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European Mathematical Society Publishing House
2024-03-29 14:14:40
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=OWR&vol=11&iss=4&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
11
2014
4
Mini-Workshop: Asymptotic Statistics on Stratified Spaces
Aasa
Feragen
University of Copenhagen, COPENHAGEN, DENMARK
Stephan
Huckemann
Georg-August-Universität Göttingen, GÖTTINGEN, GERMANY
James Stephen
Marron
University of North Carolina at Chapel Hill, CHAPEL HILL, UNITED STATES
Ezra
Miller
Duke University, DURHAM, UNITED STATES
Statistical analysis of non-Euclidean data such as data on manifolds is an active and established topic of research, for instance, in the statistical analysis of shape. However, many types of data naturally reside in metric spaces which are not smooth manifolds as a whole, rather they are unions of manifold strata of varying dimensions. These spaces form a key general family of geometric spaces for data analysis. Statistics in stratified spaces has recently found great interest in applications and mathematical theory building. While the fundamental theory is still in its beginnings, as a centerpiece the derivation and investigation of statistics and their asymptotics has materialized. Only a few basic results are known, but it is clear that the geometric constraints imposed by stratified spaces lead to unexpected asymptotic behavior of standard statistical properties, such as “stickiness” of means, see [4]. It is the scope of the proposed workshop to better understand fundamental relations between asymptotic behavior of statistical descriptors and global as well as local geometric and topological structures. This investigation calls for an intense collaboration of the fields involved: statistics & stochastics; geometry & topology; combinatorics, algorithms & numerics. This workshop sought to bring together world-leading scientists and high-potential early career researchers working in this field to collaborate on a focused set of fundamental questions.
Combinatorics
Geometry
Convex and discrete geometry
Manifolds and cell complexes
2481
2527
10.4171/OWR/2014/44
http://www.ems-ph.org/doi/10.4171/OWR/2014/44
Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions
Christoph
Böhm
Universität Münster, MÜNSTER, GERMANY
Jorge
Lauret
Universidad Nacional de Córdoba, CORDOBA, ARGENTINA
McKenzie
Wang
McMaster University, HAMILTON, ONTARIO, CANADA
Symmetry reduction methods play an important role in the study of Einstein metrics, Ricci solitons and Ricci flow. The general aim of this mini workshop was to gather researchers who have expertise in the construction of geometric examples and to survey and discuss the singularity properties of homogeneous Ricci flows and the existence question for Ricci solitons, in light of the known rigidity results and general properties. Particular topics focused on were the Alekseevskii conjecture for noncompact homogeneous Einstein spaces, the homogeneous Ricci flow and shrinking solitons.
Differential geometry
2529
2568
10.4171/OWR/2014/45
http://www.ems-ph.org/doi/10.4171/OWR/2014/45
Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations
Eugen
Mihailescu
Romanian Academy, BUCHAREST, ROMANIA
Bernd
Stratmann
Universität Bremen, BREMEN, GERMANY
The mini-workshop Differentiable Ergodic Theory, Dimension Theory and Stable Foliations brought together experts in thermodynamical formalism, hyperbolic dynamics and dimension theory from several countries. The geographic representation was broad, from Europe, USA and Japan. All participants gave interesting 1-hour talks, and there was organized also an open problem session, where directions for future work and many open problems were discussed. Among the topics presented/discussed in the workshop, there were ones related to dimension theory and probability measures on fractals, various types of hyperbolicity, systems with overlaps, complex dynamics and iterated function systems.
Dynamical systems and ergodic theory
Measure and integration
Probability theory and stochastic processes
2569
2617
10.4171/OWR/2014/46
http://www.ems-ph.org/doi/10.4171/OWR/2014/46
Arbeitsgemeinschaft: Totally Disconnected Groups
Pierre-Emmanuel
Caprace
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Nicolas
Monod
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Locally compact groups are ubiquitous in the study of many continuous or discrete structures across geometry, analysis and algebra. Every locally compact group is an extension of a connected group by a totally disconnected group. The connected case has been studied in depth, notably using Lie theory, a culminating point being reached in the 1950s with the solution to Hilbert’s 5th problem. The totally disconnected case, by contrast, remains full of challenging questions. A series of new results has been obtained in the last twenty years, and today the activity in this area is witnessing a sharp increase. These texts report on the recent Arbeitsgemeinschaft on this topic.
