Many problems in modern research require numerical discretization on high-dimensional domains. Fields where such problems arise are, for instance, quantum and stochastic physics, uncertainty quantification or financial mathematics. This integrated course exemplarily introduces into the field of high-dimensional numerics.

Content

1. Basic concepts
2. Monte Carlo and Quasi Monet Carlo
3.  Sparse Grids
4. Kernel methods
5. Tensor networks

The course is organized as follows. The lectures introduce into the basic ideas and the theory behind the different methods. For the exercises, the students will prepare presentations on current research topics from literature. These can be about methodological advances in the respective field or about applications for particular scientific problems. This will typically be such that each subtopic is teached for 1-2 weeks without exercise talks. This will be followed by a period with student talks.

For students of mathematics, computational science and all others who are interested.

Literature will be anounced at the beginning of the course.