Seminar: Wasserstein Geometry, the Otto metric and alpha-connections

We are pleased to announce an upcoming talk by Prof. Dr. Lorenz Schwachhöfer from TU Dortmund, who will be presenting on March 05, 2026, at 11:00.

Abstract:

How do we meaningfully measure the "distance" between two probability distributions? While traditional statistical methods often fail to capture the physical geometry of the underlying space, the mathematics of Optimal Transport offers a powerful alternative. In this talk, we will introduce the Wasserstein distance, which intuitively measures the optimal cost of "transporting" one distribution of mass into another. Building on this, we will explore Felix Otto's profound insight: the space of all probability measures can be viewed as an infinite-dimensional Riemannian manifold equipped with what is now known as the Otto metric.

We will then connect this to information theory by examining statistical divergences, and will report on some joint work with Nihat Ay on constructing connections with torsion based on the Otto metric.