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2024-03-28 19:34:35
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=OWR&vol=9&iss=2&update_since=2024-03-28
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
9
2012
2
Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators
Artur
Avila
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
David
Damanik
Rice University, HOUSTON, UNITED STATES
Svetlana
Jitomirskaya
University of California, Irvine, IRVINE, UNITED STATES
This Arbeitsgemeinschaft discussed the spectral properties of quasi-periodic Schrödinger operators in one space dimension. After presenting background material on Schrödinger operators with dynamically defined potentials and some results about certain classes of dynamical systems, the recently developed global theory of analytic one-frequency potentials was discussed in detail. This was supplemented by presentations on an important special case, the almost Mathieu operator, and results showing phenomena exhibited outside the analytic category.
Operator theory
Quantum theory
General
1035
1106
10.4171/OWR/2012/17
http://www.ems-ph.org/doi/10.4171/OWR/2012/17
Mini-Workshop: Generalizations of Symmetric Spaces
Ralf
Köhl
Justus-Liebig-Universität Giessen, GIESSEN, GERMANY
Aloysius
Helminck
North Carolina State University, RALEIGH, UNITED STATES
This workshop brought together experts from the areas of algebraic Lie theory, invariant theory, Kac–Moody theory and the theories of Tits buildings and of symmetric spaces. The main focus was on topics related to symmetric spaces in order to stimulate progress in current research projects or trigger new collaboration via comparison, analogy, transfer, generalization, and unification of methods. Specific topics that were covered include Kac–Moody symmetric spaces, double coset decompositions of (groups of rational points of) algebraic groups and Kac–Moody groups, and symmetric/Gelfand pairs in Lie algebras.
Nonassociative rings and algebras
Group theory and generalizations
Geometry
Differential geometry
1107
1148
10.4171/OWR/2012/18
http://www.ems-ph.org/doi/10.4171/OWR/2012/18
Mini-Workshop: Hypergraph Turán Problem
Penny
Haxell
University of Waterloo, WATERLOO, ONTARIO, CANADA
Dhruv
Mubayi
University of Illinois at Chicago, CHICAGO, UNITED STATES
Oleg
Pikhurko
University of Warwick, COVENTRY, UNITED KINGDOM
Tibor
Szabo
Freie Universität Berlin, BERLIN, GERMANY
This mini-workshop focused on the hypergraph Turán problem. The interest in this difficult and old area was recently re-invigorated by many important developments such as the hypergraph regularity lemmas, flag algebras, and stability. The purpose of this meeting was to bring together experts in this field as well as promising young mathematicians to share expertise and initiate new collaborative projects.
Combinatorics
General
1149
1182
10.4171/OWR/2012/19
http://www.ems-ph.org/doi/10.4171/OWR/2012/19
Mini-Workshop: Endomorphisms, Semigroups and C*-Algebras of Rings
Joachim
Cuntz
Universität Münster, MÜNSTER, GERMANY
Wojciech
Szymanski
Odense Universitet, ODENSE M, DENMARK
Joachim
Zacharias
University of Glasgow, GLASGOW, UNITED KINGDOM
The main aim of the workshop was to explore recent progress in the study of endomorphisms of $C*$ -algebras, semigroup crossed products, graph algebras, ring $C*$ -algebras, purely infinite $C*$ -algebras and related algebraic constructions, such as dilations or Leavitt path algebras, by bringing together experts from several different fields.
Functional analysis
General
1183
1229
10.4171/OWR/2012/20
http://www.ems-ph.org/doi/10.4171/OWR/2012/20
Toric Geometry
Klaus
Altmann
Freie Universität Berlin, BERLIN, GERMANY
Victor
Batyrev
Universität Tübingen, TÜBINGEN, GERMANY
Yael
Karshon
University of Toronto, TORONTO, ONTARIO, CANADA
Toric Geometry plays a major role where a wide variety of mathematical fields intersect, such as algebraic and symplectic geometry, algebraic groups, and combinatorics. The main feature of this workshop was to bring people from these area together to learn about mutual, possibly up till now unnoticed similarities in their respective research.
