http://publications.mfo.de/handle/mfo/2807 Oberwolfach Reports Volume 3 (2006) Wed, 08 Apr 2026 23:38:50 GMT 2026-04-08T23:38:50Z http://publications.mfo.de/handle/mfo/2986 Konvexgeometrie The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 5 years. Several examples were presented at this meeting, for example the work of Naor on the non-linear Dvoretzky theorem, that of Paouris on the distribution of the Euclidean norm on a convex domain and the results of Rudelson on the singular values of random matrices. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2986 2006-01-01T00:00:00Z The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 5 years. Several examples were presented at this meeting, for example the work of Naor on the non-linear Dvoretzky theorem, that of Paouris on the distribution of the Euclidean norm on a convex domain and the results of Rudelson on the singular values of random matrices. http://publications.mfo.de/handle/mfo/2985 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 representation theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2985 2006-01-01T00:00:00Z 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 representation theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras. http://publications.mfo.de/handle/mfo/2984 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 extend– numerical aspects of such equations. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2984 2006-01-01T00:00:00Z 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 extend– numerical aspects of such equations. http://publications.mfo.de/handle/mfo/2983 Mini-Workshop: Dirac Operators in Differential and Noncommutative Geometry Abstract. This mini-workshop brought together mathematicians and physicists working either on classical or on noncommutative differential geometry. Our aim was to show current interests, methods and results within each group and to open the possibility for interaction between the two groups. The first three days were devoted to expository presentations. The remaining two days were devoted to talks on advanced current research problems and results. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2983 2006-01-01T00:00:00Z Abstract. This mini-workshop brought together mathematicians and physicists working either on classical or on noncommutative differential geometry. Our aim was to show current interests, methods and results within each group and to open the possibility for interaction between the two groups. The first three days were devoted to expository presentations. The remaining two days were devoted to talks on advanced current research problems and results. http://publications.mfo.de/handle/mfo/2982 Mini-Workshop: Logic, Combinatorics and Independence Results This is a collection of extended abstracts of a mini-workshop “Logic, Combinatorics and Independence results” that took place on November 25 – December 2, 2006 in Oberwolfach. The mini-workshop was attended by 16 researchers from 11 countries and concentrated on one unifying theme: Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2982 2006-01-01T00:00:00Z This is a collection of extended abstracts of a mini-workshop “Logic, Combinatorics and Independence results” that took place on November 25 – December 2, 2006 in Oberwolfach. The mini-workshop was attended by 16 researchers from 11 countries and concentrated on one unifying theme: http://publications.mfo.de/handle/mfo/2981 Mini-Workshop: Statistical Methods for Inverse Problems Inverse problems appear naturally in a broad range of applications. Numerical analysis and statistics have – often independently – developed methods for regularisation and inversion. The aim of this mini-workshop is to bring together these methods and to consider their use in applications, with a focus on mathematical finance. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2981 2006-01-01T00:00:00Z Inverse problems appear naturally in a broad range of applications. Numerical analysis and statistics have – often independently – developed methods for regularisation and inversion. The aim of this mini-workshop is to bring together these methods and to consider their use in applications, with a focus on mathematical finance. http://publications.mfo.de/handle/mfo/2980 Mathematical Theory of Water Waves The water-wave problem is the study of the two- and threedimensional irrotational flow of a perfect fluid bounded above by a free surface subject to the forces of gravity and surface tension. It is a paradigm for most modern methods in nonlinear functional analysis and nonlinear dispersive wave theory. Its mathematical study calls upon many different approaches, as iteration methods, bifurcation theory, dynamical systems theory, complex variable methods, PDE methods, the calculus of variations, positive operator theory, topological degree theory, KAM theory, and symplectic geometry. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2980 2006-01-01T00:00:00Z The water-wave problem is the study of the two- and threedimensional irrotational flow of a perfect fluid bounded above by a free surface subject to the forces of gravity and surface tension. It is a paradigm for most modern methods in nonlinear functional analysis and nonlinear dispersive wave theory. Its mathematical study calls upon many different approaches, as iteration methods, bifurcation theory, dynamical systems theory, complex variable methods, PDE methods, the calculus of variations, positive operator theory, topological degree theory, KAM theory, and symplectic geometry. http://publications.mfo.de/handle/mfo/2979 Qualitative Assumptions and Regularization in High-Dimensional Statistics Important and exciting developments are currently underway in nonparametric statistics involving inter-play between qualitative constraints, penalization, and regularization methods. Some of these developments are taking place on the theoretical side (with connections in the direction of empirical process theory), while other parts of the development are occurring on the algorithmic and approximation theory sides. This workshop brought together researchers from several of these groups to exchange ideas and problems, to probe further research directions. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2979 2006-01-01T00:00:00Z Important and exciting developments are currently underway in nonparametric statistics involving inter-play between qualitative constraints, penalization, and regularization methods. Some of these developments are taking place on the theoretical side (with connections in the direction of empirical process theory), while other parts of the development are occurring on the algorithmic and approximation theory sides. This workshop brought together researchers from several of these groups to exchange ideas and problems, to probe further research directions. http://publications.mfo.de/handle/mfo/2978 Combinatorics, Probability and Computing One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas. The probabilistic point of view has turned out to be Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2978 2006-01-01T00:00:00Z One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas. The probabilistic point of view has turned out to be http://publications.mfo.de/handle/mfo/2977 Mathematical and Numerical Aspects of Quantum Chemistry Problems This workshop was aimed at strengthtening the interactions between well established experts in quantum chemistry, mathematical analysis, numerical analysis and computational metodology. Most of the mathematicians present in the worskhop have already contributed to the theoretical and numerical study of models in quantum physics and chemistry. Some others, familiar with contiguous fiels, were new to chemistry. Several distinguished researchers in theoretical chemistry participated in the workshop, and presented the mathematical and computational challenges of the field. Sun, 01 Jan 2006 00:00:00 GMT http://publications.mfo.de/handle/mfo/2977 2006-01-01T00:00:00Z This workshop was aimed at strengthtening the interactions between well established experts in quantum chemistry, mathematical analysis, numerical analysis and computational metodology. Most of the mathematicians present in the worskhop have already contributed to the theoretical and numerical study of models in quantum physics and chemistry. Some others, familiar with contiguous fiels, were new to chemistry. Several distinguished researchers in theoretical chemistry participated in the workshop, and presented the mathematical and computational challenges of the field.