Upmeier
Philipps-Universität, MARBURG, GERMANY
The major topics discussed in the workshop were Hilbert modules of analytic functions on domains in Cn, Toeplitz and Hankel operators, reproducing kernel Hilbert spaces and multiplier algebras, the interplay of complex geometry and operator theory, non-commutative function theory and operator theory, Hilbert bundles on symmetric spaces.
Several complex variables and analytic spaces
Functional analysis
Operator theory
1139
1219
10.4171/OWR/2014/21
http://www.ems-ph.org/doi/10.4171/OWR/2014/21
Modular Forms
Jan Hendrik
Bruinier
Technische Hochschule Darmstadt, DARMSTADT, GERMANY
Atsushi
Ichino
Kyoto University, KYOTO, JAPAN
Tamotsu
Ikeda
Kyoto University, KYOTO, JAPAN
Özlem
Imamoglu
ETH Zentrum, ZÜRICH, SWITZERLAND
The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
Number theory
1221
1277
10.4171/OWR/2014/22
http://www.ems-ph.org/doi/10.4171/OWR/2014/22
Stochastic Analysis in Finance and Insurance
René
Carmona
Princeton University, PRINCETON, UNITED STATES
Martin
Schweizer
ETH Zürich, ZÜRICH, SWITZERLAND
Nizar
Touzi
Ecole Polytechnique, PALAISEAU, FRANCE
This workshop brought together leading experts and a large number of younger researchers in stochastic analysis and mathematical finance from all over the world. During a highly intense week, participants exchanged many ideas during talks and discussions, and laid foundations for new collaborations and further developments in the field.
Game theory, economics, social and behavioral sciences
Probability theory and stochastic processes
1279
1312
10.4171/OWR/2014/23
http://www.ems-ph.org/doi/10.4171/OWR/2014/23
Schnelle Löser für Partielle Differentialgleichungen
Randolph
Bank
University of California, San Diego, LA JOLLA, UNITED STATES
Lars
Grasedyck
RWTH Aachen, AACHEN, GERMANY
Wolfgang
Hackbusch
Mathematik in den Naturwissenschaften, LEIPZIG, GERMANY
Gabriel
Wittum
J.W. Goethe-Universität, FRANKFURT A.M., GERMANY
This workshop was well attended by 52 participants with broad geographic representation from 11 countries and 3 continents. It was a nice blend of researchers with various backgrounds.
Numerical analysis
1313
1364
10.4171/OWR/2014/24
http://www.ems-ph.org/doi/10.4171/OWR/2014/24
Interactions between Algebraic Geometry and Noncommutative Algebra
Markus
Reineke
Bergische Universität Wuppertal, WUPPERTAL, GERMANY
J. Toby
Stafford
The University of Manchester, MANCHESTER, UNITED KINGDOM
Catharina
Stroppel
Universität Bonn, BONN, GERMANY
Michel
Van den Bergh
Hasselt University, HASSELT, BELGIUM
The workshop presented the current developments in the field of noncommutative algebra geometry and its interactions with algebraic geometry and representation theory.
Algebraic geometry
Associative rings and algebras
1365
1402
10.4171/OWR/2014/25
http://www.ems-ph.org/doi/10.4171/OWR/2014/25
Algebraic Structures in Low-Dimensional Topology
Louis
Kauffman
University of Illinois at Chicago, CHICAGO, UNITED STATES
Vassily
Manturov
Bauman Moscow State Technical University, MOSCOW, RUSSIAN FEDERATION
Kent
Orr
Indiana University, BLOOMINGTON, UNITED STATES
Robert
Schneiderman
Lehman College, City University of New York, BRONX, UNITED STATES
geometric topology, knot theory, virtual knot theory, invari- ants, parity, graph links, free knots, knot cobordism, virtual knot cobordism, groups, fundamental groups, braids, representations of groups, skein theory, knot polynomials, quandles, skein modules, quandle cohomology, distributive cohomology, manifolds, surgery
The workshop concentrated on important and interrelated invariants in low dimensional topology. This work involved virtual knot theory, knot theory, three and four dimensional manifolds and their properties.
