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2024-03-29 00:27:59
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=OWR&vol=7&iss=1&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
1
Model Theory: Around Valued Fields and Dependent Theories
Andreas
Baudisch
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Anand
Pillay
University of Leeds, LEEDS, UNITED KINGDOM
Katrin
Tent
Universität Münster, MÜNSTER, GERMANY
Martin
Ziegler
Universität Freiburg, FREIBURG, GERMANY
The general topic of the meeting was “Valued fields and related structures”. It included both applications of model theory, as well as so-called “pure” model theory: the classification of first order structures using new techniques extending those developed in stable theories.
Mathematical logic and foundations
Field theory and polynomials
General
5
53
10.4171/OWR/2010/01
http://www.ems-ph.org/doi/10.4171/OWR/2010/01
Moduli Spaces in Algebraic Geometry
Dan
Abramovich
Brown University, PROVIDENCE, UNITED STATES
Gavril
Farkas
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Stefan
Kebekus
Universität Freiburg, FREIBURG, GERMANY
The workshop on Moduli Spaces in Algebraic Geometry aimed to bring together researchers from all branches of moduli theory, in order to discuss moduli spaces from different points of view, and to give an overview of methods used in their respective fields. Highlights included a complete proof of Göttsche’s conjecture, a proof of rationality of a moduli space constructed via GIT quotient using reduction modulo p, and a proof of a conjecture of Looijenga using the ideas of mirror symmetry.
Algebraic geometry
General
55
107
10.4171/OWR/2010/02
http://www.ems-ph.org/doi/10.4171/OWR/2010/02
Mini-Workshop: History of Mathematics in Germany, 1920-1960
Moritz
Epple
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Volker
Remmert
Fachbereich A - Geschichte, WUPPERTAL, GERMANY
Norbert
Schappacher
Université de Strasbourg et CNRS, STRASBOURG CEDEX, FRANCE
The Mini-Workshop dealt with the history of mathematics in Germany between 1920 and 1960, with a particular focus on the social history of mathematics. For the period under discussion research in the history of mathematics is faced with some fundamental problems, which cannot be addressed by individuals. Consequently the Mini-Workshop’s aim was to develop future perspectives and methods for research and ways to organise new research projects. Among the topics addressed during the Mini-Workshop were the international relations of mathematicians in Germany before, during and after World War II; the prosopography of mathematicians in Germany from before 1933 into the 1950s; the role of mathematics as a key technology in World War II; and the professional policies from the 1920s to the 1950s.
History and biography
General
109
140
10.4171/OWR/2010/03
http://www.ems-ph.org/doi/10.4171/OWR/2010/03
Mini-Workshop: Valuations and Integral Geometry
Semyon
Alesker
Tel Aviv University, TEL AVIV, ISRAEL
Andreas
Bernig
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Peter
Schuster
Universität Wien, WIEN, AUSTRIA
As a generalization of the notion of measure, valuations have long played a central role in the integral geometry of convex sets. In recent years there has been a series of striking developments. Several examples were presented at this meeting, e.g. the work of Bernig and Fu on the integral geometry of groups acting transitively on the unit sphere, that of Hug and Schneider on kinematic and Crofton formulas for tensor valued valuations and a series of results by Ludwig and Reitzner on classifications of affine invariant notions of surface areas and of convex body valued valuations.
Convex and discrete geometry
Differential geometry
General
141
178
10.4171/OWR/2010/04
http://www.ems-ph.org/doi/10.4171/OWR/2010/04
Mini-Workshop: Semiparametric Modelling of Multivariate Economic Time Series With Changing Dynamics
Luc
Bauwens
, LOUVAIN-LA-NEUVE, BELGIUM
Rainer
von Sachs
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Qiwei
Yao
London School of Economics, LONDON, UNITED KINGDOM
Modelling multivariate time series of possibly high dimension calls for appropriate dimension-reduction, e.g. by some factor modelling, additive modelling, or some simplified parametric structure for the dynamics (i.e. the serial dependence) of the time series. This workshop aimed to bring together experts in this field in order to discuss recent methodology for multivariate time series dynamics which are changing over time: by an abrupt switch between two (or more) different regimes or rather smoothly evolving over time. The emphasis has been on mathematical methods for semiparametric modelling and estimation, where ”semiparametric” is to be understood in a rather broad sense: parametric models where the parameters are themselves nonparametric functions (of time), regime-switching nonparametric models with a parametric specification of the transition mechanism, and alike. An ultimate goal of these models to be applied to economic and financial time series is prediction. Another emphasis has been on comparing Bayesian with frequentist approaches, and to cover both theoretical aspects of estimation, such as consistency and efficiency, and computational aspects.
Statistics
General
179
216
10.4171/OWR/2010/05
http://www.ems-ph.org/doi/10.4171/OWR/2010/05
Statistical Issues in Prediction: what can be learned for individualized predictive medicine?
