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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
10
2013
1
Model Theory: Groups, Geometry, and Combinatorics
Ehud
Hrushovski
Hebrew University, JERUSALEM, ISRAEL
Anand
Pillay
University of Leeds, LEEDS, UNITED KINGDOM
Katrin
Tent
Universität Münster, MÜNSTER, GERMANY
Frank Olaf
Wagner
Université Lyon 1, VILLEURBANNE CEDEX, FRANCE
Overall this was a high quality meeting, with carefully chosen talks fitting in with the announced themes of the workshop.
Mathematical logic and foundations
Group theory and generalizations
5
66
10.4171/OWR/2013/01
http://www.ems-ph.org/doi/10.4171/OWR/2013/01
Graph Theory
Reinhard
Diestel
Universität Hamburg, HAMBURG, GERMANY
Robin
Thomas
Georgia Institute of Technology, ATLANTA, UNITED STATES
Gábor
Tardos
Simon Fraser University, BURNABY, BC, CANADA
This was a workshop on graph theory, with a comprehensive approach. Highlights included the emerging theories of sparse graph limits and of infinite matroids, new techniques for colouring graphs on surfaces, and extensions of graph minor theory to directed graphs and to immersions
Combinatorics
67
128
10.4171/OWR/2013/02
http://www.ems-ph.org/doi/10.4171/OWR/2013/02
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
Computational electromagnetics and acoustics revolve around a few key challenges, among which are the non-local nature of the underlying phenomena and resonance effects. The bulk of the contributions to the workshop addressed mathematical and numerical approaches meant to grapple with these two difficulties. Frequency domain integral equation methods continue to receive much attention, with a particular focus on (i) frequency robust matrix compression algorithms through so-called directional schemes or “butterfly algorithms”, and (ii) domain decomposition approaches. Time domain integral equation methods still enjoy rapid development and much progress was made in their numerical analysis. Of course, efficient and accurate absorbing boundary conditions remain a persistent topic and were covered in a few contributions. Resonance induced phenomena in a broad sense affect the analytical and numerical model for meta-materials, periodic structures, and micro-structured media. There is a lot left to be explored in this field in terms of analysis and algorithm development and a few presentations were devoted to such issues.
Numerical analysis
Optics, electromagnetic theory
129
237
10.4171/OWR/2013/03
http://www.ems-ph.org/doi/10.4171/OWR/2013/03
Numerical Methods for PDE Constrained Optimization with Uncertain Data
Matthias
Heinkenschloss
Rice University, HOUSTON, UNITED STATES
Volker
Schulz
Universität Trier, TRIER, GERMANY
Optimization problems governed by partial differential equations (PDEs) arise in many applications in the form of optimal control, optimal design, or parameter identification problems. In most applications, parameters in the governing PDEs are not deterministic, but rather have to be modeled as random variables or, more generally, as random fields. It is crucial to capture and quantify the uncertainty in such problems rather than to simply replace the uncertain coefficients with their mean values. However, treating the uncertainty adequately and in a computationally tractable manner poses many mathematical challenges. The numerical solution of optimization problems governed by stochastic PDEs builds on mathematical subareas, which so far have been largely investigated in separate communities: Stochastic Programming, Numerical Solution of Stochastic PDEs, and PDE Constrained Optimization. The workshop achieved an impulse towards cross-fertilization of those disciplines which also was the subject of several scientific discussions. It is to be expected that future exchange of ideas between these areas will give rise to new insights and powerful new numerical methods.
Partial differential equations
Calculus of variations and optimal control; optimization
Probability theory and stochastic processes
Numerical analysis
239
293
10.4171/OWR/2013/04
http://www.ems-ph.org/doi/10.4171/OWR/2013/04
Integral Geometry and its Applications
Semyon
Alesker
Tel Aviv University, TEL AVIV, ISRAEL
Andreas
Bernig
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Franz
Schuster
TU Wien, WIEN, AUSTRIA
In recent years there has been a series of striking developments in modern integral geometry which has, in particular, lead to the discovery of new relations to several branches of pure and applied mathematics. A number of examples were presented at this meeting, e.g. the work of Bernig, Solanes, and Fu on kinematic formulas on complex projective and complex hyperbolic spaces, that of Schneider and Vedel Jensen on tensor valuations and a series of results on convex body valued valuations by Abardia, Ludwig, Parapatits, and Wannerer.
Differential geometry
Abstract harmonic analysis
Convex and discrete geometry
Probability theory and stochastic processes
295
342
10.4171/OWR/2013/05
http://www.ems-ph.org/doi/10.4171/OWR/2013/05
Moduli Spaces in Algebraic Geometry
Dan
Abramovich
Brown University, PROVIDENCE, UNITED STATES
Lucia
Caporaso
Università degli studi Roma Tre, ROMA, ITALY
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 working in 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.
Algebraic geometry
343
392
10.4171/OWR/2013/06
http://www.ems-ph.org/doi/10.4171/OWR/2013/06
Mini-Workshop: Numerical Upscaling for Media with Deterministic and Stochastic Heterogeneity
Yalchin
Efendiev
Texas A&M University, COLLEGE STATION, UNITED STATES
Oleg
Iliev
ITWM, KAISERSLAUTERN, GERMANY
Panayot
Vassilevski
Lawrence Livermore National Laboratory, LIVERMORE, UNITED STATES
This minisymposium was third in series of similar events, after two very successful meetings in 2005 and 2009. The aim was to provide a forum for an extensive discussion on the theoretical aspects and on the areas of application and validity of numerical upscaling approaches for heterogeneous problems with deterministic and stochastic coefficients. The intensive discussions during the meeting contributed to a better understanding of upscaling approaches for multiscale problems with stochastic coefficients, and for synergy between scientists coming to this topic from the area of deterministic multiscale problems on one hand, and those coming from the area of SPDE on the other hand. Recent advanced results on upscaling approaches for deterministic multiscale problems were presented, well mixed with strong presentations on SDE and SPDE. The open problems in these areas were discussed, with emphasis on the case of stochastic coefficients brainstorming numerous numerical upscaling approaches. A number of young researchers, very actively working in these areas, were involved in the workshop discussing the links between scales., thus ensuring the continuity between the generations of researchers.