Manifolds and cell complexes
1403
1458
10.4171/OWR/2014/26
http://www.ems-ph.org/doi/10.4171/OWR/2014/26
Okounkov Bodies and Applications
Megumi
Harada
McMaster University, HAMILTON, ONTARIO, CANADA
Kiumars
Kaveh
University of Pittsburgh, PITTSBURGH, UNITED STATES
Askold
Khovanskii
University of Toronto, TORONTO, ONTARIO, CANADA
The theory of Newton–Okounkov bodies, also called Okounkov bodies, is a relatively new connection between algebraic geometry and convex geometry. It generalizes the well-known and extremely rich correspondence between geometry of toric varieties and combinatorics of convex integral polytopes. Following a successful MFO Mini-workshop on this topic in August 2011, the MFO Half-Workshop 1422b, “Okounkov bodies and applications”, held in May 2014, explored the development of this area in recent years, with particular attention to applications and relationships to other areas such as number theory and tropical geometry.
Algebraic geometry
Geometry
1459
1513
10.4171/OWR/2014/27
http://www.ems-ph.org/doi/10.4171/OWR/2014/27
Stochastic Analysis: Around the KPZ Universality Class
Alice
Guionnet
Massachusetts Institute of Technology, CAMBRIDGE, UNITED STATES
Martin
Hairer
University of Warwick, COVENTRY, UNITED KINGDOM
Wendelin
Werner
ETH Zürich, ZÜRICH, SWITZERLAND
The Gaussian distribution is the “universal” distribution arising in a huge variety of contexts that describes the compound effect of the random fluctuations of many independent (or weakly dependent) sources of randomness that are combined in a (close to) additive way. While this has been very well understood for a long time, the last few years have seen an explosion of results around the “KPZ universality class”, which contains many systems where strongly interacting individual components are combined in a highly non-linear way. In this class, which is still rather poorly understood from a mathematical perspective, fluctuations typically exhibit scaling exponent 1/3 instead of the exponent 1/2 familiar from the central limit theorem and limiting distributions are of Tracy-Widom type rather than Gaussian. This workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to the understanding of the KPZ equation and universality class. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to renormalisation theory, stochastic analysis, random matrix theory, classical probability theory, orthogonal polynomials, the theory of rough paths, etc.
Probability theory and stochastic processes
Partial differential equations
Statistical mechanics, structure of matter
1515
1568
10.4171/OWR/2014/28
http://www.ems-ph.org/doi/10.4171/OWR/2014/28
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 topics discussed at the meeting ranged from geometric evolution equations to minimal surfaces, Riemannian foliations and hyperbolic geometry. Because of a flexible schedule, the 53 participants had ample time for discussion.
Differential geometry
1569
1623
10.4171/OWR/2014/29
http://www.ems-ph.org/doi/10.4171/OWR/2014/29
Computational Multiscale Methods
Carsten
Carstensen
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Björn
Engquist
University of Texas at Austin, AUSTIN, UNITED STATES
Daniel
Peterseim
Universität Bonn, BONN, GERMANY
Almost all processes in engineering and the sciences are characterised by the complicated relation of features on a large range of nonseparable spatial and time scales. The workshop concerned the computer-aided simulation of such processes, the underlying numerical algorithms and the mathematics behind them to foresee their performance in practical applications.
Numerical analysis
Partial differential equations
Mechanics of particles and systems
Mechanics of deformable solids
1625
1681
10.4171/OWR/2014/30
http://www.ems-ph.org/doi/10.4171/OWR/2014/30
3
Classical Algebraic Geometry
Olivier
Debarre
École Normale Supérieure, PARIS CEDEX 05, FRANCE
David
Eisenbud
Mathematical Sciences Research Institute, BERKELEY, UNITED STATES
Gavril
Farkas
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Ravi
Vakil
Stanford University, STANFORD, UNITED STATES
Progress in algebraic geometry usually comes through the introduction of new tools and ideas to tackle the classical problems of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as Voisin’s “existence of decomposition of the diagonal”, and the extension of the class of geometric objects considered to allow constructions not previously possible, such as stacks, tropical geometry, and log structures. Many famous old problems and outstanding conjectures have been resolved in this way over the last 50 years. While the new theories are sometimes studied for their own sake, they are in the end best understood in the context of the classical questions they illuminate. The goal of the workshop was to study new developments in algebraic geometry, in the context of their application to the classical problems.
