Generalized Optimal Transport and Applications

Members:

• Luca Nenna (P.I.), Maître de conférences at Université Paris-Saclay.

• Maxime Laborde, Maître de conférences at Université Paris-Cité.

• Paul Pegon, Maître de conférences at Université Paris-Dauphine.

Open positions:

• M2 internship on neural networks and Lieb functional. Co-supervision with Virginie Ehrlacher.
• M2 internship on Entropic Optimal Transport. Co-supervision with Paul Pegon.

Objectives of the project:

This project deals with some generalizations and applications of Optimal Transport theory with a particular focus on three main topics: multi-marginal optimal transport, multi-population models and multi-marginal entropic optimal transport. The transition from the classical case to the multi-population carries some difficulties which make all these problems more delicate to treat both from the theoretical and numerical points of view. As for the former the main questions concern the dimension of the support of the solution, the development of tools for analysing PDEs involving more populations and the first-order expansion of the multi-marginal entropic regularized problem under some mild assumption on the cost function. As regards the numerical side the main objective, common to the three over mentioned topics, consists in developing suitable numerical methods to deal with the so-called curse of the dimensionality.

Publications and preprints: