# Leonie Mühlherr: Fundamental polytopes on finite metric spaces and the Wasserstein arrangement.

## Speaker: Leonie Mühlherr (Bielefeld Universität)

**Time: **
Wed 2024-10-02 10.15 - 11.15

**Location: **
3418

Abstract: We can associate a polytope to a metric on a finite set of points, the so-called fundamental polytope. The question of classifying metric spaces by the combinatorial properties of their fundamental polytopes has been posed by Vershik (2015). It has been studied for special types of metrics (generic, tree-like) in recent years. This talk gives an introduction to the basic concepts and an overview of other

classifications and their compatibility. A hyperplane arrangement dividing the metric cone according to the combinatorial type of the polytope is introduced and analysed. This is joint work with Emanuele Delucchi and Lukas Kühne.