Algebraic geometry
1695
1745
10.4171/OWR/2014/31
http://www.ems-ph.org/doi/10.4171/OWR/2014/31
Algebraische Zahlentheorie
Benjamin
Howard
Boston College, CHESTNUT HILL, UNITED STATES
Guido
Kings
Universität Regensburg, REGENSBURG, GERMANY
Ramdorai
Sujatha
University of British Columbia, VANCOUVER, CANADA
Otmar
Venjakob
Universität Heidelberg, HEIDELBERG, GERMANY
The workshop brought together leading experts in Algebraic Number Theory. The talks presented new methods and results that intertwine a multitude of topics ranging from classical diophantine themes to modern arithmetic geometry, modular forms and p-adic aspects in number theory.
Number theory
Algebraic geometry
$K$-theory
1747
1800
10.4171/OWR/2014/32
http://www.ems-ph.org/doi/10.4171/OWR/2014/32
Calculus of Variations
Simon
Brendle
Stanford University, STANFORD, UNITED STATES
Camillo
De Lellis
Universität Zürich, ZÜRICH, SWITZERLAND
Robert
Jerrard
University of Toronto, TORONTO, ONTARIO, CANADA
The Calculus of Variations is at the same time a classical subject, with long-standing open questions which have generated deep discoveries in recent decades, and a modern subject in which new types of questions arise, driven by mathematical developments and by emergent applications. This workshop balanced the traditional variational problems with novel questions with origins in diverse areas, such as economic models of the academic labor market, or differential geometry in metric emasure spaces. In particular, the meeting featured presentations on regularity theory, existence, and classification questions related to minimal surfaces, surfaces of prescribed Gaussian curvature, and mean curvature flow; domain optimization problems; nonlinear elasticity; calibrated geometries; variational formulations of certain dynamical problems; and stochastic variational problems.
Calculus of variations and optimal control; optimization
Global analysis, analysis on manifolds
1801
1860
10.4171/OWR/2014/33
http://www.ems-ph.org/doi/10.4171/OWR/2014/33
Real Analysis, Harmonic Analysis and Applications
Michael
Christ
University of California, BERKELEY, UNITED STATES
Detlef
Müller
Christian-Albrechts-Universität zu Kiel, KIEL, GERMANY
Christoph
Thiele
Universität Bonn, BONN, GERMANY
The workshop has focused on important developments within the last few years in the point of view and methods of real and harmonic Analysis as well as significant concurrent progress in the application of these to various other fields.
Fourier analysis
1861
1931
10.4171/OWR/2014/34
http://www.ems-ph.org/doi/10.4171/OWR/2014/34
Cryptography
Johannes
Buchmann
Technische Universität Darmstadt, DARMSTADT, GERMANY
Shafi
Goldwasser
The Stata Center, CAMBRIDGE, UNITED STATES
The Oberwolfach workshop Cryptography brought together scientists from cryptography with mathematicians specializing in the algorithmic problems underlying cryptographic security. The goal of the workshop was to stimulate interaction and collaboration that enables a holistic approach to designing cryptography from the mathematical foundations to practical applications. The workshop covered basic computational problems such as factoring and computing discrete logarithms and short vectors. It addressed fundamental research results leading to innovative cryptography for protecting security and privacy in cloud applications. It also covered some practical applications.
Computer science
1933
1990
10.4171/OWR/2014/35
http://www.ems-ph.org/doi/10.4171/OWR/2014/35
Analysis, Geometry and Topology of Positive Scalar Curvature Metrics
Bernd
Ammann
Universität Regensburg, REGENSBURG, GERMANY
Bernhard
Hanke
Universität Augsburg, AUGSBURG, GERMANY
Andre
Neves
Imperial College London, LONDON, UNITED KINGDOM
One of the fundamental problems in Riemannian geometry is to understand the relation of locally defined curvature invariants and global properties of smooth manifolds. This workshop was centered around the investigation of scalar curvature, addressing questions in global analysis, geometric topology, relativity and minimal surface theory.
Differential geometry
$K$-theory
Partial differential equations
Manifolds and cell complexes
1991
2046
10.4171/OWR/2014/36
http://www.ems-ph.org/doi/10.4171/OWR/2014/36
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 was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis.
Numerical analysis
Integral transforms, operational calculus
Biology and other natural sciences
2047
2114
10.4171/OWR/2014/37
http://www.ems-ph.org/doi/10.4171/OWR/2014/37
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 brought together topologists and number theorists with the intent of exploring the many tantalizing connections between these areas.
