Stochastic Partial Differential Equations: Analysis, Numerics, Geometry and Modeling

September 12 to 16, 2011

Organisers: Christoph Schwab, Martin Schweizer, Mete Soner and Josef Teichmann

Applications of sPDEs have been a rich source of problems, questions and an offspring of new concepts in several areas of mathematics like probability theory, stochastic analysis, regularity theory of partial differential equations, numerical analysis and differential geometry, among others.
For the qualitative analysis of solutions support theorems, finite factor properties, regularity results and pathwise solution properties are still lacking. Finally, to obtain efficient numerical solution methods for stochastic PDEs, a combination of ideas and techniques from rather diverse areas of mathematics like the approximation theory on infinite dimensional spaces, sparse (and adaptive, nonlinear) tensor approximations, and approximation schemes based on geometry of path spaces (cubature on Wiener space as a keyword) is needed.
Likewise, algorithms for efficient computer implementations of stochastic Galerkin methods will be based on well-established methods for deterministic problems, but also require essential new ideas. We mention here only the deeply geometric approach of rough paths which has given rise to methods, e.g. “Cubature on Wiener space'”, and sparse, adaptive tensor product approximations. The necessary summability estimates of (weak and strong) solutions of SPDEs will have to be developed together with the numerical approximation.
The present workshop aims at bringing together leading experts from the communities of stochastic partial differential equations, stochastic and numerical analysis and also from scientific computing to review recent developments in the general area of sPDEs, to identify key problems, to stimulate interaction and to initiate new, joint work.

This workshop is part of the thematic semester "High Dimensional Approximation, Learning Theory and Stochastic Partial Differential Equations" of fall 2011. See also the workshop on "High-Dimensional Problems in Statistics", which will follow the week after (September 19 - 23, 2011).