Leonhard
Held
Universität Zürich, ZÜRICH, SWITZERLAND
Robin
Henderson
University of Newcastle, NEWCASTLE UPON TYNE, GREAT BRITAIN
Ulrich
Mansmann
Universität München, MÜNCHEN, GERMANY
Error is unavoidable in prediction. And it is quite common, often sizable, and usually consequential. In a clinical context, especially when dealing with a terminal illness, error in prediction of residual life means that patients and families are misinformed about their illness, that they may take foolish actions as a result, and that they may be given inappropriate or needlesly painful treatments or denied appropriate ones. In meteorology, error in prediction of storm paths or extreme events can have devastating consequences. In finance and economics, major policy decisions are taken on the basis of predictions and forecasts. Rational approaches to reduce and assess error in prediction are presented. Ideas are introduced how to relate these statistical strategies with clinical and medical concepts in particular and how to integrate ideas from apparently different areas.
Statistics
Biology and other natural sciences
General
217
251
10.4171/OWR/2010/06
http://www.ems-ph.org/doi/10.4171/OWR/2010/06
New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries
Charles
Elliott
University of Warwick, COVENTRY, UNITED KINGDOM
Yoshikazu
Giga
University of Tokyo, TOKYO, JAPAN
Michael
Hinze
Universität Hamburg, HAMBURG, GERMANY
Vanessa
Styles
University of Sussex, BRIGHTON, UNITED KINGDOM
The field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research. Many such systems arise from mathematical models in material science, fluid dynamics and biology, for example phase separation in alloys, epitaxial growth, dynamics of multiphase fluids, evolution of cell membranes and in industrial processes such as crystal growth. The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force. Here the forcing terms depend on variables that are solutions of additional partial differential equations which hold either on the interface itself or in the surrounding bulk regions. Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified. Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries. Because of the maturity of the field of computational free boundary problems it is now timely to consider such control problems. In order to carry out design, control and simulation of such problems interaction is required between distinct mathematical fields such as analysis, modeling, computation and optimization. By bringing together leading experts and young researchers from these separate fields we intended to develop novel research directions in applied and computational mathematics. The aim of the workshop here was to focus on emerging new themes and developments in these fields and to establish and extend links between them.
Partial differential equations
Calculus of variations and optimal control; optimization
Numerical analysis
General
253
324
10.4171/OWR/2010/07
http://www.ems-ph.org/doi/10.4171/OWR/2010/07
Optimal Constants in the Theory of Sobolev Spaces and PDEs
Andrea
Cianchi
Universita di Firenze, FIRENZE, ITALY
Maria
Esteban
Université de Paris Dauphine, PARIS CEDEX 16, FRANCE
Bernd
Kawohl
Universität Köln, KÖLN, GERMANY
Recent research activities on sharp constants and optimal inequalities have shown their impact on a deeper understanding of geometric, analytical and other phenomena in the context of partial differential equations and mathematical physics. These intrinsic questions have applications not only to a-priori estimates or spectral theory but also to numerics, economics, optimization, etc.
Partial differential equations
Linear and multilinear algebra; matrix theory
Real functions
Measure and integration
325
371
10.4171/OWR/2010/08
http://www.ems-ph.org/doi/10.4171/OWR/2010/08
Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples
Christian
Fleischhack
Universität Paderborn, PADERBORN, GERMANY
Matilde
Marcolli
California Institute of Technology, PASADENA, UNITED STATES
Ryszard
Nest
University of Copenhagen, COPENHAGEN, DENMARK
Spectral triples have recently turned out to be relevant for different approaches that aim at quantizing gravity and the other fundamental forces of nature in a mathematically rigorous way. The purpose of this workshop was to bring together researchers mainly from noncommutative geometry and loop quantum gravity –two major fields that have used spectraltriples independently so far– in order to share their results and open issues.
Global analysis, analysis on manifolds
Functional analysis
Quantum theory
Relativity and gravitational theory
373
413
10.4171/OWR/2010/09
http://www.ems-ph.org/doi/10.4171/OWR/2010/09
Computational Electromagnetism and Acoustics
Ralf
Hiptmair
Eidgenössische Technische Hochschule, ZÜRICH, SWITZERLAND
Ronald
Hoppe
Universität Augsburg, AUGSBURG, GERMANY
Patrick
Joly
Domaine de Voluceau, LE CHESNAY CEDEX, FRANCE
Ulrich
Langer
Johannes Kepler Universität Linz, LINZ, AUSTRIA
The challenge inherent in the accurate and efficient numerical modeling of wave propagation phenomena is the common grand theme in both computational electromagnetics and acoustics. Many excellent contributions at this Oberwolfach workshop were devoted to this theme and a wide range of numerical techniques and algorithms were mustered to tackle this challenge. Among these methods boundary integral equation methods received particular attention, both in frequency and time domain. Combined with phase modulation techniques they pave the way for the construction of frequency robust schemes for wave scattering. This is an exciting recent development, which is complemented by the invention of high-order spectral integral equation methods. In parallel, we also witnessed soaring interest in time-domain integral equation methods. The alternative volume based schemes for wave propagation problems can also boast innovations, most notably in the context of plane wave methods. Though wave propagation is paramount, several other important aspects were addressed during the workshop ranging, among others, from the design of novel Galerkin schemes, asymptotic methods for geometrically singularly perturbed problems, analysis of spectral edge elements, to the design of preconditioners for quasi-static electromagnetics.
