Analysis & Applied Math

In this seminar, I will talk about optimal transport in globally hyperbolic spacetimes, where the cost is given by the time separation function raised to some power p<1. Moreover, I will discuss a Benamou-Brenier type formula which establishes a link between the original Kantorovitch problem and the causal continuity inequality for causal curves on the space of probability measures. This talk is based on a joint work with N. Gigli and F. Rott.