HCM Workshop: Analysis and Computation in High Dimensions

Date: October 1 - 5, 2018
Venue: Lipschitz lecture hall, Mathematics Center, Endenicher Allee 60, 53115 Bonn
Markus Bachmayr (Bonn), Albert Cohen (Paris)

Topics and aims of the workshop

The approximation or integration of functions on high-dimensional domains arises naturally in many applications, from mathematical physics and economics to machine learning and uncertainty quantification -- notably, in numerical computations involving probability distributions of many random variables.

Basic mathematical concepts such as separation of variables, mixed smoothness, and concentration of measure reflect that in high-dimensional problems, the relevant information is often clustered along lower-dimensional subsets. These observations have led to a variety of numerical techniques, for instance sparse expansions, sampling methods, ANOVA-type decompositions, or low-rank formats. Many challenging open questions remain on the connections and relative merits of these approaches for a given computational task, on the intrinsic computational complexity of problems posed in high dimensions, on the integration of real-world measurement data, and on novel concepts for problems that with available methods are still out of reach.

The aim of this workshop is to bring together experts working on high-dimensional problems from different backgrounds and to foster exchange between foundational results and more application-driven methods, as well as between classical approximation theory and stochastic aspects.

In case of questions regarding this workshop, please contact highdim18(at)hcm.uni-bonn.de.