Numerical analysis
Computer science
Mechanics of particles and systems
Mechanics of deformable solids
393
431
10.4171/OWR/2013/07
http://www.ems-ph.org/doi/10.4171/OWR/2013/07
Mini-Workshop: The p-Laplacian Operator and Applications
Lars
Diening
Ludwig-Maximilians-Universität München, MÜNCHEN, GERMANY
Peter
Lindqvist
Norwegian University of Science and Technology, TRONDHEIM, NORWAY
Bernd
Kawohl
Universität Köln, KÖLN, GERMANY
There has been a surge of interest in the $p$-Laplacian in many different contexts from game theory to mechanics and image processing. The workshop brought together experts from many different schools of thinking to exchange their knowledge and points of view.
Combinatorics
Partial differential equations
Calculus of variations and optimal control; optimization
Computer science
433
482
10.4171/OWR/2013/08
http://www.ems-ph.org/doi/10.4171/OWR/2013/08
Mini-Workshop: Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Ito Chaos Expansions and Stochastic Geometry
Matthias
Reitzner
Universität Osnabrück, OSNABRÜCK, GERMANY
Giovanni
Peccati
Université du Luxembourg, LUXEMBOURG, LUXEMBOURG
Malliavin calculus plays an important role in the stochastic analysis for Poisson point processes. This technique is tightly connected with chaotic expansions, that were introduced in the first half of the last century by Itˆo and Wiener. These techniques found an increasing number of applications, in particular in the field of stochastic geometry. This in turn inspired new research in stochastic analysis. Leading experts and young researchers of both fields met for a week for fruitful discussions and new cooperations.
Probability theory and stochastic processes
483
520
10.4171/OWR/2013/09
http://www.ems-ph.org/doi/10.4171/OWR/2013/09
Geophysical Fluid Dynamics
Yoshikazu
Giga
University of Tokyo, TOKYO, JAPAN
Matthias
Hieber
Technische Hochschule Darmstadt, DARMSTADT, GERMANY
Edriss
Titi
University of California, Irvine, IRVINE, UNITED STATES
The workshop “Geophysical Fluid Dynamics” addressed recent advances in analytical, stochastic, modeling and computational studies of geophysical rotating fluids models. Of particular interest on the analytical and stochastic sides were the contributions concerning dispersive mechanism, regularity verses finite-time formation of singularities of certain viscous and inviscid geostrophic models, the primitive equations, Boussinesq approximation, boundary layers and fast rotating fluids. Model reductions, based on asymptotic, scaling analysis and variational methods, were presented. In addition, computational investigations were provided in support of the claim that three-dimensional geophysical turbulent flows exhibit two-dimensional features, at small Rosby numbers.
Fluid mechanics
Partial differential equations
Geophysics
Probability theory and stochastic processes
521
577
10.4171/OWR/2013/10
http://www.ems-ph.org/doi/10.4171/OWR/2013/10
Structured Function Systems and Applications
Maria
Charina
Technische Universität Dortmund, DORTMUND, GERMANY
Jean Bernard
Lasserre
LAAS-CNRS, TOULOUSE CEDEX 4, FRANCE
Mihai
Putinar
University of California, SANTA BARBARA, UNITED STATES
Joachim
Stöckler
Technische Universität Dortmund, DORTMUND, GERMANY
Quite a few independent investigations have been devoted recently to the analysis and construction of structured function systems such as e.g. wavelet frames with compact support, Gabor frames, refinable functions in the context of subdivision and so on. However, difficult open questions about the existence, properties and general efficient construction methods of such structured function systems have been left without satisfactory answers. The goal of the workshop was to bring together experts in approximation theory, real algebraic geometry, complex analysis, frame theory and optimization to address key open questions on the subject in a highly interdisciplinary, unique of its kind, exchange.
Fourier analysis
Functions of a complex variable
Integral transforms, operational calculus
Operations research, mathematical programming
579
655
10.4171/OWR/2013/11
http://www.ems-ph.org/doi/10.4171/OWR/2013/11
From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history
Moritz
Epple
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Tinne
Hoff Kjeldsen
University of Copenhagen, COPENHAGEN, DENMARK
Reinhard
Siegmund-Schultze
University of Agder, KRISTIANSAND, NORWAY
The workshop investigated historical variations of the ways in which historically boundaries were drawn between ‘pure’ mathematics on the one hand and ‘mixed’ or ‘applied’ mathematics on the other from about 1500 until today. It brought together historians and philosophers of mathematics as well as several mathematicians working on applications. Emphasis was laid upon the clarification of the relation between the historical use and the historiographical usefulness and philosophical soundness of the various categories.
History and biography
657
733
10.4171/OWR/2013/12
http://www.ems-ph.org/doi/10.4171/OWR/2013/12
Representations of Lie Groups and Supergroups
Joachim
Hilgert
Universität Paderborn, PADERBORN, GERMANY
Toshiyuki
Kobayashi
University of Tokyo, TOKYO, JAPAN
Karl-Hermann
Neeb
FAU Erlangen-Nürnberg, ERLANGEN, GERMANY
Tudor
Ratiu
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
The workshop focussed on recent developments in the representation theory of group objects in several categories, mostly finite and infinite dimensional smooth manifolds and supermanifolds. The talks covered a broad range of topics, with a certain emphasis on benchmark problems and examples such as branching, limit behavior, and dual pairs. In many talks the relation to physics played an important role.
Topological groups, Lie groups
Several complex variables and analytic spaces
Functional analysis
Differential geometry
735
799
10.4171/OWR/2013/13
http://www.ems-ph.org/doi/10.4171/OWR/2013/13
Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization
Guillaume
Bal
Columbia University, NEW YORK, UNITED STATES
Björn
Engquist
University of Texas at Austin, AUSTIN, UNITED STATES
Claude
Le Bris
Cité Descartes - Champs sur Marne, MARNE LA VALLÉE CEDEX 2, FRANCE
Houman
Owhadi
California Institute of Technology, PASADENA, UNITED STATES
The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest both from the theoretical and applied viewpoints. A characteristic feature of the workshop has been to encourage discussions on the theoretical as well as numerical challenges in the field, both from the point of view of deterministic as well as stochastic modeling of the heterogeneities.