Manifolds and cell complexes
Number theory
2115
2176
10.4171/OWR/2014/38
http://www.ems-ph.org/doi/10.4171/OWR/2014/38
Komplexe Analysis
Philippe
Eyssidieux
Université Joseph Fourier, Grenoble, SAINT MARTIN D'HERES CEDEX, FRANCE
Jun-Muk
Hwang
Cheongryangri 2-Dong, SEOUL, SOUTH KOREA
Stefan
Kebekus
Universität Freiburg, FREIBURG, GERMANY
Mihai
Paun
Université Henri Poincaré, VANDOEUVRE LES NANCY, FRANCE
Complex Analysis is a very active branch of mathematics with applications in many other fields. The central aim of our workshop was to present recent results in several complex variables and complex geometry, and to survey topics that link it to other branches of mathematics.
Several complex variables and analytic spaces
2177
2234
10.4171/OWR/2014/39
http://www.ems-ph.org/doi/10.4171/OWR/2014/39
Discrete Geometry
Imre
Bárány
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Jiří
Matoušek
Charles University, PRAHA 1, CZECH REPUBLIC
Günter
Rote
Freie Universität Berlin, BERLIN, GERMANY
Several significant new developments have been reported in many branches of discrete geometry at the workshop. The area has strong connections to other fields of mathematics for instance topology, algebraic geometry, combinatorics, and harmonic analysis. Discrete geometry is very active with hundreds of open questions and many solutions. There was a large number of young participants eager to work on these questions, and the future of discrete geometry is very safe.
Convex and discrete geometry
2235
2296
10.4171/OWR/2014/40
http://www.ems-ph.org/doi/10.4171/OWR/2014/40
New Horizons in Statistical Decision Theory
Richard
Gill
Universiteit Leiden, LEIDEN, NETHERLANDS
Madalin
Guta
University of Nottingham, NOTTINGHAM, UNITED KINGDOM
Michael
Nussbaum
Cornell University, ITHACA, UNITED STATES
The classical metric theory of statistical models (experiments) has recently been extended towards an asymptotic equivalence paradigm, allowing to classify and relate problems which are essentially infinite dimensional and ill-posed. Modern statistical concepts like these are also being integrated into the emerging field of quantum statistics, which is developing on the background of technological breakthroughs in quantum engineering. The workshop brought together leading experts in these areas, with the goal of establishing a common language, and fostering collaborations between mathematical statisticians, theoretical physicists and experimentalists.
Statistics
Quantum theory
2297
2352
10.4171/OWR/2014/41
http://www.ems-ph.org/doi/10.4171/OWR/2014/41
Topologie
Thomas
Schick
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
Peter
Teichner
Max Planck Institut für Mathematik, BONN, GERMANY
Nathalie
Wahl
University of Copenhagen, COPENHAGEN, DENMARK
Michael
Weiss
Universität Münster, MÜNSTER, GERMANY
The Oberwolfach conference “Topologie” is one of only a few opportunities for researchers from many different areas in algebraic and geometric topology to meet and exchange ideas. The program covered new developments in fields such as automorphisms of manifolds, applications of algebraic topology to differential geometry, quantum field theories, combinatorial methods in low-dimensional topology, abstract and applied homotopy theory and applications of L2-cohomology. We heard about new results describing the cohomology of the automorphism spaces of some smooth manifolds, progress on spaces of positive scalar curvature metrics, a variant of the Segal conjecture without completion, advances in classifying topological quantum field theories, and a new undecidability result in combinatorial group theory, to mention some examples. As a special attraction, the conference featured a series of three talks by Dani Wise on the combinatorics of CAT(0)-cube complexes and applications to 3-manifold topology.
Algebraic topology
Category theory; homological algebra
Manifolds and cell complexes
2353
2407
10.4171/OWR/2014/42
http://www.ems-ph.org/doi/10.4171/OWR/2014/42
Reactive Flows in Deformable, Complex Media
Margot
Gerritsen
Stanford University, STANFORD, UNITED STATES
Jan Martin
Nordbotten
University of Bergen, BERGEN, NORWAY
Iuliu Sorin
Pop
Eindhoven University of Technology, EINDHOVEN, NETHERLANDS
Barbara
Wohlmuth
TU München, GARCHING, GERMANY
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today.