Algebraic geometry
Convex and discrete geometry
Differential geometry
General
1231
1306
10.4171/OWR/2012/21
http://www.ems-ph.org/doi/10.4171/OWR/2012/21
Diophantische Approximationen
Yann
Bugeaud
Université de Strasbourg, STRASBOURG CEDEX, FRANCE
Yuri
Nesterenko
Moscow Lomonosov State University, MOSCOW, RUSSIAN FEDERATION
This Number Theoretic conference was focused on the following subjects: the Littlewood conjecture, simultaneous homogeneous and inhomogeneous Diophantine approximation, geometry of numbers, irrationality, Diophantine approximation in function fields, counting questions in number fields, effective methods for resolution of Diophantine equations.
Number theory
General
1307
1359
10.4171/OWR/2012/22
http://www.ems-ph.org/doi/10.4171/OWR/2012/22
Singularity Theory and Integrable Systems
Boris
Dubrovin
SISSA, TRIESTE, ITALY
Claus
Hertling
Universität Mannheim, MANNHEIM, GERMANY
Ian
Strachan
University of Glasgow, GLASGOW, UNITED KINGDOM
Katrin
Wendland
Universität Freiburg, FREIBURG, GERMANY
The workshop brought together three very different areas of mathematics, namely singularity theory, integrable systems and quantum cohomology. They are linked by their applications in topological quantum field theory and by constructions of (often isomorphic) Frobenius manifolds. The first and second are related by a version of mirror symmetry, the link of the second and third has attracted much attention. The connection of the first and third is the least developed and was at the focus of the workshop.
Algebraic geometry
Several complex variables and analytic spaces
Dynamical systems and ergodic theory
General
1361
1403
10.4171/OWR/2012/23
http://www.ems-ph.org/doi/10.4171/OWR/2012/23
Triangulations
William
Jaco
Oklahoma State University, STILLWATER, UNITED STATES
Frank
Lutz
Technische Universität Berlin, BERLIN, GERMANY
Francisco
Santos
Universidad de Cantabria, SANTANDER, SPAIN
John
Sullivan
Technische Universität Berlin, BERLIN, GERMANY
The earliest work in topology was often based on explicit combinatorial models – usually triangulations – for the spaces being studied. Although algebraic methods in topology gradually replaced combinatorial ones in the mid-1900s, the emergence of computers later revitalized the study of triangulations. By now there are several distinct mathematical communities actively doing work on different aspects of triangulations. The goal of this workshop was to bring the researchers from these various communities together to stimulate interaction and to benefit from the exchange of ideas and methods.
Convex and discrete geometry
Number theory
Combinatorics
Manifolds and cell complexes
1405
1486
10.4171/OWR/2012/24
http://www.ems-ph.org/doi/10.4171/OWR/2012/24
Analysis and Geometric Singularities
Jochen
Brüning
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Rafe
Mazzeo
Stanford University, STANFORD, UNITED STATES
Paolo
Piazza
Università di Roma La Sapienza, ROMA, ITALY
This is a report on the Oberwolfach conference “Analysis and Geometric Singularities”, May 6-12, 2012. The main themes discussed in the meeting include the interplay between the analytic, geometric and topological study of singular spaces and noncompact spaces highly regular structure at infinity and asymptotic analysis of global spectral invariants. More specific topics include index theory on such spaces, various nonlinear geometric problems, and in particular the asymptotic structure of natural metrics on geometric moduli spaces, and techniques from linear analysis to approach such problems.
Differential geometry
Global analysis, analysis on manifolds
General
1487
1562
10.4171/OWR/2012/25
http://www.ems-ph.org/doi/10.4171/OWR/2012/25
Nonlinear Evolution Problems
Klaus
Ecker
Freie Universität Berlin, BERLIN, GERMANY
Jalal
Shatah
New York University, NEW YORK, UNITED STATES
Gigliola
Staffilani
Massachusetts Institute of Technology, CAMBRIDGE, UNITED STATES
Michael
Struwe
ETH Zürich, ZÜRICH, SWITZERLAND
In this workshop geometric evolution equations of parabolic type, nonlinear hyperbolic equations, and dispersive equations and their interrelations were the subject of 21 talks and several shorter special presentations.