Partial differential equations
Calculus of variations and optimal control; optimization
Numerical analysis
Mechanics of deformable solids
801
865
10.4171/OWR/2013/14
http://www.ems-ph.org/doi/10.4171/OWR/2013/14
Interfaces and Free Boundaries: Analysis, Control and Simulation
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
867
950
10.4171/OWR/2013/15
http://www.ems-ph.org/doi/10.4171/OWR/2013/15
2
Arbeitsgemeinschaft: Limits of Structures
László
Lovász
Eötvös Lorand University - ELTE TTK, BUDAPEST, HUNGARY
Balázs
Szegedy
University of Toronto, TORONTO, ONTARIO, CANADA
The goal of the Arbeitsgemeinschaft is to review current progress in the study of very large structures. The main emphasis is on the analytic approach that considers large structures as approximations of infinite analytic objects. This approach enables one to study graphs, hypergraphs, permutations, subsets of groups and many other fundamental structures.
Combinatorics
963
1024
10.4171/OWR/2013/16
http://www.ems-ph.org/doi/10.4171/OWR/2013/16
Algebraic Groups
Michel
Brion
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Jens Carsten
Jantzen
University of Aarhus, AARHUS, DENMARK
Zinovy
Reichstein
University of British Columbia, VANCOUVER, CANADA
Linear algebraic groups is an active research area in contemporary mathematics. It has rich connections to algebraic geometry, representation theory, algebraic combinatorics, number theory, algebraic topology, and differential equations. The foundations of this theory were laid by A. Borel, C. Chevalley, T. A. Springer and J. Tits in the second half of the 20th century. The Oberwolfach workshops on algebraic groups, led by Springer and Tits, played an important role in this effort as a forum for researchers, meeting at approximately 3 year intervals since the 1960s. The present workshop continued this tradition, featuring a number of important recent developments in the subject.
Algebraic geometry
Nonassociative rings and algebras
Group theory and generalizations
1025
1085
10.4171/OWR/2013/17
http://www.ems-ph.org/doi/10.4171/OWR/2013/17
Combinatorics and Probability
Béla
Bollobás
University of Cambridge, CAMBRIDGE, UNITED KINGDOM
Michael
Krivelevich
Sackler Faculty of Exact Sciences, TEL AVIV, ISRAEL
Emo
Welzl
ETH Zentrum, ZÜRICH, SWITZERLAND
The main theme of this workshop was the use of probabilistic methods in combinatorics and theoretical computer science. Although these methods have been around for decades, they are being refined all the time: they are getting more and more sophisticated and powerful. Another theme was the study of random combinatorial structures, either for their own sake, or to tackle extremal questions. Both themes were richly represented at the workshop, with many recent exciting results presented by the lecturers.
Combinatorics
Probability theory and stochastic processes
1087
1152
10.4171/OWR/2013/18
http://www.ems-ph.org/doi/10.4171/OWR/2013/18
Mathematical Statistics of Partially Identified Objects
Victor
Chernozhukov
Massachusetts Institute of Technology, CAMBRIDGE, UNITED STATES
Wolfgang Karl
Härdle
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Joel
Horowitz
Northwestern University, EVANSTON, UNITED STATES
Yaacov
Ritov
The Hebrew University of Jerusalem, JERUSALEM, ISRAEL
The workshop brought together leading experts in mathematical statistics, theoretical econometrics and bio-mathematics interested in mathematical objects occurring in the analysis of partially identified structures. The mathematical core of these ubiquitous structures has an impact on all three research areas and is expected to lead to the development of new algorithms for solving such problems.
Statistics
Probability theory and stochastic processes
Computer science
1153
1204
10.4171/OWR/2013/19
http://www.ems-ph.org/doi/10.4171/OWR/2013/19
Extremes in Branching Random Walk and Branching Brownian Motion
Louigi
Addario-Berry
McGill University, MONTREAL, CANADA
Nathanaël
Berestycki
University of Cambridge, CAMBRIDGE, UNITED KINGDOM
Nina
Gantert
TU München, GARCHING BEI MÜNCHEN, GERMANY
Branching random walk (BRW) and branching Brownian motion (BBM) are mathematical models for population growth and spatial displacement. When resources are plentiful, population sizes grow exponentially in time. In such a situation, exceptional (or extreme) individuals will be found far from the bulk of the population. The study of such individuals, and their ancestral lineages, was the subject of the workshop. On one hand, this is a classical topic, with well-known connections to the KPP-equation and to search algorithms. On the other hand, substantial recent developments have recently been obtained via new approaches to the subject (stopping lines and spines, the view from the tip, multivariate analytic combinatorics), or from researchers working in seemingly distinct areas (from stochastic partial differential equations to theoretical physics).
Probability theory and stochastic processes
Partial differential equations
Biology and other natural sciences
1205
1251
10.4171/OWR/2013/20
http://www.ems-ph.org/doi/10.4171/OWR/2013/20
Progress in Surface Theory
Uwe
Abresch
Ruhr-Universität Bochum, BOCHUM, GERMANY
Franz
Pedit
Universität Tübingen, TÜBINGEN, GERMANY
Masaaki
Umehara
Tokyo Institute of Technology, TOKYO, JAPAN
Over the last 30 years global surface theory has become pivotal in the understanding of low dimensional global phenomena. At the same time surface geometry became a platform on which seemingly different areas of mathematics – such as geometric and topological analysis, integrable systems, algebraic geometry of curves, and mathematical physics – coalesce to produce far reaching ideas, conjectures, methods and results. The workshop hosted talks on the resolutions of famous conjectures in surface geometry, including the Willmore conjecture, and on exciting new progress in the understanding of moduli spaces of special surface classes.
Differential geometry
Algebraic geometry
Geometry
Global analysis, analysis on manifolds
1253
1312
10.4171/OWR/2013/21
http://www.ems-ph.org/doi/10.4171/OWR/2013/21
Geometric Knot Theory
Dorothy
Buck
Imperial College, LONDON, UNITED KINGDOM
Jason
Cantarella
University of Georgia, ATHENS, UNITED STATES
John
Sullivan
Technische Universität Berlin, BERLIN, GERMANY
Heiko
von der Mosel
RWTH Aachen, AACHEN, GERMANY
Geometric knot theory studies relations between geometric properties of a space curve and the knot type it represents. As examples, knotted curves have quadrisecant lines, and have more distortion and more total curvature than (some) unknotted curves. Geometric energies for space curves – like the Möbius energy, ropelength and various regularizations – can be minimized within a given knot type to give an optimal shape for the knot. Increasing interest in this area over the past decade is partly due to various applications, for instance to random knots and polymers, to topological fluid dynamics and to the molecular biology of DNA. This workshop focused on the mathematics behind these applications, drawing on techniques from algebraic topology, differential geometry, integral geometry, geometric measure theory, calculus of variations, nonlinear optimization and harmonic analysis.