Partial differential equations
Numerical analysis
Mechanics of deformable solids
Fluid mechanics
2409
2468
10.4171/OWR/2014/43
http://www.ems-ph.org/doi/10.4171/OWR/2014/43
4
Mini-Workshop: Asymptotic Statistics on Stratified Spaces
Aasa
Feragen
University of Copenhagen, COPENHAGEN, DENMARK
Stephan
Huckemann
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
James Stephen
Marron
University of North Carolina at Chapel Hill, CHAPEL HILL, UNITED STATES
Ezra
Miller
Duke University, DURHAM, UNITED STATES
Statistical analysis of non-Euclidean data such as data on manifolds is an active and established topic of research, for instance, in the statistical analysis of shape. However, many types of data naturally reside in metric spaces which are not smooth manifolds as a whole, rather they are unions of manifold strata of varying dimensions. These spaces form a key general family of geometric spaces for data analysis. Statistics in stratified spaces has recently found great interest in applications and mathematical theory building. While the fundamental theory is still in its beginnings, as a centerpiece the derivation and investigation of statistics and their asymptotics has materialized. Only a few basic results are known, but it is clear that the geometric constraints imposed by stratified spaces lead to unexpected asymptotic behavior of standard statistical properties, such as “stickiness” of means, see [4]. It is the scope of the proposed workshop to better understand fundamental relations between asymptotic behavior of statistical descriptors and global as well as local geometric and topological structures. This investigation calls for an intense collaboration of the fields involved: statistics & stochastics; geometry & topology; combinatorics, algorithms & numerics. This workshop sought to bring together world-leading scientists and high-potential early career researchers working in this field to collaborate on a focused set of fundamental questions.
Combinatorics
Geometry
Convex and discrete geometry
Manifolds and cell complexes
2481
2527
10.4171/OWR/2014/44
http://www.ems-ph.org/doi/10.4171/OWR/2014/44
Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions
Christoph
Böhm
Universität Münster, MÜNSTER, GERMANY
Jorge
Lauret
Universidad Nacional de Córdoba, CORDOBA, ARGENTINA
McKenzie
Wang
McMaster University, HAMILTON, ONTARIO, CANADA
Symmetry reduction methods play an important role in the study of Einstein metrics, Ricci solitons and Ricci flow. The general aim of this mini workshop was to gather researchers who have expertise in the construction of geometric examples and to survey and discuss the singularity properties of homogeneous Ricci flows and the existence question for Ricci solitons, in light of the known rigidity results and general properties. Particular topics focused on were the Alekseevskii conjecture for noncompact homogeneous Einstein spaces, the homogeneous Ricci flow and shrinking solitons.
Differential geometry
2529
2568
10.4171/OWR/2014/45
http://www.ems-ph.org/doi/10.4171/OWR/2014/45
Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations
Eugen
Mihailescu
Romanian Academy, BUCHAREST, ROMANIA
Bernd
Stratmann
Universität Bremen, BREMEN, GERMANY
The mini-workshop Differentiable Ergodic Theory, Dimension Theory and Stable Foliations brought together experts in thermodynamical formalism, hyperbolic dynamics and dimension theory from several countries. The geographic representation was broad, from Europe, USA and Japan. All participants gave interesting 1-hour talks, and there was organized also an open problem session, where directions for future work and many open problems were discussed. Among the topics presented/discussed in the workshop, there were ones related to dimension theory and probability measures on fractals, various types of hyperbolicity, systems with overlaps, complex dynamics and iterated function systems.
Dynamical systems and ergodic theory
Measure and integration
Probability theory and stochastic processes
2569
2617
10.4171/OWR/2014/46
http://www.ems-ph.org/doi/10.4171/OWR/2014/46
Arbeitsgemeinschaft: Totally Disconnected Groups
Pierre-Emmanuel
Caprace
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Nicolas
Monod
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Locally compact groups are ubiquitous in the study of many continuous or discrete structures across geometry, analysis and algebra. Every locally compact group is an extension of a connected group by a totally disconnected group. The connected case has been studied in depth, notably using Lie theory, a culminating point being reached in the 1950s with the solution to Hilbert’s 5th problem. The totally disconnected case, by contrast, remains full of challenging questions. A series of new results has been obtained in the last twenty years, and today the activity in this area is witnessing a sharp increase. These texts report on the recent Arbeitsgemeinschaft on this topic.