Topological groups, Lie groups
2619
2665
10.4171/OWR/2014/47
http://www.ems-ph.org/doi/10.4171/OWR/2014/47
Dirichlet Form Theory and its Applications
Sergio
Albeverio
Universität Bonn, BONN, GERMANY
Zhen-Qing
Chen
University of Washington, SEATTLE, UNITED STATES
Masatoshi
Fukushima
Osaka University, OSAKA, JAPAN
Michael
Röckner
Universität Bielefeld, BIELEFELD, GERMANY
Theory of Dirichlet forms is one of the main achievements in modern probability theory. It provides a powerful connection between probabilistic and analytic potential theory. It is also an effective machinery for studying various stochastic models, especially those with non-smooth data, on fractal-like spaces or spaces of infinite dimensions. The Dirichlet form theory has numerous interactions with other areas of mathematics and sciences. This workshop brought together top experts in Dirichlet form theory and related fields as well as promising young researchers, with the common theme of developing new foundational methods and their applications to specific areas of probability. It provided a unique opportunity for the interaction between the established scholars and young researchers.
Potential theory
Probability theory and stochastic processes
2667
2756
10.4171/OWR/2014/48
http://www.ems-ph.org/doi/10.4171/OWR/2014/48
Valuation Theory and Its Applications
Zoé
Chatzidakis
Université Paris 7 - Case 7012, PARIS CEDEX 13, FRANCE
Franz-Viktor
Kuhlmann
University of Saskatchewan, SASKATOON SASK., CANADA
Jochen
Koenigsmann
University of Oxford, OXFORD, GREAT BRITAIN
Florian
Pop
University of Pennsylvania, PHILADELPHIA, UNITED STATES
In recent years, the applications of valuation theory in several areas of mathematics have expanded dramatically. In this workshop, we presented applications related to algebraic geometry, number theory and model theory, as well as advances in the core of valuation theory itself. Areas of particular interest were resolution of singularities and Galois theory.
Field theory and polynomials
2757
2823
10.4171/OWR/2014/49
http://www.ems-ph.org/doi/10.4171/OWR/2014/49
Probability, Trees and Algorithms
Luc
Devroye
McGill University, MONTREAL, QC, CANADA
Ralph
Neininger
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
The subject of this workshop were probabilistic aspects of algorithms for fundamental problems such as sorting, searching, selecting of and within data, random permutations, algorithms based on combinatorial trees or search trees, continuous limits of random trees and random graphs as well as random geometric graphs. The deeper understanding of the complexity of such algorithms and of shape characteristics of large discrete structures require probabilistic models and an asymptotic analysis of random discrete structures. The talks of this workshop focused on probabilistic, combinatorial and analytic techniques to study asymptotic properties of large random combinatorial structures.
Probability theory and stochastic processes
Computer science
2825
2871
10.4171/OWR/2014/50
http://www.ems-ph.org/doi/10.4171/OWR/2014/50
Combinatorial Optimization
Gérard
Cornuéjols
Carnegie Mellon University, PITTSBURGH, UNITED STATES
Friedrich
Eisenbrand
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Bruce
Shepherd
McGill University, MONTREAL, QC, CANADA
Combinatorial Optimization is an area of mathematics that thrives from a continual influx of new questions and problems from practice. Attacking these problems has required the development and combination of ideas and techniques from different mathematical areas including graph theory, matroids and combinatorics, convex and nonlinear optimization, discrete and convex geometry, algebraic and topological methods. We continued a tradition of triannual Oberwolfach workshops, bringing together the best international researchers with younger talent to discover new connections with a particular emphasis on emerging breakthrough areas.
Operations research, mathematical programming
2873
2932
10.4171/OWR/2014/51
http://www.ems-ph.org/doi/10.4171/OWR/2014/51
Mathematical Logic: Proof Theory, Constructive Mathematics
Samuel
Buss
University of California, San Diego, LA JOLLA, UNITED STATES
Ulrich
Kohlenbach
Technische Hochschule Darmstadt, DARMSTADT, GERMANY
Michael
Rathjen
University of Leeds, LEEDS, UNITED KINGDOM
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity
Mathematical logic and foundations
2933
2986
10.4171/OWR/2014/52
http://www.ems-ph.org/doi/10.4171/OWR/2014/52
Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals
Michael
Baake
Universität Bielefeld, BIELEFELD, GERMANY
David
Damanik
Rice University, HOUSTON, UNITED STATES
Uwe
Grimm
The Open University, MILTON KEYNES, UNITED KINGDOM
The dynamical (or von Neumann) spectrum of a dynamical system and the diffraction spectrum of the corresponding measure dynamical system are intimately related. While their equivalence in the case of pure point spectra is well understood, this workshop aimed at an appropriate extension to systems with mixed spectra, building on recent developments for systems of finite local complexity and for certain random systems from the theory of point processes. Another focus was the question for connections between Schr¨odinger and dynamical spectra.