Manifolds and cell complexes
Calculus of variations and optimal control; optimization
Differential geometry
1313
1358
10.4171/OWR/2013/22
http://www.ems-ph.org/doi/10.4171/OWR/2013/22
Heat Kernels, Stochastic Processes and Functional Inequalities
Masha
Gordina
University of Connecticut, STORRS, UNITED STATES
Takashi
Kumagai
Kyoto University, KYOTO, JAPAN
Laurent
Saloff-Coste
Cornell University, ITHACA, UNITED STATES
Karl-Theodor
Sturm
Universität Bonn, BONN, GERMANY
The general topic of the 2013 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments: finite and infinite-dimensional manifolds, metric spaces, fractals and graphs, including random environments. The workshop brought together leading researchers from analysis, probability and geometry and provided a unique opportunity for interaction of established and young scientists from these areas. Unifying themes were heat kernel analysis, mass transport problems and related functional inequalities such as Poincar´e, Sobolev, logarithmic Sobolev, Bakry-Emery, Otto-Villani and Talagrand inequalities. These concepts were at the heart of Perelman’s proof of Poincar´e’s conjecture, as well as of the development of the Otto calculus, and the synthetic Ricci bounds of Lott-Sturm-Villani. The workshop provided participants with an opportunity to discuss how these techniques can be used to approach problems in optimal transport for non-local operators, subelliptic operators in finite and infinite dimensions, analysis on singular spaces, as well as random walks in random media.
Global analysis, analysis on manifolds
Differential geometry
Probability theory and stochastic processes
1359
1443
10.4171/OWR/2013/23
http://www.ems-ph.org/doi/10.4171/OWR/2013/23
Mini-Workshop: Spherical Varieties and Automorphic Representations
Friedrich
Knop
Universität Erlangen-Nürnberg, ERLANGEN, GERMANY
Yiannis
Sakellaridis
Rutgers University, NEWARK, UNITED STATES
This workshop brought together, for the first time, experts on spherical varieties and experts on automorphic forms, in order to discuss subjects of common interest between the two fields. Spherical varieties have a very rich and deep structure, which leads one to attach certain root systems and, eventually, a “Langlands dual” group to them. This turns out to be important for automorphic forms, as it provides a (mostly conjectural) way to analyze periods of automorphic forms and related problems in local harmonic analysis.
Topological groups, Lie groups
Number theory
Algebraic geometry
1445
1494
10.4171/OWR/2013/24
http://www.ems-ph.org/doi/10.4171/OWR/2013/24
Mini-Workshop: Constructive Homological Algebra with Applications to Coherent Sheaves and Control Theory
Mohamed
Barakat
Universität Siegen, SIEGEN, GERMANY
Thierry
Coquand
Chalmers University of Technology, GOTHENBURG, SWEDEN
Alban
Quadrat
INRIA Saclay, GIF-SUR-YVETTE CEDEX, FRANCE
The main objective of this mini-workshop is to bring together recent developments in constructive homological algebra. There, the current state already reached a level of generality which allows simultaneous application to diverse fields of applied and theoretical mathematics. In this workshop, we want to focus on simultaneous applications to system theory on the one side and to coherent sheaves and their cohomology on the other side. Surprisingly, these apparently remote fields share a considerable amount of common constructive methods. Bringing category theory and homological algebra to the computer leads to questions in logic and type theory. One goal of this workshop is to promote and enlarge this overlap.
Algebraic geometry
Commutative rings and algebras
Category theory; homological algebra
1495
1531
10.4171/OWR/2013/25
http://www.ems-ph.org/doi/10.4171/OWR/2013/25
Mini-Workshop: Localising and Tilting in Categories
Lidia
Angeleri Hügel
Università degli Studi di Verona, VERONA, ITALY
Steffen
Koenig
Universität Stuttgart, STUTTGART, GERMANY
Changchang
Xi
Capital Normal University, BEIJING, CHINA
The workshop brought together experts on localisation theory and tilting theory from different parts of mathematics with the aim of fully exploiting the power of some recent developments in so far rather independent contexts. The intensive exchange during the workshop is expected to lead to new and strengthened synergies and to new applications.
Associative rings and algebras
Commutative rings and algebras
Category theory; homological algebra
Algebraic topology
1533
1562
10.4171/OWR/2013/26
http://www.ems-ph.org/doi/10.4171/OWR/2013/26
Complex Algebraic Geometry
Fabrizio
Catanese
Universität Bayreuth, BAYREUTH, GERMANY
Christopher
Hacon
University of Utah, SALT LAKE CITY, UNITED STATES
Yujiro
Kawamata
University of Tokyo, TOKYO, JAPAN
Bernd
Siebert
Universität Hamburg, HAMBURG, GERMANY
The conference focused on several topics, classical and modern, in the classification theory of compact algebraic and Kähler varieties, and on several methods, from singularity theory, topology, homological algebra, Geometric Invariant Theory and Moduli theory, char p methods.
Algebraic geometry
Category theory; homological algebra
Several complex variables and analytic spaces
Differential geometry
1563
1627
10.4171/OWR/2013/27
http://www.ems-ph.org/doi/10.4171/OWR/2013/27
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 overall theme of the conference was geometric group theory, interpreted quite broadly. In general, geometric group theory seeks to understand algebraic properties of groups by studying their actions on spaces with various topological and geometric properties; in particular these spaces must have enough structure-preserving symmetry to admit interesting group actions. Although traditionally geometric group theorists have focused on finitely generated (and even finitely presented) countable discrete groups, the techniques that have been developed are now applied to more general groups, such as Lie groups and Kac-Moody groups, and although metric properties of the spaces have played a key role in geometric group theory, other structure such as complex or projective structures and measure-theoretic structures are being used more and more frequently.
Group theory and generalizations
Manifolds and cell complexes
1629
1675
10.4171/OWR/2013/28
http://www.ems-ph.org/doi/10.4171/OWR/2013/28
Hyperbolic Techniques for Phase Dynamics
Rinaldo
Colombo
Università degli Studi di Brescia, BRESCIA, ITALY
Philippe
LeFloch
Université Pierre et Marie Curie, PARIS, FRANCE
Christian
Rohde
Universität Stuttgart, STUTTGART, GERMANY
The progress in the theory of hyperbolic conservation laws has always been and still is driven strongly by new fields of applications. The workshop addressed aspects of modelling, analysis and numerics for fundamental problems at the interface between hyperbolic evolution and the emerging mathematical theories of complex multiphasic materials. This includes problems in fluid and solid mechanics but also very recent applications in areas like swarm and traffic modelling.
