PROGRAMME:

14h00 - 14h30

Luigi Forcella

The electrostatic limit for the Zakharov system

Abstract: The Zakharov system describes the coupled dynamics of the electric field amplitude and the low frequency fluctuation of the ions in a unmagnetized or weakly magnetized plasma. This system couples Schrödinger-like and wave equations and in its physical derivation depends on a parameter $\alpha.$ Large value of $\alpha$ describes a plasma that is very hot, so it is meaningful to study the limit for the solutions to this system as $\alpha$ goes to infinity. In this talk we give rigorous mathematical result in this direction.

14h30 - 15h00

Luigia Ripani

Analogies between optimal transport and minimal entropy

Abstract: 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.

Luigi Forcella is a PhD student at Scuola Normale Superiore di Pisa, Italy and working in the area of "Analysis" under the supervision of Prof. Luigi Ambrosio.

Luigia Ripani 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.