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European Mathematical Society Publishing House
2024-03-29 05:57:11
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=OWR&vol=7&iss=3&update_since=2024-03-29
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
7
2010
3
Homogeneous Dynamics and Number Theory
Manfred
Einsiedler
ETH Zürich, HG G 64.2, ZÜRICH, SWITZERLAND
Dmitry
Kleinbock
Brandeis University, WALTHAM, UNITED STATES
Elon
Lindenstrauss
The Hebrew University of Jerusalem, JERUSALEM, ISRAEL
Hee
Oh
Yale University, NEW HAVEN, UNITED STATES
The theory of flows on homogeneous spaces of Lie groups has emerged as a distinct, rapidly advancing subject over the last few decades incorporating ergodic theory, geometry and number theory. The workshop showcased the latest advances in the subject as well as a wide range of applications.
Dynamical systems and ergodic theory
Number theory
Topological groups, Lie groups
General
1703
1759
10.4171/OWR/2010/29
http://www.ems-ph.org/doi/10.4171/OWR/2010/29
Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry
Gerhard
Knieper
Ruhr-Universität Bochum, BOCHUM, GERMANY
Leonid
Polterovich
Tel-Aviv University, TEL-AVIV, ISRAEL
Leonid
Potyagailo
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
The main theme of the workshop is the interaction between the speedily developing fields of mathematics mentioned in the title. One of the purposes of the workshop is to highlight new exciting developments which are happening right now on the borderline between hyperbolic dynamics, geometric group theory and symplectic geometry.
Group theory and generalizations
Topological groups, Lie groups
Dynamical systems and ergodic theory
General
1761
1825
10.4171/OWR/2010/30
http://www.ems-ph.org/doi/10.4171/OWR/2010/30
Calculus of Variations
Camillo
De Lellis
Universität Zürich, ZÜRICH, SWITZERLAND
Gerhard
Huisken
Albert-Einstein-Institut, POTSDAM, GERMANY
Robert
McCann
University of Toronto, TORONTO, ONTARIO, CANADA
Since its invention by Newton, the calculus of variations has formed one of the central techniques for studying problems in geometry, physics, and partial differential equations. This trend continues even today. On the one hand, slow but steady progress is made on long-standing questions concerning minimal surfaces, curvature flows, and related geometric objects. Basic questions also remain in such areas as mathematical physics and general relativity. On the other hand, new types of question emerge, driven by applications from economics and engineering to materials science, whose solution will depend on developing ideas and techniques in this classical branch of analysis. The July 2010 Oberwolfach workshop on the Calculus of Variations showcased a blend of continued progress in traditional areas with surprising developments which emerged from the exploration of new lines of research.
Calculus of variations and optimal control; optimization
Partial differential equations
Differential geometry
Global analysis, analysis on manifolds
1827
1884
10.4171/OWR/2010/31
http://www.ems-ph.org/doi/10.4171/OWR/2010/31
Cohomology of Finite Groups: Interactions and Applications
Alejandro
Adem
The University of British Columbia, VANCOUVER, CANADA
Jon
Carlson
University of Georgia, ATHENS, UNITED STATES
Henning
Krause
Universität Bielefeld, BIELEFELD, GERMANY
The cohomology of finite groups is an important tool in many subjects including representation theory and algebraic topology. This meeting was the third in a series that has emphasized the interactions of group cohomology with other areas.
Group theory and generalizations
Algebraic topology
Manifolds and cell complexes
General
1885
1952
10.4171/OWR/2010/32
http://www.ems-ph.org/doi/10.4171/OWR/2010/32
Wavelet and Multiscale Methods
Albert
Cohen
Université Pierre et Marie Curie, PARIS, FRANCE
Wolfgang
Dahmen
Technische Hochschule Aachen, AACHEN, GERMANY
Ronald
DeVore
Texas A&M University, COLLEGE STATION, UNITED STATES
Angela
Kunoth
Universität Paderborn, PADERBORN, GERMANY
Various scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers. These have advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines. A special emphasis was placed on high dimensional problems since these amplify even further the need for novel theory and computation.