Partial differential equations
Numerical analysis
Mechanics of deformable solids
Fluid mechanics
1677
1769
10.4171/OWR/2013/29
http://www.ems-ph.org/doi/10.4171/OWR/2013/29
The Arithmetic of Fields
Moshe
Jarden
Tel Aviv University, TEL AVIV, ISRAEL
Florian
Pop
University of Pennsylvania, PHILADELPHIA, UNITED STATES
This report includes extended abstracts of talks given in a conference on the ”Arithmetic of Fields” that was held inMathematisches Forschung Institute, Oberwolfach during 16–22 June 2013. It also includes extended abstracts of talks delivered in joint sessions by participants of a parallel conference on “Quadratic Forms and Linear Algebraic Groups”.
Field theory and polynomials
1771
1818
10.4171/OWR/2013/30
http://www.ems-ph.org/doi/10.4171/OWR/2013/30
Quadratic Forms and Linear Algebraic Groups
Detlev
Hoffmann
Technische Universität Dortmund, DORTMUND, GERMANY
Alexander
Merkurjev
University of California, LOS ANGELES, UNITED STATES
Jean-Pierre
Tignol
Université Catholique de Louvain, LOUVAIN-LA NEUVE, BELGIUM
Topics discussed at the workshop “Quadratic Forms and Linear Algebraic Groups” included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties, as well as some arithmetic aspects pertaining to the theory of quadratic forms over function fields or number fields.
Number theory
Field theory and polynomials
Algebraic geometry
Associative rings and algebras
1819
1859
10.4171/OWR/2013/31
http://www.ems-ph.org/doi/10.4171/OWR/2013/31
Algebraic K-theory and Motivic Cohomology
Thomas
Geisser
Nagoya University, NAGOYA, JAPAN
Annette
Huber-Klawitter
Universität Freiburg, FREIBURG, GERMANY
Uwe
Jannsen
Universität Regensburg, REGENSBURG, GERMANY
Marc
Levine
Universität Duisburg-Essen, ESSEN, GERMANY
Algebraic K-theory and motivic cohomology are strongly related tools providing a systematic way of producing invariants for algebraic or geometric structures. The definition and methods are taken from algebraic topology, but there have been particularly fruitful applications to problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of latest results on the theory and its applications.
$K$-theory
Algebraic geometry
1861
1913
10.4171/OWR/2013/32
http://www.ems-ph.org/doi/10.4171/OWR/2013/32
3
Differentialgeometrie im Großen
Olivier
Biquard
UPMC Université Paris 6, PARIS CEDEX 05, FRANCE
Simon
Brendle
Stanford University, STANFORD, UNITED STATES
Bernhard
Leeb
Universität München, MÜNCHEN, GERMANY
The meeting continued the biannual conference series Differentialgeometrie im Großen at the MFO which was established in the 60’s by Klingenberg and Chern. Global Riemannian geometry with its connections to topology, geometric group theory and geometric analysis remained an important focus of the conference. Special emphasis was given to Kähler manifolds, geometric flows and singular spaces of non-positive curvature.
Differential geometry
Several complex variables and analytic spaces
Geometry
Manifolds and cell complexes
1929
1974
10.4171/OWR/2013/33
http://www.ems-ph.org/doi/10.4171/OWR/2013/33
Dynamische Systeme
Håkan
Eliasson
, PARIS CEDEX 05, FRANCE
Helmut
Hofer
Institute for Advanced Study, PRINCETON, UNITED STATES
Jean-Christophe
Yoccoz
Collège de France (Annexe), PARIS CEDEX O5, FRANCE
This workshop continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser-Zehnder meeting” in 1981. The main themes of the workshop are the new results and developments in the area of dynamical systems, in particular in Hamiltonian systems and symplectic geometry related to Hamiltonian dynamics. Highlights were the solution of a fifty year old problem in Arnold diffusion and a KAM-result on quasi-linear perturbations of the KdV-equation.
Dynamical systems and ergodic theory
Partial differential equations
Differential geometry
1975
2033
10.4171/OWR/2013/34
http://www.ems-ph.org/doi/10.4171/OWR/2013/34
Explicit Methods in Number Theory
Karim
Belabas
Université de Bordeaux I et C.N.R.S., TALENCE CEDEX, FRANCE
Bjorn
Poonen
Building 2, Room 244, CAMBRIDGE, UNITED STATES
Don
Zagier
, BONN, GERMANY
These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics includes effectiveness in rational points on curves and especially on modular curves, modularity, L-functions, and many other topics.
Number theory
Field theory and polynomials
Commutative rings and algebras
Algebraic geometry
2035
2082
10.4171/OWR/2013/35
http://www.ems-ph.org/doi/10.4171/OWR/2013/35
Mini-Workshop: Direct and Inverse Spectral Theory of Almost Periodic Operators
David
Damanik
Rice University, HOUSTON, UNITED STATES
Michael
Goldstein
University of Toronto, TORONTO, ONTARIO, CANADA
This mini-workshop brought together researchers working on direct and inverse spectral theory for Schrödinger operators, Jacobi matrices, and related operators. The talks reported on recent work on these models and related ones, such as the Anderson model.
Operator theory
Statistical mechanics, structure of matter
2083
2117
10.4171/OWR/2013/36
http://www.ems-ph.org/doi/10.4171/OWR/2013/36
Mini-Workshop: The Willmore Functional and the Willmore Conjecture
Tobias
Lamm
Karlsruhe Institute of Technology (KIT), KARLSRUHE, GERMANY
Jan
Metzger
Universität Potsdam, POTSDAM, GERMANY
Andre
Neves
Imperial College London, LONDON, UNITED KINGDOM
The Willmore functional evaluated on a surface immersed into Euclidean space is given by the $L^2$-norm of its mean curvature. The interest for studying this functional comes from various directions. First, it arises in applications from biology and physics, where it is used to model surface tension in the Helfrich model for bilipid layers, or in General Relativity where it appears in Hawking’s quasi-local mass. Second, the mathematical properties justify consideration of the Willmore functional in its own right. The Willmore functional is one of the most natural extrinsic curvature functionals for immersions. Its critical points solve a fourth order Euler-Lagrange equation, which has all minimal surfaces as solutions.
