The Schrödinger problem is an entropic minimization problem and it's a regular approximation of the Monge-Kantorovich problem, at the core of the Optimal Transport theory.
In this talk I will first introduce the two problems, then I will describe some analogy between optimal transport and the Schrödinger problem such as a dual Kantorovich type formulation, the dynamical Benamou-Brenier type representation formula, as well as a characterization formula and some properties of the respective solutions.
Finally I will mention, as an application of these analogies, some contraction inequalities with respect to the entropic cost, instead of the classical Wasserstein distance.

The speaker is a PhD student at Institut Camille Jordan - Université Claude Bernard Lyon 1, France and working in the area of "PDE, Analysis" under the supervision of Prof. Ivan Gentil and Prof. Christian Léonard. 

The seminar takes place in PORTO, at 14h30m.