Associative rings and algebras
General
1953
2025
10.4171/OWR/2010/33
http://www.ems-ph.org/doi/10.4171/OWR/2010/33
Mathematical Theory and Modelling in Atmosphere-Ocean-Science
Andrew
Majda
New York University, NEW YORK, UNITED STATES
Bjorn
Stevens
Max Planck Institute for Meteorology, HAMBURG, GERMANY
Rupert
Klein
Freie Universität Berlin, BERLIN, GERMANY
Participants from around the world gathered to review application and development of mathematics in relation to problems in the atmospheric, oceanic and climate sciences.
Geophysics
Probability theory and stochastic processes
Numerical analysis
Fluid mechanics
2027
2099
10.4171/OWR/2010/34
http://www.ems-ph.org/doi/10.4171/OWR/2010/34
Low-Dimensional Topology and Number Theory
Paul
Gunnells
University of Massachusetts, AMHERST, UNITED STATES
Walter
Neumann
Barnard College, Columbia University, NEW YORK, UNITED STATES
Adam
Sikora
University at Buffalo SUNY, BUFFALO, UNITED STATES
Don
Zagier
, BONN, GERMANY
The workshop on Low-Dimensional Topology and Number Theory brought together researchers in these areas with the intent of exploring the many tantalizing connections between Low-Dimensional Topology and Number Theory. Some of the most actively discussed topics were the appearances of modularity in quantum invariants and mutual relations between hyperbolic volume, K-theory, and asymptotics of quantum invariants.
Manifolds and cell complexes
Number theory
General
2101
2163
10.4171/OWR/2010/35
http://www.ems-ph.org/doi/10.4171/OWR/2010/35
Mini-Workshop: Mechanics of Cell Motion
Wolfgang
Alt
Rheinische Friedrich-Wilhelms-Universität Bonn, BONN, GERMANY
Davide
Ambrosi
Politecnico di Milano, MILANO, ITALY
This mini-workshop brought together established researchers and newer entrants in the field of cell motility, a challenging research area located at the crossroads of biology, mathematics and physics. Cell locomotion occurs through complex interactions that involve, among others, actin polymerization, matrix degradation, chemical signaling, adhesion and pulling on the substrate and fibers. In recent years the spatial resolution of experiments at a cellular and sub-cellular level have revealed a landscape of unexpected behaviors that demand for the application of physics and classical mathematical methods to reveal the principles that are at the basis of cell motion in terms of adhesion, directionality, internal engines. The focus of the mini-workshop was on the fundamental research in mathematical methods for biophysics of the cell, especially on the mathematical framework for the mechanics of the actin network, the encadrement of cellular traction as an inverse problem and the relation between cell-to-cell communication and morphogenesis.
Biology and other natural sciences
General
2165
2193
10.4171/OWR/2010/36
http://www.ems-ph.org/doi/10.4171/OWR/2010/36
Mini-Workshop: Combinatorics on Words
Valerie
Berthe
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Juhani
Karhumäki
University of Turku, TURKU, FINLAND
Dirk
Nowotka
Universität Stuttgart, STUTTGART, GERMANY
Jeffrey
Shallit
University of Waterloo, WATERLOO, ONTARIO, CANADA
The area of combinatorics on words is concerned with properties of sequences of symbols. It is characteristic to the field that questions arise from various mathematical problems, and hence, many fundamental results on words have been established in different areas. Over the last two decades the theory has developed into a quickly growing topic of its own. This work-shop was dedicated to reflect on the current status of the field, discuss the impact of recent results, and provide new research challenges. This is a report on the meeting and presentation of extended abstracts of the lectures.
Computer science
General
2195
2244
10.4171/OWR/2010/37
http://www.ems-ph.org/doi/10.4171/OWR/2010/37
Mini-Workshop: Exploiting Symmetry in Optimization
Volker
Kaibel
Otto-von-Guericke-Universität, MAGDEBURG, GERMANY
Leo
Liberti
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Achill
Schürmann
Universität Rostock, ROSTOCK, GERMANY
Renata
Sotirov
Tilburg University, TILBURG, NETHERLANDS
The feasible regions of mathematical optimization models quite often exhibit a high degree of symmetry. In recent years, several groups of researchers have independently worked on algorithmic approaches to exploit such symmetries in a variety of contexts. Many of the techniques that have been developed are related or rely on similar computational tools. The workshop brought together researchers working on symmetry aspects in different areas of optimization. The exchange of state-of-the-art knowledge between these areas lead to identification of important directions for future research activities.
