http://publications.mfo.de/handle/mfo/2817 Oberwolfach Reports Volume 13 (2016) Thu, 09 Apr 2026 20:37:14 GMT 2026-04-09T20:37:14Z http://publications.mfo.de/handle/mfo/3564 Mini-Workshop: New Interactions between Homotopical Algebra and Quantum Field Theory Recent developments in quantum field theory strongly call for techniques from homotopical algebra to develop the mathematical foundations of quantum gauge theories. This mini-workshop brought together experts working at the interface between topological field theory, quantum field theory and homotopical algebra with the goal of triggering major advances towards understanding quantum gauge theory. This was achieved via a fruitful exchange of ideas and technologies across different research communities and encouraging a comparison between recent approaches to homotopical quantum field theory. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3564 2016-01-01T00:00:00Z Recent developments in quantum field theory strongly call for techniques from homotopical algebra to develop the mathematical foundations of quantum gauge theories. This mini-workshop brought together experts working at the interface between topological field theory, quantum field theory and homotopical algebra with the goal of triggering major advances towards understanding quantum gauge theory. This was achieved via a fruitful exchange of ideas and technologies across different research communities and encouraging a comparison between recent approaches to homotopical quantum field theory. http://publications.mfo.de/handle/mfo/3563 Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations New striking analogies between H. Hahn’s fields of generalised series with real coefficients, G. H. Hardy’s field of germs of real valued functions, and J. H. Conway’s field No of surreal numbers, have been lately discovered and exploited. The aim of the workshop was to bring quickly together experts and young researchers, to articulate and investigate current key questions and conjectures regarding these fields, and to explore emerging applications of this recent discovery. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3563 2016-01-01T00:00:00Z New striking analogies between H. Hahn’s fields of generalised series with real coefficients, G. H. Hardy’s field of germs of real valued functions, and J. H. Conway’s field No of surreal numbers, have been lately discovered and exploited. The aim of the workshop was to bring quickly together experts and young researchers, to articulate and investigate current key questions and conjectures regarding these fields, and to explore emerging applications of this recent discovery. http://publications.mfo.de/handle/mfo/3562 Mini-Workshop: Max Dehn: his Life, Work, and Influence This mini-workshop is part of a long-term project that aims to produce a book documenting Max Dehn’s singular life and career. The meeting brought together scholars with various kinds of expertise, several of whom gave talks on topics for this book. During the week a number of new ideas were discussed and a plan developed for organizing the work. A proposal for the volume is now in preparation and will be submitted to one or more publishers during the summer of 2017. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3562 2016-01-01T00:00:00Z This mini-workshop is part of a long-term project that aims to produce a book documenting Max Dehn’s singular life and career. The meeting brought together scholars with various kinds of expertise, several of whom gave talks on topics for this book. During the week a number of new ideas were discussed and a plan developed for organizing the work. A proposal for the volume is now in preparation and will be submitted to one or more publishers during the summer of 2017. http://publications.mfo.de/handle/mfo/3561 Asymptotic Phenomena in Local Algebra and Singularity Theory The goal of this workshop was to highlight, and further, the interactions between local algebra and singularity theory. The timing was serendipitous for both subjects have witnessed tremendous progress recently, much of which was reported at the workshop. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3561 2016-01-01T00:00:00Z The goal of this workshop was to highlight, and further, the interactions between local algebra and singularity theory. The timing was serendipitous for both subjects have witnessed tremendous progress recently, much of which was reported at the workshop. http://publications.mfo.de/handle/mfo/3560 Surface Bundles This workshop brought together specialists in algebraic topology, low dimensional topology, geometric group theory, algebraic geometry and neighboring fields. It provided a good overview of the current developments, and highlighted significant progress in the field. Furthermore it showed an increasing amount of interaction between specialists in different fields who are interested in the different facets of the rich theory of surface bundles. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3560 2016-01-01T00:00:00Z This workshop brought together specialists in algebraic topology, low dimensional topology, geometric group theory, algebraic geometry and neighboring fields. It provided a good overview of the current developments, and highlighted significant progress in the field. Furthermore it showed an increasing amount of interaction between specialists in different fields who are interested in the different facets of the rich theory of surface bundles. http://publications.mfo.de/handle/mfo/3559 Heat Kernels, Stochastic Processes and Functional Inequalities The general topic of the 2016 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments including smooth manifolds, fractals and graphs, metric spaces and in random environments. The workshop brought together leading researchers from analysis, geometry and probability, and provided an excellent opportunity for interactions between scientists from these areas at different stages of their career. The unifying themes were heat kernel analysis, mass transportation problems and functional inequalities while the program straddled across a great variety of subjects and across the divide that exists between discrete and continuous mathematics. Other unifying concepts such as the notions of metric measure space, Otto Calculus and Lott-Sturm-Villani synthetic Ricci curvature bounds played an important part in the discussions. Novel directions including the study of Liouville quantum gravity were included. The workshop provided participants with an opportunity to discuss how these ideas and techniques can be used to approach problems regarding optimal transport, Riemannian and sub-Riemannian geometry, and analysis and stochastic processes in random media. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3559 2016-01-01T00:00:00Z The general topic of the 2016 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments including smooth manifolds, fractals and graphs, metric spaces and in random environments. The workshop brought together leading researchers from analysis, geometry and probability, and provided an excellent opportunity for interactions between scientists from these areas at different stages of their career. The unifying themes were heat kernel analysis, mass transportation problems and functional inequalities while the program straddled across a great variety of subjects and across the divide that exists between discrete and continuous mathematics. Other unifying concepts such as the notions of metric measure space, Otto Calculus and Lott-Sturm-Villani synthetic Ricci curvature bounds played an important part in the discussions. Novel directions including the study of Liouville quantum gravity were included. The workshop provided participants with an opportunity to discuss how these ideas and techniques can be used to approach problems regarding optimal transport, Riemannian and sub-Riemannian geometry, and analysis and stochastic processes in random media. http://publications.mfo.de/handle/mfo/3558 Large Scale Stochastic Dynamics The goal of this workshop was to explore the recent advances in the mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 53 participants, including 4 postdocs and graduate students, working in diverse intertwining areas of probability and statistical mechanics. During the meeting, 24 talks of 50 minutes were scheduled and an evening session was organised with 10 more short talks of 10 minutes, mostly by younger participants. These talks addressed the following topics: hydrodynamic limits and hydrodynamic fluctuations with a special emphasis on KPZ fluctuations, scaling limits in percolation and random walks, approach to equilibrium in reversible systems with a strong focus on kinetically constrained dynamics. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3558 2016-01-01T00:00:00Z The goal of this workshop was to explore the recent advances in the mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 53 participants, including 4 postdocs and graduate students, working in diverse intertwining areas of probability and statistical mechanics. During the meeting, 24 talks of 50 minutes were scheduled and an evening session was organised with 10 more short talks of 10 minutes, mostly by younger participants. These talks addressed the following topics: hydrodynamic limits and hydrodynamic fluctuations with a special emphasis on KPZ fluctuations, scaling limits in percolation and random walks, approach to equilibrium in reversible systems with a strong focus on kinetically constrained dynamics. http://publications.mfo.de/handle/mfo/3557 Analytic Number Theory Analytic number theory has flourished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3557 2016-01-01T00:00:00Z Analytic number theory has flourished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject http://publications.mfo.de/handle/mfo/3556 Mini-Workshop: Mathematics of Magnetoelastic Materials The unifying theme of the workshop was the mathematical modeling, analysis, and numerical simulation of materials which involve magnetic and elastic interactions. During the workshop we identified several open problems from the calculus of variations, partial differential equations and modeling which appear to be essential in the understanding of the behavior of magnetoelastic materials. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3556 2016-01-01T00:00:00Z The unifying theme of the workshop was the mathematical modeling, analysis, and numerical simulation of materials which involve magnetic and elastic interactions. During the workshop we identified several open problems from the calculus of variations, partial differential equations and modeling which appear to be essential in the understanding of the behavior of magnetoelastic materials. http://publications.mfo.de/handle/mfo/3555 Mini-Workshop: Fast Solvers for Highly Oscillatory Problems The efficient numerical solution of highly oscillatory problems is one of the grand challenges of Applied Mathematics with diverse applications across the natural sciences and engineering. This workshop brings together experts in domain based methods and integral equation methods to share novel ideas and to discuss challenges on the way to developing efficient solvers at high frequencies. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/3555 2016-01-01T00:00:00Z The efficient numerical solution of highly oscillatory problems is one of the grand challenges of Applied Mathematics with diverse applications across the natural sciences and engineering. This workshop brings together experts in domain based methods and integral equation methods to share novel ideas and to discuss challenges on the way to developing efficient solvers at high frequencies.