Numerical analysis
Optics, electromagnetic theory
General
415
519
10.4171/OWR/2010/10
http://www.ems-ph.org/doi/10.4171/OWR/2010/10
Graph Theory
Reinhard
Diestel
Universität Hamburg, HAMBURG, GERMANY
Alexander
Schrijver
Centrum voor Wiskunde en Informatica, AMSTERDAM, NETHERLANDS
Paul
Seymour
Princeton University, PRINCETON, UNITED STATES
Highlights of this workshop on structural graph theory included new developments on graph and matroid minors, continuous structures arising as limits of finite graphs, and new approaches to higher graph connectivity via tree structures.
Combinatorics
General
521
580
10.4171/OWR/2010/11
http://www.ems-ph.org/doi/10.4171/OWR/2010/11
Disciplines and Styles in Pure Mathematics, 1800-2000
David
Rowe
Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
Klaus
Volkert
Bergische Universität, WUPPERTAL, GERMANY
Pierre-A.
Vuillermot
Université Henri Poincaré, VANDOEUVRE-LÈS-NANCY CEDEX, FRANCE
Volker
Remmert
Fachbereich A - Geschichte, WUPPERTAL, GERMANY
This workshop addressed issues of discipline and style in number theory, algebra, geometry, topology, analysis, and mathematical physics. Most speakers presented case studies, but some offered global surveys of how stylistic shifts informed the transition and transformation of special research fields. Older traditions in established research communities were considered alongside newer trends, including changing views regarding the role of proof.
History and biography
General
581
665
10.4171/OWR/2010/12
http://www.ems-ph.org/doi/10.4171/OWR/2010/12
C*-Algebren
Claire
Anantharaman-Delaroche
Université d'Orléans, ORLÉANS CEDEX 2, FRANCE
Siegfried
Echterhoff
Universität Münster, MÜNSTER, GERMANY
Mikael
Rørdam
Københavns Universitetet, COPENHAGEN, DENMARK
Dan-Virgil
Voiculescu
University of California, BERKELEY, UNITED STATES
The theory of C*-algebras plays a major role in many areas of modern mathematics, like Non-commutative Geometry, Dynamical Systems, Harmonic Analysis, and Topology, to name a few. The aim of the conference “C*-algebras” is to bring together experts from all those areas to provide a present day picture and to initiate new cooperations in this fast growing mathematical field.
Functional analysis
$K$-theory
Topological groups, Lie groups
Dynamical systems and ergodic theory
667
732
10.4171/OWR/2010/13
http://www.ems-ph.org/doi/10.4171/OWR/2010/13
Microstructures in Solids: From Quantum Models to Continua
Alexander
Mielke
Angewandte Analysis und Stochastik, BERLIN, GERMANY
Michael
Ortiz
California Institute of Technology, PASADENA, UNITED STATES
The mathematical theory of solids was studied from the modern perspective of materials with microcstructures. The discussed topics ranged from experimental findings, via numerical simulations and mathematical modeling to the analysis of models with microstructures. A special emphasis was given to theories providing rigorous insight into and justification of the limit passage between different scales.
Partial differential equations
Calculus of variations and optimal control; optimization
Mechanics of deformable solids
Statistical mechanics, structure of matter
733
798
10.4171/OWR/2010/14
http://www.ems-ph.org/doi/10.4171/OWR/2010/14
Combinatorial Representation Theory
Christine
Bessenrodt
Leibniz Universität Hannover, HANNOVER, GERMANY
Francesco
Brenti
Università di Roma Tor Vergata, ROMA, ITALY
Alexander
Kleshchev
University of Oregon, EUGENE, UNITED STATES
Arun
Ram
University of Melbourne, PARKVILLE VIC, AUSTRALIA
The workshop brought together researchers from different fields in representation theory and algebraic combinatorics for a fruitful interaction. New results, methods and developments ranging from classical and modular representation theory, the theory of symmetric functions and Lie theory to cluster algebras and connections to physics and geometry were discussed.
Combinatorics
Algebraic geometry
Associative rings and algebras
Nonassociative rings and algebras
799
882
10.4171/OWR/2010/15
http://www.ems-ph.org/doi/10.4171/OWR/2010/15
Modern Nonparametric Statistics: Going Beyond Asymptotic Minimax
Lucien
Birgé
Université Paris VI, PARIS CEDEX 05, FRANCE
Iain
Johnstone
Stanford University, STANFORD, UNITED STATES
Vladimir
Spokoiny
Angewandte Analysis und Stochastik, BERLIN, GERMANY
During the years 1975-1990 a major emphasis in nonparametric estimation was put on computing the asymptotic minimax risk for many classes of functions. Modern statistical practice indicates some serious limitations of the asymptotic minimax approach and calls for some new ideas and methods which can cope with the numerous challenges brought to statisticians by modern sets of data.
Statistics
General
883
939
10.4171/OWR/2010/16
http://www.ems-ph.org/doi/10.4171/OWR/2010/16