http://publications.mfo.de/handle/mfo/2809 Oberwolfach Reports Volume 5 (2008) Wed, 08 Apr 2026 11:39:02 GMT 2026-04-08T11:39:02Z http://publications.mfo.de/handle/mfo/3101 Dynamics of Patterns This workshop focused on the dynamics of nonlinear waves and spatio-temporal patterns, which arise in functional and partial differential equations. Among the outstanding problems in this area are the dynamical selection of patterns, gaining a theoretical understanding of transient dynamics, the nonlinear stability of patterns in unbounded domains, and the development of efficient numerical techniques to capture specific dynamical effects. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3101 2008-01-01T00:00:00Z This workshop focused on the dynamics of nonlinear waves and spatio-temporal patterns, which arise in functional and partial differential equations. Among the outstanding problems in this area are the dynamical selection of patterns, gaining a theoretical understanding of transient dynamics, the nonlinear stability of patterns in unbounded domains, and the development of efficient numerical techniques to capture specific dynamical effects. http://publications.mfo.de/handle/mfo/3100 Hyperbolic Conservation Laws The subject of this workshop concerned the analysis and numerical investigation of hyperbolic systems. In particular the interactions between theoretical and numerical contributions were in the focus of this meeting. Many theoretical results have been initiated by numerical methods and experiments and rigorous numerical results are based on fundamental theorems. In particular during this workshop recent results about hyperbolic Monge Ampere systems, elastodynamics, dissipation in systems of conservation laws, Boussinesq, Boltzmann and (error control for the) Navier Stokes equations, mixture of fluids, anelastic and weakly compressible models for atmospherical flows, hydrodynamic limits, wetting and drying for shallow water problems, potential flows, divergence free transport equations, initial boundary Riemann problems, various Discontinuous Galerkin and operator splitting methods, IMEX schemes, entropy stable methods, well balancing schemes, convergence rate for the Glimm scheme and reduced basis methods for conservation laws were discussed. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3100 2008-01-01T00:00:00Z The subject of this workshop concerned the analysis and numerical investigation of hyperbolic systems. In particular the interactions between theoretical and numerical contributions were in the focus of this meeting. Many theoretical results have been initiated by numerical methods and experiments and rigorous numerical results are based on fundamental theorems. In particular during this workshop recent results about hyperbolic Monge Ampere systems, elastodynamics, dissipation in systems of conservation laws, Boussinesq, Boltzmann and (error control for the) Navier Stokes equations, mixture of fluids, anelastic and weakly compressible models for atmospherical flows, hydrodynamic limits, wetting and drying for shallow water problems, potential flows, divergence free transport equations, initial boundary Riemann problems, various Discontinuous Galerkin and operator splitting methods, IMEX schemes, entropy stable methods, well balancing schemes, convergence rate for the Glimm scheme and reduced basis methods for conservation laws were discussed. http://publications.mfo.de/handle/mfo/3099 Interplay of Analysis and Probability in Physics It is widely recognised that stochastic effects need to be included in the modelling of many physical systems, while reciprocally the sciences provide a challenging potential area of application of stochastic processes. This creates an increasing need to combine analytic and stochastic techniques. The aim of this workshop was to address this need and contribute to the efforts to surmount the language barrier between analysts and probabilists by stimulating and encouraging exchange and joint research between the two communities. The focus of the workshop was on recent and currently emerging progress in the investigation of complex physical systems, using a combination of analytical and stochastic methods. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3099 2008-01-01T00:00:00Z It is widely recognised that stochastic effects need to be included in the modelling of many physical systems, while reciprocally the sciences provide a challenging potential area of application of stochastic processes. This creates an increasing need to combine analytic and stochastic techniques. The aim of this workshop was to address this need and contribute to the efforts to surmount the language barrier between analysts and probabilists by stimulating and encouraging exchange and joint research between the two communities. The focus of the workshop was on recent and currently emerging progress in the investigation of complex physical systems, using a combination of analytical and stochastic methods. http://publications.mfo.de/handle/mfo/3098 Mini-Workshop: Group Actions on Curves: Reduction and Lifting Group actions on algebraic curves over local, global and finite fields play an important role in modern algebraic and arithmetic geometry. From the arithmetic perspective, the most difficult and interesting case occurs when a group with a nontrivial p-subgroup acts on a curve over a p-adic field or a finite field of characteristic p. The goal of this workshop was to bring together a group of active and mostly young researchers working in this area, to discuss the latest developments and to stimulate further research. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3098 2008-01-01T00:00:00Z Group actions on algebraic curves over local, global and finite fields play an important role in modern algebraic and arithmetic geometry. From the arithmetic perspective, the most difficult and interesting case occurs when a group with a nontrivial p-subgroup acts on a curve over a p-adic field or a finite field of characteristic p. The goal of this workshop was to bring together a group of active and mostly young researchers working in this area, to discuss the latest developments and to stimulate further research. http://publications.mfo.de/handle/mfo/3097 Mini-Workshop: Symmetric Varieties and Involutions of Algebraic Groups This conference brought together experts from the areas of algebraic groups, Kac–Moody groups, Tits buildings, and symmetric varieties. The main theme presented and discussed during the workshop was the geometry of involutions of algebraic and Kac–Moody groups. In particular, symmetric varieties and the induced action of involutions on buildings. More specific topics that were covered include the Tits centre conjecture, compactifications of locally symmetric spaces and of buildings, Kac-Moody groups over ultrametric fields, and the structure of locally compact groups. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3097 2008-01-01T00:00:00Z This conference brought together experts from the areas of algebraic groups, Kac–Moody groups, Tits buildings, and symmetric varieties. The main theme presented and discussed during the workshop was the geometry of involutions of algebraic and Kac–Moody groups. In particular, symmetric varieties and the induced action of involutions on buildings. More specific topics that were covered include the Tits centre conjecture, compactifications of locally symmetric spaces and of buildings, Kac-Moody groups over ultrametric fields, and the structure of locally compact groups. http://publications.mfo.de/handle/mfo/3096 Mini-Workshop: Numerics for Kinetic Equations Kinetic equations are crucial to an adequate description of many processes of scientific and industrial importance. In recent years there have been intensified research activities in the field of numerical algorithms for kinetic equations related to new areas of application. Typical gas flows in micro- and nanomachines are in the rarefied regime. Thus the classical Boltzmann equation is often used to model such flows. Furthermore, the inelastic Boltzmann equation describes low density flows of granular material. Finally, flows of electrically charged particles are described by semiconductor transport equations. There are significant numerical challenges related to these applications. In low Mach number rarefied flows there is a very small signal-to-noise ratio. Therefore, variance reduction techniques for the commonly used Direct Simulation Monte Carlo method are needed. On the other hand, deterministic algorithms become more competitive. The workshop brought together leading experts from various fields to discuss recent approaches addressing the numerical challenges related to the novel applications mentioned above. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3096 2008-01-01T00:00:00Z Kinetic equations are crucial to an adequate description of many processes of scientific and industrial importance. In recent years there have been intensified research activities in the field of numerical algorithms for kinetic equations related to new areas of application. Typical gas flows in micro- and nanomachines are in the rarefied regime. Thus the classical Boltzmann equation is often used to model such flows. Furthermore, the inelastic Boltzmann equation describes low density flows of granular material. Finally, flows of electrically charged particles are described by semiconductor transport equations. There are significant numerical challenges related to these applications. In low Mach number rarefied flows there is a very small signal-to-noise ratio. Therefore, variance reduction techniques for the commonly used Direct Simulation Monte Carlo method are needed. On the other hand, deterministic algorithms become more competitive. The workshop brought together leading experts from various fields to discuss recent approaches addressing the numerical challenges related to the novel applications mentioned above. http://publications.mfo.de/handle/mfo/3095 Combinatorial Optimization The field of Combinatorial Optimization brings together techniques from a variety of mathematical disciplines to study optimization problems over discrete structures. The field is very active and continues to make strong advances in theory, computation, and applications. This Oberwolfach Workshop in Combinatorial Optimization follows a long tradition of such meetings that have helped to enrich the field and to establish new or deepen existing research collaborations. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3095 2008-01-01T00:00:00Z The field of Combinatorial Optimization brings together techniques from a variety of mathematical disciplines to study optimization problems over discrete structures. The field is very active and continues to make strong advances in theory, computation, and applications. This Oberwolfach Workshop in Combinatorial Optimization follows a long tradition of such meetings that have helped to enrich the field and to establish new or deepen existing research collaborations. http://publications.mfo.de/handle/mfo/3094 Infinite Dimensional Random Dynamical Systems and Their Applications The theory of infinite dimensional random dynamical systems shares many of the concepts and results for finite dimensional random dynamical systems, but with considerably more technical complications. Many examples are generated by stochastic partial differential equations (SPDE) which are used to model climate dynamics, turbulence, porous media, random surface motions and many other systems of physical interest, etc. The workshop covered broad spectrum of issues ranging from the theoretical to applications and numerics. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3094 2008-01-01T00:00:00Z The theory of infinite dimensional random dynamical systems shares many of the concepts and results for finite dimensional random dynamical systems, but with considerably more technical complications. Many examples are generated by stochastic partial differential equations (SPDE) which are used to model climate dynamics, turbulence, porous media, random surface motions and many other systems of physical interest, etc. The workshop covered broad spectrum of issues ranging from the theoretical to applications and numerics. http://publications.mfo.de/handle/mfo/3093 Von Neumann Algebras and Ergodic Theory of Group Actions The theory of von Neumann algebras has seen some dramatic advances in the last few years. Von Neumann algebras are objects which can capture and analyze symmetries of mathematical or physical situations whenever these symmetries can be cast in terms of generalized morphisms of the algebra (Hilbert bimodules, or correspondences). Analyzing these symmetries led to an amazing wealth of new mathematics and the solution of several long-standing problems in the theory. Popa’s new deformation and rigidity theory has culminated in the discovery of new cocycle superrigidity results à la Zimmer, thus establishing a new link to orbit equivalence ergodic theory. The workshop brought together world-class researchers in von Neumann algebras and ergodic theory to focus on these recent developments. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3093 2008-01-01T00:00:00Z The theory of von Neumann algebras has seen some dramatic advances in the last few years. Von Neumann algebras are objects which can capture and analyze symmetries of mathematical or physical situations whenever these symmetries can be cast in terms of generalized morphisms of the algebra (Hilbert bimodules, or correspondences). Analyzing these symmetries led to an amazing wealth of new mathematics and the solution of several long-standing problems in the theory. Popa’s new deformation and rigidity theory has culminated in the discovery of new cocycle superrigidity results à la Zimmer, thus establishing a new link to orbit equivalence ergodic theory. The workshop brought together world-class researchers in von Neumann algebras and ergodic theory to focus on these recent developments. http://publications.mfo.de/handle/mfo/3092 New Perspectives in Stochastic Geometry The workshop was devoted to the discussion and exploration of recent developments in stochastic geometry. Two main themes were new results and methodology in classical stochastic geometry and allocation and matching procedures for point processes and random measures. Tue, 01 Jan 2008 00:00:00 GMT http://publications.mfo.de/handle/mfo/3092 2008-01-01T00:00:00Z The workshop was devoted to the discussion and exploration of recent developments in stochastic geometry. Two main themes were new results and methodology in classical stochastic geometry and allocation and matching procedures for point processes and random measures.