http://publications.mfo.de/handle/mfo/2811 Oberwolfach Reports Volume 7 (2010) Wed, 08 Apr 2026 11:39:02 GMT 2026-04-08T11:39:02Z http://publications.mfo.de/handle/mfo/3215 Mini-Workshop: Wellposedness and Controllability of Evolution Equations This mini-workshop brought together mathematicians engaged in partial differential equations, operator theory, functional analysis and harmonic analysis in order to address a number of current problems in the wellposedness and controllability of infinite-dimensional systems. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3215 2010-01-01T00:00:00Z This mini-workshop brought together mathematicians engaged in partial differential equations, operator theory, functional analysis and harmonic analysis in order to address a number of current problems in the wellposedness and controllability of infinite-dimensional systems. http://publications.mfo.de/handle/mfo/3214 Mini-Workshop: 1-Motives One-motives were introduced by Deligne in 1974 [10], as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives [31], it can be understood as motives of level ≤ 1. While Voevosdky’s more general theory of mixed motives contains deep conjectures which at present seem to be out of reach, one-motives are much more accessible. In this mini-workshop, recent progresses were discussed: various aspects of one-motives and their realizations were explained, some applications in arithmetic algebraic geometry were given. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3214 2010-01-01T00:00:00Z One-motives were introduced by Deligne in 1974 [10], as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives [31], it can be understood as motives of level ≤ 1. While Voevosdky’s more general theory of mixed motives contains deep conjectures which at present seem to be out of reach, one-motives are much more accessible. In this mini-workshop, recent progresses were discussed: various aspects of one-motives and their realizations were explained, some applications in arithmetic algebraic geometry were given. http://publications.mfo.de/handle/mfo/3213 Mini-Workshop: Algebraic and Analytic Techniques for Polynomial Vector Fields Polynomial vector fields are in the focus of research in various areas of mathematics and its applications. As a consequence, researchers from rather different disciplines work with polynomial vector fields. The main goal of this mini workshop was to create new and consolidate existing interdisciplinary exchange on the subject. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3213 2010-01-01T00:00:00Z Polynomial vector fields are in the focus of research in various areas of mathematics and its applications. As a consequence, researchers from rather different disciplines work with polynomial vector fields. The main goal of this mini workshop was to create new and consolidate existing interdisciplinary exchange on the subject. http://publications.mfo.de/handle/mfo/3212 Classical and Quantum Mechanical Models of Many-Particle Systems The topic of this meeting were non-linear partial differential and integro-differential equations (in particular kinetic equations and their macroscopic/fluid-dynamical limits) modeling the dynamics of many-particle systems with applications in physics, engineering, and mathematical biology. Typical questions of interest were the derivation of macro-models from micro-models, the mathematical analysis (well-posedness, stability, asymptotic behavior of solutions), and “to a lesser extent” numerical aspects of such equations. A highlight of this meeting was a mini-course on the recent mathematical theory of Landau damping. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3212 2010-01-01T00:00:00Z The topic of this meeting were non-linear partial differential and integro-differential equations (in particular kinetic equations and their macroscopic/fluid-dynamical limits) modeling the dynamics of many-particle systems with applications in physics, engineering, and mathematical biology. Typical questions of interest were the derivation of macro-models from micro-models, the mathematical analysis (well-posedness, stability, asymptotic behavior of solutions), and “to a lesser extent” numerical aspects of such equations. A highlight of this meeting was a mini-course on the recent mathematical theory of Landau damping. http://publications.mfo.de/handle/mfo/3211 Teichmüller Theory This is a report on the workshop on Teichmüller theory held in Oberwolfach, from November 28 to December 4, 2010. The workshop brought together people working in various aspects of the field, with a focus on recent developments. The topics discussed included higher Teichmüller theory, moduli spaces of flat connections, cluster algebras, quantization of Teichmüller spaces, the dynamical aspects of the Teichmüller and Weil-Petersson geodesic flows, the metric and the boundary theory of Teichmüller space including the new developments on Thurston’s asymmetric metric, string topology, geometric analysis on moduli spaces, and relations with three-manifold topology and with minimal surface theory were also highlighted. The mapping class group was also discussed in detail, from various points of view, including its actions on simplicial complexes and on infinite-dimensional Teichmüller spaces, its asymptotic dimension, the relation with the arc operad, the generalizations of the Johnson homomorphisms to the monoid of homology cylinders, making contact with knot theory and with the Casson invariant and other 3-manifolds invariants. There was an open problem session, which is also reported on here. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3211 2010-01-01T00:00:00Z This is a report on the workshop on Teichmüller theory held in Oberwolfach, from November 28 to December 4, 2010. The workshop brought together people working in various aspects of the field, with a focus on recent developments. The topics discussed included higher Teichmüller theory, moduli spaces of flat connections, cluster algebras, quantization of Teichmüller spaces, the dynamical aspects of the Teichmüller and Weil-Petersson geodesic flows, the metric and the boundary theory of Teichmüller space including the new developments on Thurston’s asymmetric metric, string topology, geometric analysis on moduli spaces, and relations with three-manifold topology and with minimal surface theory were also highlighted. The mapping class group was also discussed in detail, from various points of view, including its actions on simplicial complexes and on infinite-dimensional Teichmüller spaces, its asymptotic dimension, the relation with the arc operad, the generalizations of the Johnson homomorphisms to the monoid of homology cylinders, making contact with knot theory and with the Casson invariant and other 3-manifolds invariants. There was an open problem session, which is also reported on here. http://publications.mfo.de/handle/mfo/3210 Representation Theory and Harmonic Analysis The workshop gave an overview of current research in the representation theory and harmonic analysis of reductive Lie groups and its relation to algebraic number theory. Some particular topics covered in the 17 talks related to unitarity questions and globalizations for Harish–Chandra modules, Fourier transformation on symmetric spaces and p–adic groups, affine Hecke algebras or the spectral theory of automorphic forms and trace formulas. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3210 2010-01-01T00:00:00Z The workshop gave an overview of current research in the representation theory and harmonic analysis of reductive Lie groups and its relation to algebraic number theory. Some particular topics covered in the 17 talks related to unitarity questions and globalizations for Harish–Chandra modules, Fourier transformation on symmetric spaces and p–adic groups, affine Hecke algebras or the spectral theory of automorphic forms and trace formulas. http://publications.mfo.de/handle/mfo/3209 Infinite Dimensional Lie Theory The workshop focussed on recent developments in infinite-dimensional Lie theory. The talks covered a broad range of topics, such as structure and classification theory of infinite-dimensional Lie algebras, geometry of infinite-dimensional Lie groups and homogeneous spaces and representations theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3209 2010-01-01T00:00:00Z The workshop focussed on recent developments in infinite-dimensional Lie theory. The talks covered a broad range of topics, such as structure and classification theory of infinite-dimensional Lie algebras, geometry of infinite-dimensional Lie groups and homogeneous spaces and representations theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras. http://publications.mfo.de/handle/mfo/3208 Large Scale Stochastic Dynamics In focus are interacting stochastic systems with many components, ranging from stochastic partial differential equations to discrete systems as interacting particles on a lattice moving through random jumps. More specifically one wants to understand the large scale behavior, large in spatial extent but also over long time spans, as entailed by the characterization of stationary measures, effective macroscopic evolution laws, transport of conserved fields, homogenization, self-similar structure and scaling, critical dynamics, aging, dynamical phase transitions, large deviations, to mention only a few key items. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3208 2010-01-01T00:00:00Z In focus are interacting stochastic systems with many components, ranging from stochastic partial differential equations to discrete systems as interacting particles on a lattice moving through random jumps. More specifically one wants to understand the large scale behavior, large in spatial extent but also over long time spans, as entailed by the characterization of stationary measures, effective macroscopic evolution laws, transport of conserved fields, homogenization, self-similar structure and scaling, critical dynamics, aging, dynamical phase transitions, large deviations, to mention only a few key items. http://publications.mfo.de/handle/mfo/3207 Operator Theory and Harmonic Analysis The major topics discussed in this workshop were the Feichtinger conjecture and related questions of harmonic analysis, the corona problem for the ball Bn, the weighted approximation problem, and questions related to the model spaces, to multipliers, (hyper-)cyclicity, differentiability, Bezout and Fermat equations, traces and Toeplitz operators in different function spaces. A list of open problems raised at this workshop is also included. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3207 2010-01-01T00:00:00Z The major topics discussed in this workshop were the Feichtinger conjecture and related questions of harmonic analysis, the corona problem for the ball Bn, the weighted approximation problem, and questions related to the model spaces, to multipliers, (hyper-)cyclicity, differentiability, Bezout and Fermat equations, traces and Toeplitz operators in different function spaces. A list of open problems raised at this workshop is also included. http://publications.mfo.de/handle/mfo/3206 Mathematical Challenges in Stochastic Networks The workshop was devoted to the discussion of recent progress in modern stochastic network theory and to the exploration of open mathematical challenging problems in the field. The workshop covered a wide range of mathematical topics; while being centered around applied probability, it also included a substantial amount of graph theory and (combinatorial) optimization. Fri, 01 Jan 2010 00:00:00 GMT http://publications.mfo.de/handle/mfo/3206 2010-01-01T00:00:00Z The workshop was devoted to the discussion of recent progress in modern stochastic network theory and to the exploration of open mathematical challenging problems in the field. The workshop covered a wide range of mathematical topics; while being centered around applied probability, it also included a substantial amount of graph theory and (combinatorial) optimization.