SS 2026

PD Dr. Mario Ullrich (Linz)
Titel: Optimal sampling and complexity for high-dimensional approximation

Abstract: I consider the approximation of functions based on function
evaluations. This is a well-studied problem in optimal recovery,
machine learning, and numerical analysis in general, but many
fundamental insights were obtained only recently.
I will discuss some of these insights, including the optimality of
least squares in a worst-case setting and corresponding (random)
sampling strategies. I conclude with a novel semi-constructive
algorithm that is provably superior to sparse grid interpolation for
L2-approximation in simple 'tensor product spaces'. Explicit
constructions in this regime are still unknown.

Dr. Fabio Frommer (Mainz)

Titel: The inverse Henderson problem from statistical mechanics for
multi-species models

Abstract: The inverse Henderson problem of statistical mechanics is the theoretical
foundation for many bottom-up coarse-graining techniques for the numerical
simulation of complex soft matter physics. This inverse problem concerns
classical particles in continuous space interacting according to a pair
potential depending on the distance of the particles. Roughly stated,
it asks for the interaction potential given the pair correlation function
of the system. We show that the solution to this inverse problem is
unique and can be rewritten as a minimization problem for a certain
relative entropy functional. Lastly, we show how this framework can
be adapted to multi-species models using marked Gibbs measures.

Prof. Dr. Andreas Neuenkirch (Mannheim)
Titel: A Quasi-Monte Carlo Approach to Consensus-Based Optimization

Abstract

This talk is based on joint work with Jacob Heieck and
Simone Göttlich ( Universität Mannheim).