Operator theory
Partial differential equations
Differential geometry
General
1563
1637
10.4171/OWR/2012/26
http://www.ems-ph.org/doi/10.4171/OWR/2012/26
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
During the meeting a wide range of topics in geometry was discussed. There were 18 one hour talks and four half an hour talks which took place after dinner.
Differential geometry
General
1639
1686
10.4171/OWR/2012/27
http://www.ems-ph.org/doi/10.4171/OWR/2012/27
Invariants in Low-Dimensional Topology and Knot Theory
Selman
Akbulut
Michigan State University, EAST LANSING, UNITED STATES
Stefan Alois
Bauer
Universität Bielefeld, BIELEFELD, GERMANY
Louis
Kauffman
University of Illinois at Chicago, CHICAGO, UNITED STATES
Vassily
Manturov
Bauman Moscow State Technical University, MOSCOW, RUSSIAN FEDERATION
This meeting concentrated on topological invariants in low dimensional topology and knot theory. We include both three and four dimensional manifolds in our phrase “low dimensional topology”. The intent of the conference was to understand the reach of knot theoretic invariants into four dimensions, including results in Khovanov homology, variants of Floer homology and quandle cohomology and to understand relationships among categorification, topological quantum field theories and four dimensional manifold invariants as in particular Seiberg-Witten invariants.
Algebraic topology
Manifolds and cell complexes
General
1687
1758
10.4171/OWR/2012/28
http://www.ems-ph.org/doi/10.4171/OWR/2012/28
Applied Harmonic Analysis and Sparse Approximation
Ingrid
Daubechies
Duke University, DURHAM, UNITED STATES
Gitta
Kutyniok
Technische Universität Berlin, BERLIN, GERMANY
Holger
Rauhut
RWTH Aachen, AACHEN, GERMANY
Thomas
Strohmer
University of California at Davis, DAVIS, UNITED STATES
Applied harmonic analysis and sparse approximation are highly active research areas with a lot of recent exciting developments. Their methods have become crucial for a wide range of applications in technology and science, such as signal and image processing. Understanding of the underlying mathematics has grown vastly. Interestingly, there are a lot of connections to other fields, such as convex optimization, probability theory and Banach space geometry. Yet, many problems in these areas remain unsolved or even unattacked. The workshop intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations.
Fourier analysis
Linear and multilinear algebra; matrix theory
Numerical analysis
Information and communication, circuits
1759
1843
10.4171/OWR/2012/29
http://www.ems-ph.org/doi/10.4171/OWR/2012/29
Classical Algebraic Geometry
Olivier
Debarre
École Normale Supérieure, PARIS CEDEX 05, FRANCE
David
Eisenbud
Mathematical Sciences Research Institute, BERKELEY, UNITED STATES
Frank-Olaf
Schreyer
Universität des Saarlandes, SAARBRÜCKEN, GERMANY
Ravi
Vakil
Stanford University, STANFORD, UNITED STATES
Progress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems the development of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as the derived category, and the extension of the class of geometric objects considered to allow constructions not previously possible, such as the transition from varieties to schemes or from schemes to stacks. 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, with a view toward their application to the classical problems.
Algebraic geometry
General
1845
1893
10.4171/OWR/2012/30
http://www.ems-ph.org/doi/10.4171/OWR/2012/30
Learning Theory and Approximation
Kurt
Jetter
Universität Hohenheim, STUTTGART, GERMANY
Steve
Smale
City University of Hong Kong, HONG KONG, HONG KONG
Ding-Xuan
Zhou
City University of Hong Kong, HONG KONG, CHINA
Learning theory studies data structures from samples and aims at understanding unknown function relations behind them. This leads to interesting theoretical problems which can be often attacked with methods from Approximation Theory. This workshop - the second one of this type at the MFO - has concentrated on the following recent topics: Learning of manifolds and the geometry of data; sparsity and dimension reduction; error analysis and algorithmic aspects, including kernel based methods for regression and classification; application of multiscale aspects and of refinement algorithms to learning.
Computer science
Approximations and expansions
Statistics
General
1895
1948
10.4171/OWR/2012/31
http://www.ems-ph.org/doi/10.4171/OWR/2012/31