Colloquium du Ceremade (Filippo Santambrogio, mardi 7 mai)

15 avril 24

Le prochain Colloquium du Ceremade est prévu le mardi 7 mai à 15h30 en salle A709 avec l'intervention de Filippo Santambrogio (Université Claude Bernard, Lyon 1).

Title{Euclidean, metric, and Wasserstein} Gradient flows

Abstract :

At the beginning of the presentation, I will explain what a gradient flow is in the simplest case: a curve in R^n solution of x'=-DF(x). In particular I will introduce a very natural time-discretization which is well-defined even when we replace the Euclidean space with a metric space, and I will briefly introduce some notions of gradient flow in a metric framework. We will then focus on the case where the metric space is the space of probability measures endowed with the Wasserstein distance, defined in terms of optimal transport. In this case we look for a mass distribution which evolves in time, and we can characterize it by PDEs. I will show how certain well-known diffusion PDEs (including the heat equation) fit into this framework.  

[The content of the seminar can be found in the survey accessible here]