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Applications of Asymptotic Analysis
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.
Finite Fields: Theory and Applications
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.
Adaptive Numerical Methods for PDEs
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.
Arbeitsgemeinschaft: Percolation
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.