Topological groups, Lie groups
2619
2665
10.4171/OWR/2014/47
http://www.ems-ph.org/doi/10.4171/OWR/2014/47
Dirichlet Form Theory and its Applications
Sergio
Albeverio
Universität Bonn, BONN, GERMANY
Zhen-Qing
Chen
University of Washington, SEATTLE, UNITED STATES
Masatoshi
Fukushima
Osaka University, OSAKA, JAPAN
Michael
Röckner
Universität Bielefeld, BIELEFELD, GERMANY
Theory of Dirichlet forms is one of the main achievements in modern probability theory. It provides a powerful connection between probabilistic and analytic potential theory. It is also an effective machinery for studying various stochastic models, especially those with non-smooth data, on fractal-like spaces or spaces of infinite dimensions. The Dirichlet form theory has numerous interactions with other areas of mathematics and sciences. This workshop brought together top experts in Dirichlet form theory and related fields as well as promising young researchers, with the common theme of developing new foundational methods and their applications to specific areas of probability. It provided a unique opportunity for the interaction between the established scholars and young researchers.
Potential theory
Probability theory and stochastic processes
2667
2756
10.4171/OWR/2014/48
http://www.ems-ph.org/doi/10.4171/OWR/2014/48
Valuation Theory and Its Applications
Zoé
Chatzidakis
Université Paris 7 - Case 7012, PARIS CEDEX 13, FRANCE
Franz-Viktor
Kuhlmann
University of Saskatchewan, SASKATOON SASK., CANADA
Jochen
Koenigsmann
University of Oxford, OXFORD, GREAT BRITAIN
Florian
Pop
University of Pennsylvania, PHILADELPHIA, UNITED STATES
In recent years, the applications of valuation theory in several areas of mathematics have expanded dramatically. In this workshop, we presented applications related to algebraic geometry, number theory and model theory, as well as advances in the core of valuation theory itself. Areas of particular interest were resolution of singularities and Galois theory.
Field theory and polynomials
2757
2823
10.4171/OWR/2014/49
http://www.ems-ph.org/doi/10.4171/OWR/2014/49
Probability, Trees and Algorithms
Luc
Devroye
McGill University, MONTREAL, QC, CANADA
Ralph
Neininger
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
The subject of this workshop were probabilistic aspects of algorithms for fundamental problems such as sorting, searching, selecting of and within data, random permutations, algorithms based on combinatorial trees or search trees, continuous limits of random trees and random graphs as well as random geometric graphs. The deeper understanding of the complexity of such algorithms and of shape characteristics of large discrete structures require probabilistic models and an asymptotic analysis of random discrete structures. The talks of this workshop focused on probabilistic, combinatorial and analytic techniques to study asymptotic properties of large random combinatorial structures.
Probability theory and stochastic processes
Computer science
2825
2871
10.4171/OWR/2014/50
http://www.ems-ph.org/doi/10.4171/OWR/2014/50
Combinatorial Optimization
Gérard
Cornuéjols
Carnegie Mellon University, PITTSBURGH, UNITED STATES
Friedrich
Eisenbrand
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Bruce
Shepherd
McGill University, MONTREAL, QC, CANADA
Combinatorial Optimization is an area of mathematics that thrives from a continual influx of new questions and problems from practice. Attacking these problems has required the development and combination of ideas and techniques from different mathematical areas including graph theory, matroids and combinatorics, convex and nonlinear optimization, discrete and convex geometry, algebraic and topological methods. We continued a tradition of triannual Oberwolfach workshops, bringing together the best international researchers with younger talent to discover new connections with a particular emphasis on emerging breakthrough areas.
Operations research, mathematical programming
2873
2932
10.4171/OWR/2014/51
http://www.ems-ph.org/doi/10.4171/OWR/2014/51
Mathematical Logic: Proof Theory, Constructive Mathematics
Samuel
Buss
University of California, San Diego, LA JOLLA, UNITED STATES
Ulrich
Kohlenbach
Technische Hochschule Darmstadt, DARMSTADT, GERMANY
Michael
Rathjen
University of Leeds, LEEDS, UNITED KINGDOM
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity
Mathematical logic and foundations
2933
2986
10.4171/OWR/2014/52
http://www.ems-ph.org/doi/10.4171/OWR/2014/52
Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals
Michael
Baake
Universität Bielefeld, BIELEFELD, GERMANY
David
Damanik
Rice University, HOUSTON, UNITED STATES
Uwe
Grimm
The Open University, MILTON KEYNES, UNITED KINGDOM
The dynamical (or von Neumann) spectrum of a dynamical system and the diffraction spectrum of the corresponding measure dynamical system are intimately related. While their equivalence in the case of pure point spectra is well understood, this workshop aimed at an appropriate extension to systems with mixed spectra, building on recent developments for systems of finite local complexity and for certain random systems from the theory of point processes. Another focus was the question for connections between Schr¨odinger and dynamical spectra.