Differential geometry
Partial differential equations
Calculus of variations and optimal control; optimization
Global analysis, analysis on manifolds
2119
2153
10.4171/OWR/2013/37
http://www.ems-ph.org/doi/10.4171/OWR/2013/37
Mini-Workshop: New Crossroads between Mathematics and Field Theory
Romeo
Brunetti
Università di Trento, POVO (TRENTO), ITALY
Christian
Bär
Universität Potsdam, POTSDAM, GERMANY
Claudio
Dappiaggi
Università di Pavia, PAVIA, ITALY
Klaus
Fredenhagen
Universität Hamburg, HAMBURG, GERMANY
In the last few years, it has been strongly emphasized the need to use new mathematical tools and structures which are not part of the traditional pool of expertise of the community working on the analysis of the mathematical and structural properties of classical and quantum field theory. Goal of the workshop has been to bring together some of the major experts in these topics to discuss the latest results and the new insights brought to field theory by techniques, such as microlocal analysis, infinite dimensional geometry and homological algebra.
Quantum theory
2155
2177
10.4171/OWR/2013/38
http://www.ems-ph.org/doi/10.4171/OWR/2013/38
Multiscale and High-Dimensional Problems
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
High-dimensional problems appear naturally in various scientific areas, such as PDEs describing complex processes in computational chemistry and physics, or stochastic or parameter-dependent PDEs leading to deterministic problems with a large number of variables. Other highly visible examples are regression and classification with high-dimensional data as input and/or output in the context of learning theory. High dimensional problems cannot be solved by traditional numerical techniques, because of the so-called curse of dimensionality. Such problems therefore amplify the need for novel theoretical and computational approaches, in order to make them, first of all, tractable and, second, offering finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. 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 in a high dimensional context leads to tasks that are not tractable by existing methods. The last decade has seen the emergence of several new computational methodologies to address the above obstacles. 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 adaptive grid solvers, tensor product, sparse grid and hyperbolic wavelet approximations and model reduction approaches. These have drastically advanced the frontiers of computability for certain problem classes in numerical analysis. This workshop deepened the understanding of the underlying mathematical concepts that drive this new evolution of computation and promoted the exchange of ideas emerging in various disciplines about the handling of multiscale and high-dimensional problems.
Associative rings and algebras
2179
2257
10.4171/OWR/2013/39
http://www.ems-ph.org/doi/10.4171/OWR/2013/39
Partial Differential Equations
Sun-Yung Alice
Chang
Princeton University, PRINCETON, UNITED STATES
Camillo
De Lellis
Universität Zürich, ZÜRICH, SWITZERLAND
Reiner
Schätzle
Universität Tübingen, TÜBINGEN, GERMANY
The workshop dealt with partial differential equations in geometry and technical applications. The main topics were the combination of nonlinear partial differential equations and geometric problems, and fourth order equations in conformal geometry.
Partial differential equations
Calculus of variations and optimal control; optimization
Differential geometry
Global analysis, analysis on manifolds
2259
2319
10.4171/OWR/2013/40
http://www.ems-ph.org/doi/10.4171/OWR/2013/40
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
Nonlinear dispersive equations are models for nonlinear waves in a wide range of physical contexts. Mathematically they display an interplay between linear dispersion and nonlinear interactions, which can result in a wide range of outcomes from finite time blow-up to scattering. They are linked to many areas of mathematics and physics, ranging from integrable systems and harmonic analysis to fluid dynamics and general relativity. The conference did focus on the analytic aspects and PDE aspects.
Dynamical systems and ergodic theory
2321
2374
10.4171/OWR/2013/41
http://www.ems-ph.org/doi/10.4171/OWR/2013/41
Group Theory, Measure, and Asymptotic Invariants
Miklós
Abért
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Damien
Gaboriau
École Normale Supérieure de Lyon, LYON CEDEX 07, FRANCE
Andreas
Thom
Technische Universität Dresden, DRESDEN, GERMANY
The workshop ‘Group Theory, Measure, and Asymptotic Invariants’ organized by Miklos Abert (Budapest), Damien Gaboriau (Lyon) and Andreas Thom (Leipzig) was held 18 - 24 August 2013. The event was a continuation of the previous Oberwolfach workshop ‘Actions and Invariants of Residually Finite Groups: Asymptotic Methods’ organized by Miklos Abert (Budapest), Damien Gaboriau (Lyon) and Fritz Grunewald (Dusseldorf) that was held September 5 - September 11, 2010. Fritz Grunewald passed away in March 2010 and Andreas Thom joined the organizing team. The workshop aimed to study finitely generated groups and group actions using ergodic and measure theoretic methods, incorporating asymptotic invariants, such as ℓ2-invariants, the rank gradient, cost, torsion growth, entropy-type invariants and invariants coming from random walks and percolation theory. The participant body came from a wide range of areas: finite and infinite group theory, geometry, ergodic theory, graph theory, topology, probability theory, representation theory, von Neumann algebras and $\mathcal l^2$-theory. The participants typically did not speak each other’s mathematical dialect fluently. To address this situation, the organizers asked the speakers to put a special emphasis on the first, introductory part of their talks. This aspect worked very well. As a general rule, the organizers asked speakers to talk about specific subjects, not just any nice piece of their research. In some cases, this meant sacrificing hearing about some new results from excellent mathematicians that were further away from the workshop’s main directions.
Group theory and generalizations
Combinatorics
Topological groups, Lie groups
Dynamical systems and ergodic theory
2375
2422
10.4171/OWR/2013/42
http://www.ems-ph.org/doi/10.4171/OWR/2013/42
C*-Algebren
Siegfried
Echterhoff
Universität Münster, MÜNSTER, GERMANY
Mikael
Rørdam
Københavns Universitetet, COPENHAGEN, DENMARK
Stefaan
Vaes
Katholieke Universiteit Leuven, LEUVEN, BELGIUM
Dan-Virgil
Voiculescu
University of California, BERKELEY, UNITED STATES
C*-algebras play an important role in many modern areas of mathematics, like Noncommutative Geometry and Topology, Dynamical Systems, Harmonic Analysis and others. The conference “C*-algebras” brings together leading experts from those areas in order to strengthen the cooperation and to keep the researchers informed about major developments in the field.
