Nonlinear and Adaptive Approximation in High Dimensions

Date: December 10-15, 2007

Venue: Physikzentrum Bad Honnef, Germany

Organizers: Wolfgang Dahmen (RWTH Aachen), Angela Kunoth (Universitaet Bonn), Reinhold Schneider (Universitaet Kiel), Christoph Schwab (ETH Zuerich)

Numerical problems in high spatial dimension arise in an increasing number of active and important research areas:

  • mathematical finance
  • data mining and computational biology
  • ab initio electronic structure calculation
  • numerical solution of stochastic PDEs and
  • numerical solution of multiple-scale problems.

The well-known curse of dimension prevents efficient numerical treatment for most of these problems by standard discretizations of tensor product type. The resulting enormous computational challenges cannot be met merely by larger computational platforms, but require fundamentally new mathematical and algorithmic ideas.

The meeting aims at bringing together leading experts from those areas in order to compile an account of the current state of the art. We plan to address several research areas involving problems in high dimensions. Key topics are sparse grid methods, linear and nonlinear approximation theory for sparse representations, learning theory, numerical quantization, applications to mathematical finance and to stochastic PDEs, as well as models and PDEs in high dimensions (e.g. related to molecular dynamics, computational physics, climate models).

The first such workshop took place December 14-18, 2005, see

Invited Speakers:
Peter Binev (South Carolina), Albert Cohen (Paris VI) , Ron DeVore (South Carolina), Thomas Gerstner (Bonn), Helmut Harbrecht (Bonn), Claude Le Bris (Cermics), Christian Lubich (Tuebingen), Mauro Maggioni (Duke), Klaus Ritter (TU Darmstadt), Endre Sueli (Oxford), Jared Tanner (University of Utah), Eugene Tyrtyshnikov (Moskau)