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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
14
2017
1
Combinatorics
Jeff
Kahn
Rutgers University, Piscataway, USA
Angelika
Steger
ETH Zentrum, Zürich, Switzerland
Benjamin
Sudakov
ETH Zürich, Switzerland
Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing abstracts of the presentations and a summary of the problem session.
Combinatorics
General
5
81
10.4171/OWR/2017/1
http://www.ems-ph.org/doi/10.4171/OWR/2017/1
1
2
2018
Mini-Workshop: Women in Mathematics: Historical and Modern Perspectives
Tinne
Hoff Kjeldsen
University of Copenhagen, Denmark
Nicola
Oswald
Bergische Universität Wuppertal, Germany
Renate
Tobies
Friedrich-Schiller-Universität Jena, Germany
The aim of the workshop is to build a bridge between research on the situation of women in mathematics at the beginning of coeducative studies and the current circumstances in academia. The issue of women in mathematics has been a recent political and social hot topic in the mathematical community. As thematic foci we place a double comparison: besides shedding light on differences and similarities in several European countries, we complete this investigation by comparing the developments of women studies from the beginnings. This shall lead to new results on tradition and suggest improvements on the present situation.
History and biography
General
83
131
10.4171/OWR/2017/2
http://www.ems-ph.org/doi/10.4171/OWR/2017/2
1
2
2018
Mini-Workshop: Spaces and Moduli Spaces of Riemannian Metrics
F. Thomas
Farrell
Tsinghua University, Beijing, China and Binghamton University, USA
Wilderich
Tuschmann
Karlsruhe Institute of Technology, Germany
The mini-workshop focused on central questions and new results concerning spaces and moduli spaces of Riemannian metrics with lower or upper curvature bounds on open and closed manifolds and, moreover, related themes from Anosov geometry. These are all described in detail below. The event brought together young and senior researchers working about (moduli) spaces of negative and nonnegative sectional, nonnegative Ricci and positive scalar curvature as well as Anosov metrics, and the talks and discussions brought about many new and inspiring research problems to pursue.
Differential geometry
Global analysis, analysis on manifolds
133
166
10.4171/OWR/2017/3
http://www.ems-ph.org/doi/10.4171/OWR/2017/3
1
2
2018
Mini-Workshop: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs
Max
Gunzburger
Florida State University, Tallahassee, USA
Karl
Kunisch
Karl-Franzens-Universität Graz, Austria
Angela
Kunoth
Universität zu Köln, Germany
Optimization problems constrained by time-dependent PDEs (Partial Differential Equations) are challenging from a computational point of view: even in the simplest case, one needs to solve a system of PDEs coupled globally in time and space for the unknown solutions (the state, the costate and the control of the system). Typical and practically relevant examples are the control of nonlinear heat equations as they appear in laser hardening or the thermic control of flow problems (Boussinesq equations). Specifically for PDEs with a long time horizon, conventional time-stepping methods require an enormous storage of the respective other variables. In contrast, adaptive methods aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities and are, therefore, most promising.
Numerical analysis
Calculus of variations and optimal control; optimization
167
211
10.4171/OWR/2017/4
http://www.ems-ph.org/doi/10.4171/OWR/2017/4
1
2
2018
Cryptography
Johannes
Buchmann
Technische Universität Darmstadt, Germany
Shafi
Goldwasser
The Stata Center, Cambridge, USA
The Oberwolfach workshop Cryptography brought together scientists from cryptography with mathematicians specializing in the algorithmic problems underlying cryptographic security. The goal of the workshop was to stimulate interaction and collaboration that enables a holistic approach to designing cryptography from the mathematical foundations to practical applications. The workshop addressed fundamental research results leading to innovative cryptography for protecting security and privacy.
Information and communication, circuits
213
266
10.4171/OWR/2017/5
http://www.ems-ph.org/doi/10.4171/OWR/2017/5
1
2
2018
Emerging Developments in Interfaces and Free Boundaries
Charles
Elliott
University of Warwick, Coventry, UK
Yoshikazu
Giga
University of Tokyo, Japan
Michael
Hinze
Universität Hamburg, Germany
Vanessa
Styles
University of Sussex, Brighton, UK
The field of the mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a well established and flourishing area of research. This workshop focused on recent developments and emerging new themes. By bringing together experts in these fields we achieved progress in open questions and developed novel research directions in mathematics related to interfaces and free boundaries. This interdisciplinary workshop brought together researchers from distinct mathematical fields such as analysis, computation, optimisation and modelling to discuss emerging challenges.
Partial differential equations
Numerical analysis
267
338
10.4171/OWR/2017/6
http://www.ems-ph.org/doi/10.4171/OWR/2017/6
1
2
2018
Applications of Optimal Transportation in the Natural Sciences
Jean-David
Benamou
INRIA Rocquencourt, Le Chesnay, France
Virginie
Ehrlacher
CERMICS - ENPC, Marne-la-Vallée, France
Daniel
Matthes
TU München, Garching, Germany
The aim of this workshop was to gather a mixed group of experts and young researchers from different areas of applied mathematics in which optimal transport plays a central role. Applications in one of the classical areas of natural sciences, like physics, chemistry and (mathematical) biology were the main focus of the workshop.
Measure and integration
Partial differential equations
Quantum theory
Biology and other natural sciences
339
416
10.4171/OWR/2017/7
http://www.ems-ph.org/doi/10.4171/OWR/2017/7
1
2
2018
Mini-Workshop: Cluster Expansions: From Combinatorics to Analysis through Probability
Roberto
Fernández
Universiteit Utrecht, Netherlands
Sabine
Jansen
University of Sussex, Brighton, UK
Dimitrios
Tsagkarogiannis
University of Sussex, Brighton, UK
The workshop addressed the interplay between theory and applications of cluster expansions. These expansions, historically geared towards the study of systems in statistical mechanics, thermodynamics, and physical chemistry, have recently found applications in different areas of current mathematical research, such as point processes, random graphs, coloring issues, logics and inverse problems in numerical analysis. The workshop developed both directions of the theory–application interplay. On the one hand, speakers presented advances in the theoretical foundations of the abstract polymer model and improved tree-graph inequalities, and explored their consequences for the theory of liquids and other applied issues. On the other hand, researchers in stochastic modelisation exposed needs and challenges brought by concrete models of liquids and liquid crystal to the theory of cluster expansions. In addition other complementary methods were discussed, such as disagrement percolation – an expansion-free approach to uniqueness and decay of correlations – and lace expansions – an expansion technique popular for its applications to random walks and percolation problems.
