November 26 (Wednesday) (10:00-11:00) room E.118.2 (main building, 1st floor)
Tamás Titkos (Corvinus University)
Metric symmetries of Wasserstein spaces
In recent decades, the theory of optimal transport has advanced rapidly, finding an ever-growing range of applications (including even game theory). The original problem of Monge is to find the cheapest way to transform one probability distribution into another when the cost is proportional to the distance. One of the most important metric structures that is related to optimal transport is the so-called p-Wasserstein space. The pioneering work of Bertrand and Kloeckner started to explore fundamental geometric features of certain 2-Wasserstein spaces, including the description of complete geodesics and geodesic rays, determining their different types of ranks, and understanding the structure of their isometry group. In this talk I will mainly focus on isometry groups of and some curious properties of Wasserstein spaces.