http://publications.mfo.de/handle/mfo/2815 Oberwolfach Reports Volume 11 (2014) Thu, 09 Apr 2026 20:46:55 GMT 2026-04-09T20:46:55Z http://publications.mfo.de/handle/mfo/3447 Variational Methods for Evolution 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3447 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3446 Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3446 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3445 Mini-Workshop: Dynamical versus Diffraction Spectra in the Theory of Quasicrystals 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3445 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3444 Mini-Workshop: Eigenvalue Problems in Surface Superconductivity 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3444 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3443 Mini-Workshop: Reflection Positivity in Representation Theory, Stochastics and Physics 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3443 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3442 Mathematical Logic: Proof theory, Constructive Mathematics 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 Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3442 2014-01-01T00:00:00Z 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 http://publications.mfo.de/handle/mfo/3441 Combinatorial Optimization 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3441 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3440 Probability, Trees and Algorithms 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3440 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3439 Valuation Theory and Its Applications 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3439 2014-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3438 Dirichlet Form Theory and its Applications 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. Wed, 01 Jan 2014 00:00:00 GMT http://publications.mfo.de/handle/mfo/3438 2014-01-01T00:00:00Z 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.