Statistical mechanics, structure of matter
Combinatorics
Probability theory and stochastic processes
Numerical analysis
417
452
10.4171/OWR/2017/8
http://www.ems-ph.org/doi/10.4171/OWR/2017/8
1
2
2018
Mini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions
Martin
Hutzenthaler
Universität Duisburg-Essen, Germany
Annika
Lang
Chalmers University of Technology, Göteborg and Göteborg University, Sweden
Lukasz
Szpruch
Edinburgh University, UK
Larisa
Yaroslavtseva
Universität Passau, Germany
This Mini-Workshop is devoted to regularity and numerical analysis of stochastic ordinary and partial differential equations (SDEs for both). The standard assumption in the literature on SDEs is global Lipschitz continuity of the coefficient functions. However, many SDEs arising from applications fail to have globally Lipschitz continuous coefficients. Recent years have seen a prosper growth of the literature on regularity and numerical approximations for SDEs with non-globally Lipschitz coefficients. Some surprising results have been obtained – e.g., the Euler–Maruyama method diverges for a large class of SDEs with super-linearly growing coefficients, and the limiting equation of a spatial discretization of the stochastic Burgers equation depends on whether the discretization is symmetric or not. Several positive results have been obtained. However the regularity of numerous important SDEs and the closely related question of convergence and convergence rates of numerical approximations remain open. The aim of this workshop is to bring together the main contributers in this direction and to foster significant progress.
Numerical analysis
Probability theory and stochastic processes
453
498
10.4171/OWR/2017/9
http://www.ems-ph.org/doi/10.4171/OWR/2017/9
1
2
2018
Mini-Workshop: Perspectives in High-Dimensional Probability and Convexity
Joscha
Prochno
University of Hull, UK
Christoph
Thäle
Ruhr-Universität Bochum, Germany
Elisabeth
Werner
Case Western Reserve University, Cleveland, USA
Understanding the geometric structure of systems involving a huge amount of parameters is a central problem in mathematics and applied sciences today. Here, geometric and analytical ideas meet in a non-trivial way and powerful probabilistic tools play a key role in many discoveries. Two essentially independent areas of mathematics concerned with high-dimensional problems are asymptotic geometric analysis and information-based complexity. In this Mini-Workshop we brought together researchers from both fields to explore the connections and form synergies to develop new perspectives.
Convex and discrete geometry
Number theory
Probability theory and stochastic processes
Numerical analysis
499
526
10.4171/OWR/2017/10
http://www.ems-ph.org/doi/10.4171/OWR/2017/10
1
2
2018
Set Theory
Ilijas
Farah
York University, Toronto, Canada
Sy-David
Friedman
Universität Wien, Austria
Ralf-Dieter
Schindler
Universität Münster, Germany
W. Hugh
Woodin
Harvard University, Cambridge, USA
This workshop included selected talks on pure set theory and its applications, simultaneously showing diversity and coherence of the subject.
Mathematical logic and foundations
527
589
10.4171/OWR/2017/11
http://www.ems-ph.org/doi/10.4171/OWR/2017/11
1
2
2018
Representation Theory of Quivers and Finite Dimensional Algebras
William
Crawley-Boevey
University of Leeds, UK
Osamu
Iyama
Nagoya University, Japan
Henning
Krause
Universität Bielefeld, Germany
Methods and results from the representation theory of quivers and finite dimensional algebras have led to many interactions with other areas of mathematics. Such areas include the theory of Lie algebras and quantum groups, commutative algebra, algebraic geometry and topology, and in particular the theory of cluster algebras. The aim of this workshop was to further develop such interactions and to stimulate progress in the representation theory of algebras.
Associative rings and algebras
Commutative rings and algebras
Linear and multilinear algebra; matrix theory
Category theory; homological algebra
591
681
10.4171/OWR/2017/12
http://www.ems-ph.org/doi/10.4171/OWR/2017/12
1
2
2018
Mathematics of Quantitative Finance
Peter
Friz
Technische Universität Berlin, Germany
Antoine
Jacquier
Imperial College London, UK
Josef
Teichmann
ETH Zürich, Switzerland
The workshop on Mathematics of Quantitative Finance, organised at the Mathematisches Forschungsinstitut Oberwolfach from 26 February to 4 March 2017, focused on cutting edge areas of mathematical finance, with an emphasis on the applicability of the new techniques and models presented by the participants.
Game theory, economics, social and behavioral sciences
Ordinary differential equations
Probability theory and stochastic processes
683
769
10.4171/OWR/2017/13
http://www.ems-ph.org/doi/10.4171/OWR/2017/13
1
2
2018
Real Algebraic Geometry With a View Toward Moment Problems and Optimization
Didier
Henrion
LAAS-CNRS, Toulouse, France
Maria
Infusino
Universität Konstanz, Germany
Salma
Kuhlmann
Universität Konstanz, Germany
Victor
Vinnikov
Ben Gurion University of the Negev, Beer-Sheva, Israel
Continuing the tradition initiated inMFO workshop held in 2014, the aim of this workshop was to foster the interaction between real algebraic geometry, operator theory, optimization, and algorithms for systems control. A particular emphasis was given to moment problems through an interesting dialogue between researchers working on these problems in finite and infinite dimensional settings, from which emerged new challenges and interdisciplinary applications.
Field theory and polynomials
Commutative rings and algebras
Algebraic geometry
Integral transforms, operational calculus
771
862
10.4171/OWR/2017/14
http://www.ems-ph.org/doi/10.4171/OWR/2017/14
1
2
2018
Space-time Methods for Time-dependent Partial Differential Equations
Ricardo
Nochetto
University of Maryland, College Park, USA
Stefan
Sauter
Universität Zürich, Switzerland
Christian
Wieners
Karlsruher Institut für Technologie (KIT), Germany
Modern discretizations of time-dependent PDEs consider the full problem in the space-time cylinder and aim to overcome limitations of classical approaches such as the method of lines (first discretize in space and then solve the resulting ODE) and the Rothe method (first discretize in time and then solve the PDE). A main advantage of a holistic space-time method is the direct access to space-time adaptivity and to the backward problem (required for the dual problem in optimization or error control). Moreover, this allows for parallel solution strategies simultaneously in time and space. Several space-time concepts where proposed (different conforming and nonconforming space-time finite elements, the parareal method, wavefront relaxation etc.) but this topic has become a rapidly growing field in numerical analysis and scientific computing. In this workshop the focus is the development of adaptive and flexible space-time discretization methods for solving parabolic and hyperbolic space-time partial differential equations.