Dynamical systems and ergodic theory
Convex and discrete geometry
Quantum theory
2987
3013
10.4171/OWR/2014/53
http://www.ems-ph.org/doi/10.4171/OWR/2014/53
Mini-Workshop: Eigenvalue Problems in Surface Superconductivity
Virginie
Bonnaillie-Noël
Ecole Normale Superieure, PARIS CEDEX 05, FRANCE
Hynek
Kovařík
Università degli Studi di Brescia, BRESCIA, ITALY
Konstantin
Pankrashkin
Université Paris-Sud, ORSAY CEDEX, FRANCE
The aim of the meeting is to discuss several classes of Schrödinger equations appearing within the Ginzburg-Landau theory of superconductivity. The related problems are discussed from several perspectives including semiclassical analysis, PDE in non-smooth domains, geometric spectral theory and operator theory, which should provide a new insight into various phenomena appearing in superconducting systems.
Partial differential equations
Numerical analysis
3015
3057
10.4171/OWR/2014/54
http://www.ems-ph.org/doi/10.4171/OWR/2014/54
Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics
Karl-Hermann
Neeb
FAU Erlangen-Nürnberg, ERLANGEN, GERMANY
Gestur
Olafsson
Louisiana State University, BATON ROUGE, UNITED STATES
Palle
Jorgensen
University of Iowa, IOWA CITY, UNITED STATES
The central focus of the workshop was reflection positivity, its occurrence in physics, representation theory, abstract harmonic analysis, and stochastic analysis. The program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity.
Topological groups, Lie groups
Nonassociative rings and algebras
Quantum theory
3059
3102
10.4171/OWR/2014/55
http://www.ems-ph.org/doi/10.4171/OWR/2014/55
Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics
Rolf
Biehler
Universität Paderborn, PADERBORN, GERMANY
Reinhard
Hochmuth
Universität Hannover, HANNOVER, GERMANY
Dame Celia
Hoyles
University of London, LONDON, UNITED KINGDOM
Patrick
Thompson
Arizona State University, TEMPE, UNITED STATES
The topic of undergraduate mathematics is of considerable concern for mathematicians in universities, but also for those teaching mathematics as part of undergraduate studies other than mathematics, for employers seeking to employ a mathematically skilled workforce, and for teacher education. Different countries have made and continue to make massive efforts to improve the quality of mathematics education across all age ranges, with most of the research undertaken particularly at the school level. A growing number of mathematicians and mathematics educators now see the need for undertaking interdisciplinary research and collaborative reflections around issues at the tertiary level. The conference aimed to share research results and experiences as a background to establishing a scientific community of mathematicians and mathematics educators whose concern is the theoretical reflection, the research-based empirical investigation, and the exchange of best-practice examples of mathematics education at the tertiary level. The focus of the conference was mathematics education for mathematics, engineering and economy majors and for future mathematics teachers.
Mathematics education
3103
3175
10.4171/OWR/2014/56
http://www.ems-ph.org/doi/10.4171/OWR/2014/56
Variational Methods for Evolution
Luigi
Ambrosio
Scuola Normale Superiore, PISA, ITALY
Alexander
Mielke
Angewandte Analysis und Stochastik, BERLIN, GERMANY
Mark
Peletier
Eindhoven University of Technology, EINDHOVEN, NETHERLANDS
Giuseppe
Savaré
Università di Pavia, PAVIA, ITALY
The workshop brought together researchers from geometry, nonlinear functional analysis, calculus of variations, partial differential equations, and stochastics around a common topic: systems whose evolution is driven by variational principles such as gradient or Hamiltonian systems. The talks covered a wide range of topics, including variational tools such as incremental minimization approximations, Gamma convergence, and optimal transport, reaction-diffusion systems, singular perturbation and homogenization, rate-independent models for visco-plasticity and fracture, Hamiltonian and hyperbolic systems, stochastic models and new gradient structures for Markov processes or variational large-deviation principles.
Partial differential equations
Calculus of variations and optimal control; optimization
Probability theory and stochastic processes
Fluid mechanics
3177
3254
10.4171/OWR/2014/57
http://www.ems-ph.org/doi/10.4171/OWR/2014/57