Séminaire Jeunes chercheurs (Julien Guérin, jeudi 12 novembre 2026)

Une séance exceptionnelle du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 12 novembre 2026 à 17h en salle A709. Nous aurons le plaisir d'écouter Julien Guérin (CEREMADE), qui nous parlera de

Introduction au transport optimal.

Abstract
Optimal transport asks how to move one probability distribution onto another at minimal cost. This talk will introduce the subject through its two classical formulations, due to Monge and Kantorovich, and the associated duality principle. For the quadratic cost, we will explain Brenier’s theorem, which, under suitable assumptions, solves Monge’s problem by establishing the existence and uniqueness of an optimal transport map between two probability distributions. We will then discuss connections with partial differential equations through the Monge–Ampère equation and illustrate how transport maps can be used to transfer functional inequalities through Caffarelli’s contraction theorem. Finally, we will introduce the geometric viewpoint offered by Wasserstein distances, moving from McCann’s displacement interpolation to the dynamic formulation of Benamou–Brenier and Wasserstein barycenters.