Numerical analysis
863
947
10.4171/OWR/2017/15
http://www.ems-ph.org/doi/10.4171/OWR/2017/15
1
2
2018
Statistical Recovery of Discrete, Geometric and Invariant Structures
Peter
Bühlmann
ETH Zentrum, Zürich, Switzerland
Axel
Munk
Georg-August-Universität Göttingen, Germany
Martin
Wainwright
University of California, Berkeley, USA
Bin
Yu
University of California, Berkeley, USA
The main objective of the workshop was to bring together researchers in mathematical statistics and related areas in order to discuss recent advances and problems associated with statistical recovery of geometric and invariant structures. Topics include adaptive estimation, confidence sets and testing techniques, as well as statistical algorithms for geometrical structure recovery and data analysis.
Statistics
Probability theory and stochastic processes
949
999
10.4171/OWR/2017/16
http://www.ems-ph.org/doi/10.4171/OWR/2017/16
1
2
2018
Multiscale and High-Dimensional Problems
Albert
Cohen
Université Pierre et Marie Curie, Paris, France
Wolfgang
Dahmen
Technische Hochschule Aachen, Germany
Ronald
DeVore
Texas A&M University, College Station, USA
Angela
Kunoth
Universität zu Köln, Germany
High-dimensional problems appear naturally in various scientific areas. Two primary examples are PDEs describing complex processes in computational chemistry and physics, and stochastic/ parameter-dependent PDEs arising in uncertainty quantification and optimal control. Other highly visible examples are big data analysis including regression and classification which typically encounters high-dimensional data as input and/or output. High dimensional problems cannot be solved by traditional numerical techniques, because of the so-called curse of dimensionality. Rather, they require the development of novel theoretical and computational approaches to make them tractable and to capture fine resolutions and relevant features. Paradoxically, increasing computational power may even serve to heighten this demand, since the wealth of new computational 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 setting constitute challenging tasks from both theoretical and numerical perspective. The last decade has seen the emergence of several new computational methodologies which address the obstacles to solving high dimensional problems. These include adaptive methods based on mesh refinement or sparsity, random forests, model reduction, compressed sensing, sparse grid and hyperbolic wavelet approximations, and various new tensor structures. Their common features are the nonlinearity of the solution method that prioritize variables and separate solution characteristics living on different scales. These methods have already drastically advanced the frontiers of computability for certain problem classes. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computational methods and to promote the exchange of ideas emerging in various disciplines about how to treat multiscale and high-dimensional problems.
Numerical analysis
Approximations and expansions
1001
1051
10.4171/OWR/2017/17
http://www.ems-ph.org/doi/10.4171/OWR/2017/17
1
2
2018
2
Arbeitsgemeinschaft: Higher Gross Zagier Formulas
Zhiwei
Yun
Stanford University, USA
Wei
Zhang
Columbia University, New York, USA
The aim of this Arbeitsgemeinschaft is to go over the proof of the higher Gross–Zagier formula established in the paper [YZ15]. The formula relates arbitrary order central derivative of the base change $L$-function of an unramifed automorphic representation of PGL$_2$ over a function field to the self-intersection number of a certain algebraic cycle on the moduli stack of Shtukas.
Number theory
Topological groups, Lie groups
1067
1134
10.4171/OWR/2017/18
http://www.ems-ph.org/doi/10.4171/OWR/2017/18
4
27
2018
Discrete Geometry
Imre
Bárány
University College London, UK, and Hungarian Academy of Sciences, Budapest, Hungary
Xavier
Goaoc
Université Paris-Est, Marne-la-Vallée, France
Günter
Rote
Freie Universität Berlin, Germany
A number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics or algebraic geometry. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry.
Convex and discrete geometry
1135
1205
10.4171/OWR/2017/19
http://www.ems-ph.org/doi/10.4171/OWR/2017/19
4
27
2018
Algebraic Statistics
Mathias
Drton
University of Washington, Seattle, USA
Thomas
Kahle
Otto-von-Guericke-Universität, Magdeburg, Germany
Bernd
Sturmfels
University of California, Berkeley, USA, and Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Caroline
Uhler
Massachusetts Institute of Technology, Cambridge, USA
Algebraic Statistics is concerned with the interplay of techniques from commutative algebra, combinatorics, (real) algebraic geometry, and related fields with problems arising in statistics and data science. This workshop was the first at Oberwolfach dedicated to this emerging subject area. The participants highlighted recent achievements in this field, explored exciting new applications, and mapped out future directions for research.
Commutative rings and algebras
Linear and multilinear algebra; matrix theory
Convex and discrete geometry
Statistics
1207
1279
10.4171/OWR/2017/20
http://www.ems-ph.org/doi/10.4171/OWR/2017/20
4
27
2018
Algebraic Groups
Corrado
De Concini
Università di Roma La Sapienza, Italy
Peter
Littelmann
Universität Köln, Germany
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, J.-P. Serre, 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, covering a range of topics, with an emphasis on recent developments in the subject.
Algebraic geometry
Nonassociative rings and algebras
Group theory and generalizations
1281
1347
10.4171/OWR/2017/21
http://www.ems-ph.org/doi/10.4171/OWR/2017/21
4
27
2018
O-Minimality and its Applications to Number Theory and Analysis
Tobias
Kaiser
Universität Passau, Germany
Jonathan
Pila
University of Oxford, UK
Patrick
Speissegger
McMaster University, Hamilton, Canada
Alex
Wilkie
University of Manchester, UK and University of Oxford, UK
The workshop brought together researchers in the areas of o-minimal structures, analysis and number theory. The latest developments in o-minimality and their applications to number theory and analysis were presented in a series of talks; one focus, in particular, was on the Pila–Wilkie Theorem and its impact on diophantine problems.
Mathematical logic and foundations
Number theory
Algebraic geometry
Several complex variables and analytic spaces
1349
1420
10.4171/OWR/2017/22
http://www.ems-ph.org/doi/10.4171/OWR/2017/22
4
27
2018
Geophysical Fluid Dynamics
Yoshikazu
Giga
University of Tokyo, Japan
Matthias
Hieber
Technische Hochschule Darmstadt, Germany
Edriss
Titi
Texas A&M University, College Station, USA, and The Weizmann Institute of Science, Rehovot, Israel
The workshop “Geophysical Fluid Dynamics” addressed recent advances in analytical, stochastic, modeling and computational studies of geophysical fluid models. Of central interest were the reduced geophysical models, that are derived by means of asymptotic and scaling techniques, and their investigations by methods from the above disciplines. In particular, contributions concerning the viscous and inviscid geostrophic models, the primitive equations of oceanic and atmospheric dynamics, tropical atmospheric models and their coupling to nonlinear dynamics of phase changes moisture, thermodynamical effects, stratifying effects, as well as boundary layers were presented and discussed.
Fluid mechanics
Partial differential equations
Probability theory and stochastic processes
Geophysics
1421
1462
10.4171/OWR/2017/23
http://www.ems-ph.org/doi/10.4171/OWR/2017/23
4
27
2018
Computational Inverse Problems for Partial Differential Equations
Liliana
Borcea
University of Michigan, Ann Arbor, USA
Thorsten
Hohage
Georg-August-Universität Göttingen, Germany
Barbara
Kaltenbacher
Universität Alpen-Adria, Klagenfurt, Austria
The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges.
Partial differential equations
Numerical analysis
Geophysics
1463
1549
10.4171/OWR/2017/24
http://www.ems-ph.org/doi/10.4171/OWR/2017/24
4
27
2018
Harmonic Analysis and the Trace Formula
Werner
Müller
Universität Bonn, Germany
Sug Woo
Shin
University of California, Berkeley, USA
Birgit
Speh
Cornell University, Ithaca, USA
Nicolas
Templier
Cornell University, Ithaca, USA
The purpose of this workshop was to discuss recent results in harmonic analysis that arise in the study of the trace formula. This theme is common to different directions of research on automorphic forms such as representation theory, periods, and families.
Number theory
Algebraic geometry
Topological groups, Lie groups
1551
1630
10.4171/OWR/2017/25
http://www.ems-ph.org/doi/10.4171/OWR/2017/25
4
27
2018
Stochastic Analysis: Geometry of Random Processes
Alice
Guionnet
École Normale Supérieure de Lyon, France
Martin
Hairer
University of Warwick, Coventry, UK
Grégory
Miermont
École Normale Supérieure de Lyon, France
A common feature shared by many natural objects arising in probability theory is that they tend to be very “rough”, as opposed to the “smooth” objects usually studied in other branches of mathematics. It is however still desirable to understand their geometric properties, be it from a metric, a topological, or a measure-theoretic perspective. In recent years, our understanding of such “random geometries” has seen spectacular advances on a number of fronts.
Probability theory and stochastic processes
Statistical mechanics, structure of matter
1631
1679
10.4171/OWR/2017/26
http://www.ems-ph.org/doi/10.4171/OWR/2017/26
4
27
2018
Nonlinear Waves and Dispersive Equations
Herbert
Koch
Universität Bonn, Germany
Pierre
Raphaël
Université de Nice Sophia Antipolis, France
Daniel
Tataru
University of California, Berkeley, USA
Monica
Visan
UCLA, Los Angeles, USA
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 solitons and scattering. They are linked to many areas of mathematics and physics, ranging from integrable systems and harmonic analysis to fluid dynamics, geometry, general relativity and probability.
Partial differential equations
Dynamical systems and ergodic theory
Mechanics of deformable solids
1681
1745
10.4171/OWR/2017/27
http://www.ems-ph.org/doi/10.4171/OWR/2017/27
4
27
2018
Reaction Networks and Population Dynamics
Ellen
Baake
Universität Bielefeld, Germany
Tom
Kurtz
University of Wisconsin, Madison, USA
Carsten
Wiuf
University of Copenhagen, Denmark
Reaction systems and population dynamics constitute two highly developed areas of research that build on well-defined model classes, both in terms of dynamical systems and stochastic processes. Despite a significant core of common structures, the two fields have largely led separate lives. The workshop brought the communities together and emphasised concepts, methods and results that have, so far, appeared in one area but are potentially useful in the other as well.
Biology and other natural sciences
Ordinary differential equations
Probability theory and stochastic processes
1747
1804
10.4171/OWR/2017/28
http://www.ems-ph.org/doi/10.4171/OWR/2017/28
4
27
2018
Nonlinear Partial Differential Equations on Graphs
Reika
Fukuizumi
Tohoku University, Sendai, Japan
Jeremy
Marzuola
University of North Carolina at Chapel Hill, USA
Dmitry
Pelinovsky
McMaster University, Hamilton, Canada
Guido
Schneider
Universität Stuttgart, Germany
One-dimensional metric graphs in two and three-dimensional spaces play an important role in emerging areas of modern science such as nano-technology, quantum physics, and biological networks. The workshop focused on the analysis of nonlinear partial differential equations on metric graphs, especially on the bifurcation and stability of nonlinear waves on complex graphs, on the justification of Kirchhoff boundary conditions, on spectral properties and the validity of amplitude equations for periodic graphs, and the existence of ground states for the NLS equation with and without potential.
Partial differential equations
Quantum theory
1805
1868
10.4171/OWR/2017/29
http://www.ems-ph.org/doi/10.4171/OWR/2017/29
4
27
2018
Geometric Structures in Group Theory
Martin
Bridson
University of Oxford, UK
Linus
Kramer
Universität Münster, Germany
Bertrand
Rémy
École Polytechnique, Palaiseau, France
Karen
Vogtmann
University of Warwick, Coventry, UK
Geometric group theory has natural connections and rich interfaces with many of the other major fields of modern mathematics. The basic motif of the field is the construction and exploration of actions by infinite groups on spaces that admit further structure, with an emphasis on geometric structures of different sorts: one usually seeks actions in order to illuminate the structure of groups of particular interest, but one also explores actions in order to understand the underlying spaces. The dramatic growth of the field in the late twentieth century was closely associated with the study of generalized forms of non-positive and negative curvature, and classically the spaces at hand were cell complexes with some additional structure. But the scope of the field, the range of groups embraced by its techniques, and the nature of the spaces studied, have expanded enormously in recent years, and they continue to do so. This meeting provided an exciting snapshot of some of the main strands in the recent development of the subject.
Group theory and generalizations
Manifolds and cell complexes
1869
1915
10.4171/OWR/2017/30
http://www.ems-ph.org/doi/10.4171/OWR/2017/30
4
27
2018
Differentialgeometrie im Großen
Gérard
Besson
Université Joseph Fourier, Grenoble, Saint-Martin-d’Hères, France
Ursula
Hamenstädt
Universität Bonn, Germany
Michael
Kapovich
University of California at Davis, USA
Ben
Weinkove
Northwestern University, Evanston, USA
The topics discussed at the meeting were Kähler geometry, geometric evolution equations, manifolds of nonnegative curvature, metric geometry and geometric representations of groups. The choice of topics reflects current trends in the development of differential geometry.
Differential geometry
1917
1971
10.4171/OWR/2017/31
http://www.ems-ph.org/doi/10.4171/OWR/2017/31
4
27
2018
3
Dynamische Systeme
Håkan
Eliasson
Université Pierre et Marie Curie-Université Paris Diderot, Paris, France
Helmut
Hofer
Institute for Advanced Study, Princeton, USA
Vadim
Kaloshin
University of Maryland, College Park, USA
Jean-Christophe
Yoccoz
Collège de France, Paris, 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. This year special emphasis where laid on symplectic methods with applications to dynamics. The workshop was dedicated to the memory of John Mather, Jean-Christophe Yoccoz and Krzysztof Wysocki.
Dynamical systems and ergodic theory
Differential geometry
Mechanics of particles and systems
1987
2046
10.4171/OWR/2017/32
http://www.ems-ph.org/doi/10.4171/OWR/2017/32
7
4
2018
Material Theories
Sergio
Conti
Universität Bonn, Germany
Antonio
DeSimone
SISSA-ISAS, Trieste, Italy
Stephan
Luckhaus
Universität Leipzig, Germany
Lev
Truskinovsky
ESPCI ParisTech, Paris, France
Material theories is a series of workshops concerned with a broad range of topics related to the mechanics and mathematics of materials. As such, this edition brought together researchers from diverse fields converging toward the interaction between mathematics, mechanics, and material science.
Mechanics of particles and systems
Mechanics of deformable solids
Fluid mechanics
Statistical mechanics, structure of matter
2047
2099
10.4171/OWR/2017/33
http://www.ems-ph.org/doi/10.4171/OWR/2017/33
7
4
2018
Real Analysis, Harmonic Analysis, and Applications
Michael
Christ
University of California, Berkeley, USA
Detlef
Müller
Christian-Albrechts-Universität zu Kiel, Germany
Christoph
Thiele
Universität Bonn, Germany
The workshop focused on important developments within the last few years in real and harmonic analysis, including polynomial partitioning and decoupling as well as significant concurrent progress in the application of these for example to number theory and partial differential equations.
Fourier analysis
2101
2164
10.4171/OWR/2017/34
http://www.ems-ph.org/doi/10.4171/OWR/2017/34
7
4
2018
Partial Differential Equations
Camillo
De Lellis
Universität Zürich, Switzerland
Richard
Schoen
University of California, Irvine, USA
Peter
Topping
University of Warwick, Coventry, UK
The workshop dealt with nonlinear partial differential equations and some applications in geometry, touching several different topics such as minimal surfaces and geometric measure theory, conformal geometry, geometric flows, metric geometry and structure of Riemannian manifolds.
Measure and integration
Partial differential equations
Differential geometry
2165
2222
10.4171/OWR/2017/35
http://www.ems-ph.org/doi/10.4171/OWR/2017/35
7
4
2018
Analysis, Geometry and Topology of Positive Scalar Curvature Metrics
Bernd
Ammann
Universität Regensburg, Germany
Bernhard
Hanke
Universität Augsburg, Germany
André
Neves
Imperial College London, UK
Riemannian manifolds with positive scalar curvature play an important role in mathematics and general relativity. Obstruction and existence results are connected to index theory, bordism theory and homotopy theory, using methods from partial differential equations and functional analysis. The workshop led to a lively interaction between mathematicians working in these areas.
Differential geometry
$K$-theory
Partial differential equations
Manifolds and cell complexes
2223
2298
10.4171/OWR/2017/36
http://www.ems-ph.org/doi/10.4171/OWR/2017/36
7
4
2018
Proof Complexity and Beyond
Albert
Atserias
Universitat Politècnica de Catalunya, Barcelona, Spain
Jakob
Nordström
KTH - Royal Institute of Technology, Stockholm, Sweden
Toniann
Pitassi
University of Toronto, Canada
Alexander
Razborov
University of Chicago, USA
Proof complexity is a multi-disciplinary intellectual endeavor that addresses questions of the general form “how difficult is it to prove certain mathematical facts?” The current workshop focused on recent advances in our understanding of logic-based proof systems and on connections to algorithms, geometry and combinatorics research, such as the analysis of approximation algorithms, or the size of linear or semidefinite programming formulations of combinatorial optimization problems, to name just two important examples.
Mathematical logic and foundations
Computer science
Operations research, mathematical programming
2299
2361
10.4171/OWR/2017/37
http://www.ems-ph.org/doi/10.4171/OWR/2017/37
7
4
2018
Low-dimensional Topology and Number Theory
Paul
Gunnells
University of Massachusetts, Amherst, USA
Walter
Neumann
Columbia University, New York, USA
Adam
Sikora
State University of New York, Buffalo, USA
Don
Zagier
Max-Planck-Institut für Mathematik, Bonn, Germany
The workshop brought together topologists and number theorists with the intent of exploring the many tantalizing connections between these areas.
Manifolds and cell complexes
Number theory
2363
2426
10.4171/OWR/2017/38
http://www.ems-ph.org/doi/10.4171/OWR/2017/38
7
4
2018
Komplexe Analysis
Philippe
Eyssidieux
Université Joseph Fourier, Grenoble, Saint-Martin-d’Hères, France
Jun-Muk
Hwang
Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
Stefan
Kebekus
Universität Freiburg, Freiburg i. Br., Germany
Mihai
Paun
Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
Complex Analysis is a very active branch of mathematics. The aim of this workshop was to discuss recent developments in several complex variables and complex geometry. Topics included singular Kähler–Einstein metrics, positivity of higher direct images, cycle spaces and extension theorems.
Several complex variables and analytic spaces
Algebraic geometry
2427
2473
10.4171/OWR/2017/39
http://www.ems-ph.org/doi/10.4171/OWR/2017/39
7
4
2018
Automorphic Forms and Arithmetic
Valentin
Blomer
Georg-August-Universität Göttingen, Germany
Emmanuel
Kowalski
ETH Zürich, Switzerland
Philippe
Michel
Ecole Polytechnique Fédérale de Lausanne, Switzerland
The workshop brought together leading experts and young researchers at the interface of automorphic forms and analytic number theory to disseminate, discuss and develop important recent methods and results. A particular focus was on higher rank groups, as well as their arithmetic applications. This includes, for instance, the study of various aspects of $L$-functions, the fine distribution properties of their Fourier coefficients and Hecke eigenvalues, the mass distribution of automorphic forms on general symmetric spaces, and applications of results of algebraic geometry to automorphic forms.
Number theory
Topological groups, Lie groups
2475
2537
10.4171/OWR/2017/40
http://www.ems-ph.org/doi/10.4171/OWR/2017/40
7
4
2018
Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications
Volker
Bach
Technische Universität Braunschweig, Germany
Miguel
Ballesteros
Universidad Nacional Autónoma de México, México D.F., Mexico
Dirk-André
Deckert
Ludwig-Maximilians-Universität München, Germany
Israel Michael
Sigal
University of Toronto, Canada
Quantum field theory (QFT) may be considered one of the most fundamental frameworks of theoretical physics. Quantum Electrodynamics (QED) is the part of QFT that describes the interaction between matter and light. Although it is one of the experimentally best tested theories, it yet faces many open mathematical questions and challenges. The mathematical rigorous framework of QED and the implications deriving from it is the topic of Workshop 1737 held at MFO from September 11 through 15, 2017, bringing together mathematicians and theoretical physicists to discuss topics such as high- and low-energy QED, external field QED, quantum optics, many-boson and many-fermion systems, transport properties in condensed matter.
Quantum theory
2539
2599
10.4171/OWR/2017/41
http://www.ems-ph.org/doi/10.4171/OWR/2017/41
7
4
2018
Mini-Workshop: MASAs and Automorphisms of C*-Algebras
Selçuk
Barlak
University of Southern Denmark, Odense, Denmark
Wojciech
Szymański
University of Southern Denmark, Odense, Denmark
Wilhelm
Winter
Westfälische Wilhelms-Universität Münster, Germany
The main aim of this workshop was to study maximal abelian *-subalgebras of C*-algebras from various points of view. A chief motivation is the UCT problem, which asks whether all separable nuclear C*-algebras satisfy the universal coefficient theorem of Rosenberg and Schochet. The connection, in terms of existence of invariant Cartan MASAs for certain *-automorphisms of the Cuntz algebra, has been brought up only very recently; it opens up a line of new perspectives on pressing questions in the structure and classification theory of simple nuclear C*-algebras and their automorphism groups, which has made giant leaps forward in the past five years. Connections to other areas, in particular von Neumann algebras and coarse geometry, have been explored as well.
Functional analysis
2601
2629
10.4171/OWR/2017/42
http://www.ems-ph.org/doi/10.4171/OWR/2017/42
7
4
2018
Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies
Mihai
Fulger
University of Connecticut, Storrs, USA
Alex
Küronya
Goethe-Universität Frankfurt, Germany
Brian
Lehmann
Boston College, Chestnut Hill, USA
There are several flavors of positivity in Algebraic Geometry. They range from conditions that determine vanishing of cohomology, to intersection theoretic properties, and to convex geometry. They offer excellent invariants that have been shown to govern the classification and the parameterization programs in Algebraic Geometry, and are finer than the classical topological ones. This mini-workshop aims to facilitate research collaboration in the area, strengthening the relationship between various positivity notions, beyond the now classical case of divisors/line bundles.
Algebraic geometry
2631
2657
10.4171/OWR/2017/43
http://www.ems-ph.org/doi/10.4171/OWR/2017/43
7
4
2018
Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications
Takayuki
Hibi
Osaka University, Japan
Akihiro
Higashitani
Kyoto Sangyo University, Japan
Katharina
Jochemko
KTH - Royal Institute of Technology, Stockholm, Sweden
Benjamin
Nill
Otto-von-Guericke-Universität, Magdeburg, Germany
Lattice polytopes arise naturally in many different branches of pure and applied mathematics such as number theory, commutative algebra, combinatorics, toric geometry, optimization, and mirror symmetry. The miniworkshop on “Lattice polytopes: methods, advances, applications” focused on two current hot topics: the classification of lattice polytopes with few lattice points and unimodality questions for Ehrhart polynomials. The workshop consisted of morning talks on recent breakthroughs and new methods, and afternoon discussion groups where participants from a variety of different backgrounds explored further applications, identified open questions and future research directions, discussed specific examples and conjectures, and collaboratively tackled open research problems.
Convex and discrete geometry
2659
2701
10.4171/OWR/2017/44
http://www.ems-ph.org/doi/10.4171/OWR/2017/44
7
4
2018
Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces
Christopher
Hacon
University of Utah, Salt Lake City, USA
Daniel
Huybrechts
Universität Bonn, Germany
Bernd
Siebert
Universität Hamburg, Germany
Chenyang
Xu
Beijing University, China
The workshop covered a number of active areas of research in algebraic geometry with a focus on derived categories, moduli spaces (of varieties and sheaves) and birational geometry (often in positive characteristic) and their interactions. Special emphasis was put on hyperkähler manifolds and singularity theory.
Algebraic geometry
2703
2767
10.4171/OWR/2017/45
http://www.ems-ph.org/doi/10.4171/OWR/2017/45
7
4
2018
4
Spectral Structures and Topological Methods in Mathematical Quasicrystals
Michael
Baake
Universität Bielefeld, Germany
David
Damanik
Rice University, Houston, USA
Johannes
Kellendonk
Université Lyon 1, Villeurbanne, France
Daniel
Lenz
Friedrich-Schiller-Universität Jena, Germany
The mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 by Shechtman. Many mathematical disciplines have contributed to the development of this field. In this meeting, the goal was to bring leading researchers from several of them together to exchange the state of affairs, with special focus on spectral aspects, dynamics and topology.
Convex and discrete geometry
Number theory
Measure and integration
Dynamical systems and ergodic theory
2781
2845
10.4171/OWR/2017/46
http://www.ems-ph.org/doi/10.4171/OWR/2017/46
12
18
2018
Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry
Emmanuel
Breuillard
Universität Münster, Germany
Michael
Hochman
The Hebrew University of Jerusalem, Israel
Pablo
Shmerkin
Universidad Torcuato Di Tella, Buenos Aires, Argentina
The aim of the workshop was to survey recent developments in fractal geometry, specifically those related to projections and slices of planar self-similar sets, and dimension and absolute continuity of self-similar measures on the line, in particular Bernoulli convolutions. The methods combine ergodic theory, additive combinatorics, and algebraic number theory. Talks were high-level descriptions of the results, aimed at a mixed audience with minimal background in real analysis, ergodic theory and dimension theory.
Measure and integration
General
2847
2905
10.4171/OWR/2017/47
http://www.ems-ph.org/doi/10.4171/OWR/2017/47
12
18
2018
Mini-Workshop: PDE Models of Motility and Invasion in Active Biosystems
Leonid
Berlyand
Pennsylvania State University, University Park, USA
Jan
Fuhrmann
Universität Heidelberg, Germany
Anna
Marciniak-Czochra
Universität Heidelberg, Germany
Christina
Surulescu
Technische Universität Kaiserslautern, Germany
Cell migration is crucial for the development and functioning of multicellular organisms; it plays an essential role in, e.g., morphogenesis, immune system dynamics, wound healing, angiogenesis, bacterial motion and biofilm formation, tumor growth and metastasis. Cell motility is a highly complex phenomenon involving a plethora of biophysical and biochemical events occuring on several time and space scales. The associated dynamics range from the subcellular level over individual cell behavior and up to the macroscopic level of cell populations; all these scales are tightly interrelated. For decades, partial differential equations have been used to model the motility of single cells as well as the collective motion of cell assemblies like tumors. Mathematical models for both individual motile cells and invading tumors have major features in common. The active nature of cells leads to very similar nonlinear systems of coupled equations, the solutions of which often determine the position and shape of the objects of interest. Recently, several types of models attracted particular attention in the description of these systems: free boundary problems, phase field models, reaction-diffusion-taxis and kinetic transport equations. Both tumor growth/invasion and cell motility can be described by parabolic, hyperbolic, or elliptic equations; in case of free boundary problems, the boundary conditions are very similar. Thereby, the involved free boundaries can describe cell membranes, tumor margins, or interfaces between different tissues. In this mini-workshop applied mathematicians and biophysicists using these model classes to describe different but related biological systems came together, presented their recent work and identified commonalities and differences in their approaches. Moreover, they discussed possible model extensions and their application to different, but related problems, along with the innovative utilization of certain mathematical tools to the analysis of the resulting systems.
Biology and other natural sciences
Partial differential equations
2907
2942
10.4171/OWR/2017/48
http://www.ems-ph.org/doi/10.4171/OWR/2017/48
12
18
2018
Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures
David
Damanik
Rice University, Houston, USA
Fritz
Gesztesy
Baylor University, Waco, USA
Peter
Yuditskii
Johannes Kepler University Linz, Austria
Reflectionless operators in one dimension are particularly amenable to inverse scattering and are intimately related to integrable systems like KdV and Toda. Recent work has indicated a strong (but not equivalent) relationship between reflectionless operators and almost periodic potentials with absolutely continuous spectrum. This makes the realm of reflectionless operators a natural place to begin addressing Deift’s conjecture on integrable flows with almost periodic initial conditions and Simon’s conjecture on gems of spectral theory establishing correspondences between certain coefficient and spectral properties.
Partial differential equations
Operator theory
2943
2985
10.4171/OWR/2017/49
http://www.ems-ph.org/doi/10.4171/OWR/2017/49
12
18
2018
Mini-Workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry
Stefan
Friedl
Universität Regensburg, Germany
Laurentiu
Maxim
University of Wisconsin-Madison, USA
Alexander
Suciu
Northeastern University, Boston, USA
Recent developments exhibit a strong connection between low-dimensional topology and complex algebraic geometry. A common theme is provided by the Alexander polynomial and its many avatars. The mini-Workshop brought together at Oberwolfach groups of researchers working in mostly separate areas, but sharing common interests in a vibrant, emerging field at the crossroads of Topology, Group Theory, and Geometry.
Group theory and generalizations
Algebraic geometry
Algebraic topology
Manifolds and cell complexes
2987
3033
10.4171/OWR/2017/50
http://www.ems-ph.org/doi/10.4171/OWR/2017/50
12
18
2018
Mini-Workshop: Interplay between Number Theory and Analysis for Dirichlet Series
Frédéric
Bayart
Université Blaise Pascal, Aubière, France
Kaisa
Matomäki
University of Turku, Finland
Eero
Saksmann
University of Helsinki, Finland
Kristian
Seip
Norwegian University of Science and Technology, Trondheim, Norway
In recent years a number of challenging research problems have crystallized in the analytic theory of Dirichlet series and its interaction with function theory in polydiscs. Their solutions appear to require unconventional combinations of expertise from harmonic, functional, and complex analysis, and especially from analytic number theory. This MFO workshop provided an ideal arena for the exchange of ideas needed to nurture further progress and to solve important problems.
Number theory
Functions of a complex variable
3035
3069
10.4171/OWR/2017/51
http://www.ems-ph.org/doi/10.4171/OWR/2017/51
12
18
2018
Copositivity and Complete Positivity
Abraham
Berman
Technion - Israel Institute of Technology, Haifa, Israel
Immanuel
Bomze
Universität Wien, Austria
Mirjam
Dür
Universität Augsburg, Germany
Naomi
Shaked-Monderer
The Max Stern Yezreel Valley College, Yezreel Valley, Israel
A real matrix $A$ is called copositive if $x^TAx \ge 0$ holds for all $x \in \mathbb R^n_+$. A matrix $A$ is called completely positive if it can be factorized as $A = BB^T$ , where $B$ is an entrywise nonnegative matrix. The concept of copositivity can be traced back to Theodore Motzkin in 1952, and that of complete positivity to Marshal Hall Jr. in 1958. The two classes are related, and both have received considerable attention in the linear algebra community and in the last two decades also in the mathematical optimization community. These matrix classes have important applications in various fields, in which they arise naturally, including mathematical modeling, optimization, dynamical systems and statistics. More applications constantly arise. The workshop brought together people working in various disciplines related to copositivity and complete positivity, in order to discuss these concepts from different viewpoints and to join forces to better understand these difficult but fascinating classes of matrices.