Functional analysis
$K$-theory
Topological groups, Lie groups
Dynamical systems and ergodic theory
2423
2500
10.4171/OWR/2013/43
http://www.ems-ph.org/doi/10.4171/OWR/2013/43
Matrix Factorizations in Algebra, Geometry, and Physics
Ragnar-Olaf
Buchweitz
University of Toronto at Scarborough, TORONTO, CANADA
Kentaro
Hori
The University of Tokyo, KASHIWA, JAPAN
Henning
Krause
Universität Bielefeld, BIELEFELD, GERMANY
Christoph
Schweigert
Universität Hamburg, HAMBURG, GERMANY
Let $W$ be a polynomial or power series in several variables, or, more generally, a nonzero element in some regular commutative ring. A matrix factorization of $W$ consists of a pair of square matrices $X$ and $Y$ of the same size, with entries in the given ring, such that the matrix product $XY$ is $W$ multiplied by the identity matrix. For example, if $X$ is a matrix whose determinant is $W$ and $Y$ is its adjoint matrix, then $(X, Y)$ is a matrix factorization of $W$. Such matrix factorizations are nowadays ubiquitous in several different fields in physics and mathematics, including String Theory, Commutative Algebra, Algebraic Geometry, both in its classical and its noncommutative version, Singularity Theory, Representation Theory, Topology, there in particular in Knot Theory. The workshop has brought together leading researchers and young colleagues from the various input fields; it was the first workshop on this topic in Oberwolfach. For some leading researchers from neighboring fields, this was their first visit to Oberwolfach.
Category theory; homological algebra
Commutative rings and algebras
Algebraic geometry
Quantum theory
2501
2552
10.4171/OWR/2013/44
http://www.ems-ph.org/doi/10.4171/OWR/2013/44
Noncommutative Geometry
Alain
Connes
Le Bois-Marie, BURES-SUR-YVETTE, FRANCE
Joachim
Cuntz
Universität Münster, MÜNSTER, GERMANY
Marc
Rieffel
University of California, BERKELEY, UNITED STATES
Guoliang
Yu
Texas A&M University, COLLEGE STATION, UNITED STATES
Noncommutative Geometry applies ideas from geometry to mathematical structures determined by noncommuting variables. This meeting emphasized the connections of Noncommutative Geometry to number theory and ergodic theory.
Number theory
Associative rings and algebras
$K$-theory
Measure and integration
2553
2629
10.4171/OWR/2013/45
http://www.ems-ph.org/doi/10.4171/OWR/2013/45
Lattice Differential Equations
Guillaume
James
Université Joseph Fourier, GRENOBLE CEDEX, FRANCE
Dmitry
Pelinovsky
McMaster University, HAMILTON, ONTARIO, CANADA
Zoi
Rapti
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Guido
Schneider
Universität Stuttgart, STUTTGART, GERMANY
The workshop focused on recent advances in the analysis of lattice differential equations such as discrete Klein-Gordon and nonlinear Schrödinger equations as well as the Fermi-Pasta-Ulam lattice. Lattice differential equations play an important role in emergent directions of modern science. These equations are fascinating subjects for mathematicians because they exhibit phenomena, which are not encountered in classical partial differential equations, on one hand, but they may present toy problems for understanding more complicated Hamiltonian differential equations, on the other hand.
Ordinary differential equations
2631
2689
10.4171/OWR/2013/46
http://www.ems-ph.org/doi/10.4171/OWR/2013/46
High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs
Bruno
Després
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Michael
Dumbser
Università degli Studi di Trento, TRENTO, ITALY
James
Kamm
Sandia National Laboratories, ALBUQUERQUE, UNITED STATES
Manuel
Torrilhon
RWTH Aachen, AACHEN, GERMANY
Partial differential equations constrained by involutions provide the highest fidelity mathematical models for a large number of complex physical systems of fundamental interest in critical scientific and technological disciplines. The applications described by these models include electromagnetics, continuum dynamics of solid media, and general relativity. This workshop brought together pure and applied mathematicians to discuss current research that cuts across these various disciplines’ boundaries. The presented material illuminated fundamental issues as well as evolving theoretical and algorithmic approaches for PDEs with involutions. The scope of the material covered was broad, and the discussions conducted during the workshop were lively and far-reaching.
Global analysis, analysis on manifolds
Numerical analysis
Mechanics of deformable solids
Optics, electromagnetic theory
2691
2747
10.4171/OWR/2013/47
http://www.ems-ph.org/doi/10.4171/OWR/2013/47
Statistical Inference for Complex Time Series Data
Rainer
Dahlhaus
Universität Heidelberg, HEIDELBERG, GERMANY
Oliver
Linton
University of Cambridge, CAMBRIDGE, UNITED KINGDOM
Wei-Biao
Wu
University of Chicago, CHICAGO, UNITED STATES
Qiwei
Yao
London School of Economics, LONDON, UNITED KINGDOM
During recent years the focus of scientific interest has turned from low dimensional stationary time series to nonstationary time series and high dimensional time series. In addition new methodological challenges are coming from high frequency finance where data are recorded and analyzed on a millisecond basis. The three topics “nonstationarity”, “high dimensionality” and “high frequency” are on the forefront of present research in time series analysis. The topics also have some overlap in that there already exists work on the intersection of these three topics, e.g. on locally stationary diffusion models, on high dimensional covariance matrices for high frequency data, or on multivariate dynamic factor models for nonstationary processes. The aim of the workshop was to bring together researchers from time series analysis, nonparametric statistics, econometrics and empirical finance to work on these topics. This aim was successfully achieved and the workshops was very well attended.
Statistics
2749
2823
10.4171/OWR/2013/48
http://www.ems-ph.org/doi/10.4171/OWR/2013/48
4
Uniform Distribution Theory and Applications
Michael
Gnewuch
Universität Kaiserslautern, KAISERSLAUTERN, GERMANY
Frances
Kuo
University of New South Wales, SYDNEY, AUSTRALIA
Harald
Niederreiter
Austrian Academy of Sciences, LINZ, AUSTRIA
Henryk
Woźniakowski
Columbia University, NEW YORK, UNITED STATES
The topics of the workshop were recent progress in the theory of uniform distribution theory (also known as discrepancy theory) and new developments in its applications in analysis, approximation theory, computer science, numerics, pseudo-randomness and stochastic simulation.
