Mathematics

In the first part of the talk, I will give a short introduction to the theory of Optimal Entropy-Transport problems, a generalization of the classical Optimal Transport problems. I will focus on the metric properties of these problems, emphasizing the role of the so-called "marginal perspective cost", a function obtained by a minimizing procedure involving a cost and an entropy function. I will discuss various examples, which include some well-known entropy functionals like the Hellinger distance, the Jensen-Shannon divergence, the total variation and their transport variants.
Finally, I will show how these metrics can be used to construct new distances between metric measure spaces with possibly different total mass.
This is a joint work with Andrea Mondino and Giuseppe Savaré.