Linear and multilinear algebra; matrix theory
Dynamical systems and ergodic theory
Operations research, mathematical programming
3071
3120
10.4171/OWR/2017/52
http://www.ems-ph.org/doi/10.4171/OWR/2017/52
12
18
2018
Mathematical Logic: Proof Theory, Constructive Mathematics
Samuel
Buss
University of California at San Diego, La Jolla, USA
Rosalie
Iemhoff
Utrecht University, Netherlands
Ulrich
Kohlenbach
Technische Hochschule Darmstadt, Germany
Michael
Rathjen
University of Leeds, UK
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of core mathematics and theoretical computer science as well as homotopy type theory and logical aspects of computational complexity.
Mathematical logic and foundations
3121
3183
10.4171/OWR/2017/53
http://www.ems-ph.org/doi/10.4171/OWR/2017/53
12
18
2018
Variational Methods for Evolution
Alexander
Mielke
Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Mark
Peletier
Eindhoven University of Technology, Netherlands
Dejan
Slepčev
Carnegie Mellon University, Pittsburgh, USA
Many evolutionary systems, as for example gradient flows or Hamiltonian systems, can be formulated in terms of variational principles or can be approximated using time-incremental minimization. Hence they can be studied using the mathematical techniques of the field of calculus of variations. This viewpoint has led to many discoveries and rapid expansion of the field over the last two decades. Relevant applications arise in mechanics of fluids and solids, in reaction-diffusion systems, in biology, in many-particle models, as well as in emerging uses in data science. This workshop brought together a broad spectrum of researchers from calculus of variations, partial differential equations, metric geometry, and stochastics, as well as applied and computational scientists to discuss and exchange ideas. It focused on variational tools such as minimizing movement schemes, Gamma convergence, optimal transport, gradient flows, and large-deviation principles for time-continuous Markov processes.
Calculus of variations and optimal control; optimization
Partial differential equations
Global analysis, analysis on manifolds
Mechanics of particles and systems
3185
3261
10.4171/OWR/2017/54
http://www.ems-ph.org/doi/10.4171/OWR/2017/54
12
18
2018
Reflection Positivity
Arthur
Jaffe
Harvard University, Cambridge, USA
Karl-Hermann
Neeb
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Gestur
Olafsson
Louisiana State University, Baton Rouge, USA
Benjamin
Schlein
Universität Zürich, Switzerland
The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representation Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, Analysis and Statistical Mechanics. Accordingly, the program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity.
Nonassociative rings and algebras
Topological groups, Lie groups
Quantum theory
3263
3343
10.4171/OWR/2017/55
http://www.ems-ph.org/doi/10.4171/OWR/2017/55
12
18
2018
Classical and Quantum Mechanical Models of Many-Particle Systems
Anton
Arnold
Technische Universität Wien, Austria
Eric
Carlen
Rutgers University, Piscataway, USA
Laurent
Desvillettes
Université Paris Diderot, Paris, France
This workshop was dedicated to the presentation of recent results in the field of the mathematical study of kinetic theory and its naturalextensions (statistical physics and fluid mechanics). The main models are the Vlasov(-Poisson) equation and the Boltzmann equation, which are obtainedas limits of many-body equations (Newton’s equations in the classical case and Schrödinger’s equation in the quantum case) thanks to the mean-field and Boltzmann-Grad scalings. Numerical aspects and applications to mechanics, physics, engineering and biology were also discussed.
Fluid mechanics
Partial differential equations
Integral equations
Statistical mechanics, structure of matter
3345
3425
10.4171/OWR/2017/56
http://www.ems-ph.org/doi/10.4171/OWR/2017/56
12
18
2018
Network Models: Structure and Function
Louigi
Addario-Berry
McGill University, Montreal, Canada
Shankar
Bhamidi
University of North Carolina, Chapel Hill, USA
Remco
van der Hofstad
TU Eindhoven, Netherlands
Frank
den Hollander
Universiteit Leiden, Netherlands
The focus of the meeting was on the mathematical analysis of complex networks, both on how networks emerge through microscopic interaction rules as well as on dynamic processes and optimization problems on networks, including random walks, interacting particle systems and search algorithms. Topics that were addressed included: percolation on graphs and critical regimes for the emergence of a giant component; graph limits and graphons; epidemics, propagation and competition; trees and forests; dynamic random graphs; local versus global algorithms; statistical learning on networks.
Probability theory and stochastic processes
Statistical mechanics, structure of matter
3427
3470
10.4171/OWR/2017/57
http://www.ems-ph.org/doi/10.4171/OWR/2017/57
12
18
2018
Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950
Samuel
Gessner
Universidade de Lisboa, Portugal
Ulf
Hashagen
Deutsches Museum, München, Germany
Jeanne
Pfeiffer
Centre Alexandre-Koiré, Paris, France
Dominique
Tournès
Sainte-Clotilde Reunion, France
Since 1950, mathematicians have become increasingly familiar with the digital computer in their professional practice. Previously, however, many other instruments, now mostly forgotten, were commonly used to compute numerical solutions, generate geometrical objects, investigate mathematical problems, derive new results, and apply mathematics in a variety of scientific contexts. The problem of characterizing the mathematical objects that can be constructed with a given set of instruments frequently prompted deep theoretical investigations, from the Euclidean geometry of constructions with straightedge and compass, to Shannon’s theorem which, in 1941, stated that the functions constructible with a differential analyzer are exactly the solutions of algebraic differential equations. Beyond these mathematical considerations, instruments should also be viewed as social objects of a given time period and cultural tradition that can amalgamate the perspectives of the inventor, the maker, the user, and the collector; in this sense, mathematical instruments are an important part of the mathematical cultural heritage and are thus widely used in many science museums to demonstrate the cultural value of mathematics to the public. This workshop brought together mathematicians, historians, philosophers, collection curators, and scholars of education to address the various approaches to the history of mathematical instruments and compare the definition and role of these instruments over time, with the following fundamental questions in mind – What is mathematical in a mathematical instrument? What kind of mathematics is involved? What does it mean to embody mathematics in a material artefact, and how do non-mathematicians engage with this kind of embodied mathematics?
History and biography
Measure and integration
Dynamical systems and ergodic theory
Fourier analysis
3471
3560
10.4171/OWR/2017/58
http://www.ems-ph.org/doi/10.4171/OWR/2017/58
12
18
2018