Wasserstein barycenters from a PDE perspective (Carlier, Université Paris Dauphine)

Guillaume Carlier ( Université Paris Dauphine) (https://www.ceremade.dauphine.fr/~carlier/)

The Wasserstein barycenter is a way to interpolate between several probability measures that has become quite popular in machine learning and statistics. Such objects are characterized by an obstacle problem for a system of Monge-Ampère equations. I will give some regularity results and describe a regularization from which one can obtain further results, including a central limit theorem.