Dynamical systems and ergodic theory
Convex and discrete geometry
Quantum theory
2987
3013
10.4171/OWR/2014/53
http://www.ems-ph.org/doi/10.4171/OWR/2014/53
Mini-Workshop: Eigenvalue Problems in Surface Superconductivity
Virginie
Bonnaillie-Noël
Ecole Normale Superieure, PARIS CEDEX 05, FRANCE
Hynek
Kovařík
Università degli Studi di Brescia, BRESCIA, ITALY
Konstantin
Pankrashkin
Université Paris-Sud, ORSAY CEDEX, FRANCE
The aim of the meeting is to discuss several classes of Schrödinger equations appearing within the Ginzburg-Landau theory of superconductivity. The related problems are discussed from several perspectives including semiclassical analysis, PDE in non-smooth domains, geometric spectral theory and operator theory, which should provide a new insight into various phenomena appearing in superconducting systems.
Partial differential equations
Numerical analysis
3015
3057
10.4171/OWR/2014/54
http://www.ems-ph.org/doi/10.4171/OWR/2014/54
Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics
Karl-Hermann
Neeb
FAU Erlangen-Nürnberg, ERLANGEN, GERMANY
Gestur
Olafsson
Louisiana State University, BATON ROUGE, UNITED STATES
Palle
Jorgensen
University of Iowa, IOWA CITY, UNITED STATES
The central focus of the workshop was reflection positivity, its occurrence in physics, representation theory, abstract harmonic analysis, and stochastic analysis. The program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity.
Topological groups, Lie groups
Nonassociative rings and algebras
Quantum theory
3059
3102
10.4171/OWR/2014/55
http://www.ems-ph.org/doi/10.4171/OWR/2014/55
Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics
Rolf
Biehler
Universität Paderborn, PADERBORN, GERMANY
Reinhard
Hochmuth
Universität Hannover, HANNOVER, GERMANY
Dame Celia
Hoyles
University of London, LONDON, UNITED KINGDOM
Patrick
Thompson
Arizona State University, TEMPE, UNITED STATES
The topic of undergraduate mathematics is of considerable concern for mathematicians in universities, but also for those teaching mathematics as part of undergraduate studies other than mathematics, for employers seeking to employ a mathematically skilled workforce, and for teacher education. Different countries have made and continue to make massive efforts to improve the quality of mathematics education across all age ranges, with most of the research undertaken particularly at the school level. A growing number of mathematicians and mathematics educators now see the need for undertaking interdisciplinary research and collaborative reflections around issues at the tertiary level. The conference aimed to share research results and experiences as a background to establishing a scientific community of mathematicians and mathematics educators whose concern is the theoretical reflection, the research-based empirical investigation, and the exchange of best-practice examples of mathematics education at the tertiary level. The focus of the conference was mathematics education for mathematics, engineering and economy majors and for future mathematics teachers.
Mathematics education
3103
3175
10.4171/OWR/2014/56
http://www.ems-ph.org/doi/10.4171/OWR/2014/56
Variational Methods for Evolution
Luigi
Ambrosio
Scuola Normale Superiore, PISA, ITALY
Alexander
Mielke
Angewandte Analysis und Stochastik, BERLIN, GERMANY
Mark
Peletier
Eindhoven University of Technology, EINDHOVEN, NETHERLANDS
Giuseppe
Savaré
Università di Pavia, PAVIA, ITALY
The workshop brought together researchers from geometry, nonlinear functional analysis, calculus of variations, partial differential equations, and stochastics around a common topic: systems whose evolution is driven by variational principles such as gradient or Hamiltonian systems. The talks covered a wide range of topics, including variational tools such as incremental minimization approximations, Gamma convergence, and optimal transport, reaction-diffusion systems, singular perturbation and homogenization, rate-independent models for visco-plasticity and fracture, Hamiltonian and hyperbolic systems, stochastic models and new gradient structures for Markov processes or variational large-deviation principles.
Partial differential equations
Calculus of variations and optimal control; optimization
Probability theory and stochastic processes
Fluid mechanics
3177
3254
10.4171/OWR/2014/57
http://www.ems-ph.org/doi/10.4171/OWR/2014/57