Operations research, mathematical programming
Combinatorics
Group theory and generalizations
Convex and discrete geometry
2245
2281
10.4171/OWR/2010/38
http://www.ems-ph.org/doi/10.4171/OWR/2010/38
Komplexe Analysis
Jean-Pierre
Demailly
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Klaus
Hulek
Universität Hannover, HANNOVER, GERMANY
Thomas
Peternell
Universität Bayreuth, BAYREUTH, GERMANY
The aim of this workshop was to discuss recent developments in several complex variables and complex geometry. Special emphasis was put on the interaction between model theory and the classification theory of complex manifolds. Other topics included Kähler geometry, foliations, complex symplectic manifolds and moduli theory.
Several complex variables and analytic spaces
Algebraic geometry
General
2283
2333
10.4171/OWR/2010/39
http://www.ems-ph.org/doi/10.4171/OWR/2010/39
Actions and Invariants of Residually Finite Groups: Asymptotic Methods
George
Glauberman
University of Chicago, CHICAGO, UNITED STATES
Damien
Gaboriau
École Normale Supérieure de Lyon, LYON CEDEX 07, FRANCE
Fritz
Grunewald
Heinrich-Heine-Universität, DÜSSELDORF, GERMANY
The workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.
Group theory and generalizations
Topological groups, Lie groups
Ordinary differential equations
Dynamical systems and ergodic theory
2335
2391
10.4171/OWR/2010/40
http://www.ems-ph.org/doi/10.4171/OWR/2010/40
Nonlinear Waves and Dispersive Equations
Carlos
Kenig
University of Chicago, CHICAGO, UNITED STATES
Herbert
Koch
Universität Bonn, BONN, GERMANY
Daniel
Tataru
University of California, BERKELEY, UNITED STATES
The aim of the workshop was to discuss current developments in nonlinear waves and dispersive equations from a PDE based view. The talks centered around rough initial data, long time and global existence, perturbations of special solutions, and applications.
Partial differential equations
General
2393
2463
10.4171/OWR/2010/41
http://www.ems-ph.org/doi/10.4171/OWR/2010/41
Topologie
Thomas
Schick
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
Peter
Teichner
University of California, BERKELEY, UNITED STATES
Nathalie
Wahl
University of Copenhagen, COPENHAGEN, DENMARK
Michael
Weiss
University of Aberdeen, ABERDEEN, UNITED KINGDOM
This conference is one of the few occasions where researchers from many different areas in algebraic and geometric topology are able to meet and exchange ideas. Accordingly, the program covered a wide range of new developments in such fields as geometric group theory, rigidity of group actions, knot theory, and stable and unstable homotopy theory. More specifically, we discussed progress on problems such as the Farrell-Jones conjecture, the Levine conjecture in grope cobordism of knots and Rosenberg’s conjecture about homotopy invariance of negative algebraic K-theory, to mention just a few subjects with a name attached. One of the highlights was a series of four talks on the solution of Arf-Kervaire invariant problem by Mike Hill and Doug Ravenel, reporting on their joint work with Mike Hopkins.
Algebraic topology
Manifolds and cell complexes
General
2465
2502
10.4171/OWR/2010/42
http://www.ems-ph.org/doi/10.4171/OWR/2010/42
Deformation Methods in Mathematics and Physics
Alice
Fialowski
ELTE TTK, BUDAPEST, HUNGARY
Jürg
Fröhlich
ETH Zürich, ZÜRICH, SWITZERLAND
Martin
Schlichenmaier
Université du Luxembourg, LUXEMBOURG, LUXEMBOURG
Deformations of mathematical structures play an important role in most parts of mathematics but also in theoretical physics. In this interdisciplinary workshop, different aspects of deformations and their applications were discussed. The workshop was attended by experts in the fields, but also by quite a number of young post-docs and PhD students. One of the goals was to foster interactions between different communities.
Associative rings and algebras
Nonassociative rings and algebras
Differential geometry
Mechanics of particles and systems
2503
2560
10.4171/OWR/2010/43
http://www.ems-ph.org/doi/10.4171/OWR/2010/43