Number theory
Approximations and expansions
Abstract harmonic analysis
Probability theory and stochastic processes
2837
2917
10.4171/OWR/2013/49
http://www.ems-ph.org/doi/10.4171/OWR/2013/49
Arbeitsgemeinschaft: Sofic Entropy
Lewis
Bowen
The University of Texas at Austin, AUSTIN, UNITED STATES
David
Kerr
Texas A&M University, COLLEGE STATION, UNITED STATES
The notion of soficity for a group is a weak type of finite approximation property that simultaneously generalizes both amenability and residual finiteness. In 2008 L. Bowen discovered how it can be used to significantly broaden the scope of the classical theory of dynamical entropy beyond the setting of amenable acting groups. This Arbeitsgemeinschaft aimed to provide a comprehensive picture of the subject of sofic entropy as it has developed over the last five years.
Dynamical systems and ergodic theory
2919
2961
10.4171/OWR/2013/50
http://www.ems-ph.org/doi/10.4171/OWR/2013/50
Analytic Number Theory
Jörg
Brüdern
Universität Göttingen, GÖTTINGEN, GERMANY
Hugh
Montgomery
University of Michigan, ANN ARBOR, UNITED STATES
Robert
Vaughan
The Pennsylvania State University, UNIVERSITY PARK, UNITED STATES
Trevor
Wooley
University of Bristol, BRISTOL, UNITED KINGDOM
Analytic number theory has florished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject.
Number theory
Algebraic geometry
2963
3037
10.4171/OWR/2013/51
http://www.ems-ph.org/doi/10.4171/OWR/2013/51
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, dynamical phase transitions, metastability, large deviations, to mention only a few key items.
Probability theory and stochastic processes
Partial differential equations
Statistical mechanics, structure of matter
3039
3113
10.4171/OWR/2013/52
http://www.ems-ph.org/doi/10.4171/OWR/2013/52
Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry
Anna
Fino
Università degli Studi di Torino, TORINO, ITALY
Uwe
Semmelmann
Universität Stuttgart, STUTTGART, GERMANY
Jaroslaw
Wisniewski
Warsaw University, WARSZAWA, POLAND
Frederik
Witt
Universität Münster, MÜNSTER, GERMANY
Metrics of special holonomy are of central interest in both Riemannian and complex algebraic geometry. We focus on an important classification problem of a particular type of special holonomy manifolds, namely compact quaternion-Kähler with positive scalar curvature (Salamon-LeBrun conjecture). In the language of algebraic geometry this corresponds to the classification of Fano contact manifolds. By bringing together leading experts in both fields this workshop pursued a two-fold goal: First, to revise old and to develop new strategies for proving the most central conjecture in the field of quaternionic Kähler geometry. Second, to introduce young researchers at PhD/PostDoc level to this interdisciplinary circle of ideas.
Algebraic geometry
Several complex variables and analytic spaces
Differential geometry
3115
3145
10.4171/OWR/2013/53
http://www.ems-ph.org/doi/10.4171/OWR/2013/53
Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations
Patrick
Dondl
Universität Freiburg, FREIBURG, GERMANY
Celia
Reina
University of Pennsylvania, PHILADELPHIA, UNITED STATES
The workshop brought together 15 scientists, which included leaders in the fields of mathematics (partial differential equations, statistical mechanics and calculus of variations) and mechanics (continuum mechanics, computational mechanics, microstructure and material science) as well as mid- and early-career participants. We addressed the themes of modeling crystal plasticity, crystallization and fracture, and non-equilibrium thermodynamics.
Mechanics of deformable solids
Partial differential equations
Calculus of variations and optimal control; optimization
Statistical mechanics, structure of matter
3147
3188
10.4171/OWR/2013/54
http://www.ems-ph.org/doi/10.4171/OWR/2013/54
Design and Analysis of Infectious Disease Studies
Martin
Eichner
Universität Tübingen, TÜBINGEN, GERMANY
Elizabeth
Halloran
University of Washington, SEATTLE, UNITED STATES
Philip
O'Neill
University of Nottingham, NOTTINGHAM, UNITED KINGDOM
The fourth workshop on this theme is devoted to the statistical problems of planning and analyzing studies in infectious disease epidemiology.
Biology and other natural sciences
3189
3219
10.4171/OWR/2013/55
http://www.ems-ph.org/doi/10.4171/OWR/2013/55
Numerical Solution of PDE Eigenvalue Problems
Andrew
Knyazev
Mitsubishi Electric Research Laboratories, CAMBRIDGE, UNITED STATES
Volker
Mehrmann
Technische Universität Berlin, BERLIN, GERMANY
Jinchao
Xu
The Pennsylvania State University, UNIVERSITY PARK, UNITED STATES
This workshop brought together researchers from many different areas of numerical analysis, scientific computing and application areas, ranging from quantum mechanics, acoustic field computation to material science, working on eigenvalue problems for partial differential equations. Major challenges and new research directions were identified and the interdisciplinary cooperation was strengthened through a very lively workshop with many discussions.
Partial differential equations
Integral equations
Numerical analysis
3221
3304
10.4171/OWR/2013/56
http://www.ems-ph.org/doi/10.4171/OWR/2013/56
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
This meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010.
Partial differential equations
Quantum theory
Statistical mechanics, structure of matter
3305
3378
10.4171/OWR/2013/57
http://www.ems-ph.org/doi/10.4171/OWR/2013/57
Cluster Algebras and Related Topics
Bernhard
Keller
Université Paris Diderot - Paris 7, PARIS CEDEX 13, FRANCE
Bernard
Leclerc
Université de Caen, CAEN CEDEX, FRANCE
Jan
Schröer
Rheinische Friedrich-Wilhelms-Universität Bonn, BONN, GERMANY
Cluster algebras are a class of commutative algebras intoduced by Fomin and Zelevinsky in 2000. Their original purpose was to obtain a combinatorial approach to Lusztig’s dual canonical bases of quantum groups and to total positivity. Since then numerous connections between other areas of mathematics have been discovered. The aim of this workshop was to further strengthen these connections and to develop interactions.
Commutative rings and algebras
3379
3432
10.4171/OWR/2013/58
http://www.ems-ph.org/doi/10.4171/OWR/2013/58
Material Theories
Antonio
DeSimone
SISSA-ISAS, TRIESTE, ITALY
Stephan
Luckhaus
Universität Leipzig, LEIPZIG, GERMANY
Lev
Truskinovsky
UMR-CNRS 7649, PALAISEAU CEDEX, FRANCE
The subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory.
Mechanics of deformable solids
Fluid mechanics
Classical thermodynamics, heat transfer
3433
3485
10.4171/OWR/2013/59
http://www.ems-ph.org/doi/10.4171/OWR/2013/59