2004, Kings, Guido, Wildeshaus, Jörg

[no abstract available]

2007, van den Berg, Jacob, Camia, Federico

Abstract. Percolation as a mathematical theory is more than fifty years old. During its life, it has attracted the attention of both physicists and mathematicians. This is due in large part to the fact that it represents one of the simplest examples of a statistical mechanical model undergoing a phase transition, and that several interesting results can be obtained rigorously. In recent years the interest in percolation has spread even further, following the introduction by Oded Schramm of the Schramm-Loewner Evolution (SLE) and a theorem by Stanislav Smirnov showing the conformal invariance of the continuum scaling limit of two-dimensional critical percolation. These results establish a new, powerful and mathematically rigorous, link between lattice-based statistical mechanical models and conformally invariant models in the plane, studied by physicists under the name of Conformal Field Theory (CFT). The Arbeitsgemeinschaft on percolation has attracted more than thirty participants, most of them young researchers, from several countries in Europe, North America, and Brazil. The main focus has been on recent developments, but several classical results have also been presented.

2008, Fiedler, Bernold, Sandstede, Björn

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.

2005, Tobiska, Lutz, Walkington, Noel J.

Multiple difficulties are encountered when designing algorithms to simulate flows having free surfaces, embedded particles, or elastic containers. One difficulty common to all of these problems is that the associated interfaces are Lagrangian in character, while the fluid equations are naturally posed in the Eulerian frame. This workshop explores different approaches and algorithms developed to resolve these issues.

2007, Süli, Endre, Verfürth, Rüdiger

This collection contains the extended abstracts of the talks given at the Oberwolfach Conference on “Adaptive Numerical Methods for PDEs”, June 10th - June 16th, 2007. These talks covered various aspects of a posteriori error estimation and mesh as well as model adaptation in solving partial differential equations. The topics ranged from the theoretical convergence analysis of self-adaptive methods, over the derivation of a posteriori error estimates for the finite element Galerkin discretization of various types of problems to the practical implementation and application of adaptive methods.

2004, Shparlinski, Igor E., Stichtenoth, Henning

Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation.

2009, Eschmeier, Jörg, Upmeier, Harald

The major topics discussed in this workshop were Hilbert modules of analytic functions on domains in ℂn, Toeplitz and Hankel operators, the interplay of commutative algebra, complex analytic geometry and multivariable operator theory, coherent and quasi-coherent sheaves as localizations of Hilbert modules, Hilbert bundles and Jordan varieties on Cartan domains.

2006, Palencia, E. Sanchez, Sokolowski, Jan, Wagner, Barbara

This workshop focused on asymptotic analysis and its fundamental role in the derivation and understanding of the nonlinear structure of mathematical models in various fields of applications, its impact on the development of new numerical methods and on other fields of applied mathematics such as shape optimization. This was complemented by a review as well as the presentation of some of the latest developments of singular perturbation methods.

2006, Freed, Dan, Schick, Thomas

The “Arbeitsgemeinsschaft mit aktuellem Thema ‘Twisted KTheory’ ” gave an introduction to several aspects of twisted K-theory. It started with a couple of different definitions of twisted K-theory, suitable in situations of varying complexity from spaces to topological stacks. Then the AG presented tools of calculations like Chern characters with values in the corresponding twisted ordinary cohomology theories, and example calculations e.g. for Lie groups, or via T-duality. The program culminated in the theorem of Freed-Hopkins-Teleman calculating equivariant twisted K-theory of simple Lie groups in term of the Verlinde algebra of loop group representations.

2009, Bollobas, Bela, Wegener, Ingo

The effective application of probabilistic reasoning in the study of problems in diverse areas is one of the most exciting recent developments in Mathematics. Probabilistic methods turned out to be very powerful in Discrete Mathematics, Analysis, Number Theory and Theoretical Computer Science. The meeting was dedicated to recent developments in these areas, focusing on the investigation of combinatorial problems for random sets and probabilistic methods, on the study of of questions in percolation, on the design and analysis of randomized algorithms and derandomization techniques, and on applications of probabilistic ideas in the study of questions in Combinatorial Number Theory and in Combinatorial Geometry.