Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.

A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.

Food and drinks are served after the event, usually in Espace 7!

If you know good speakers whom you would love to hear, do not hesitate to suggest their names to the two organizers: Justin Salez and Cristina Toninelli.

Date: Tuesday, May 7th 2024 (15:30-16:30, room A709)

Speaker: Filippo Santambrogio (Université 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.

• April 2024 - Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics). The Random Lorentz Gas.
• March 2024 - Ismaël Castillo (Sorbonne Université). A tale of heavy tails.
• February 2024 - Josselin Garnier (École polytechnique). Utilisation de modèles d'ordre réduit pour l'imagerie par ondes.
• December 2023 - Pietro Caputo (Università Roma Tre). Navigating Networks by Random Walks.
• November 2023 - Bertrand Maury (Université Paris-Saclay). Sciences sociales et flots de gradient.
• October 2023 - Marc Lelarge (INRIA). Mathématiques et Intelligence Artificielle.
• June 2023 - Pierre Youssef (NYUAD). Phenomena in High Dimensions.
• April 2023 - Nalini Anantharaman (Université de Strasbourg). Principes d'incertitude, inégalités d'incertitude.
• January 2023 - Mathieu Rosenbaum (Ecole Polytechnique). Autour de la modélisation statistique par les processus de Hawkes.
• December 2022 - Alexandre Stauffer (University of Bath). Random growth processes: dendritic formation and competition.
• October 2022 - Hanne Van Den Bosch (Universidad de Chile). Solitary waves in non-linear Dirac equations.
• May 2022 - Michael Loss (Georgia Institute of Technology). Optimal criteria for magnetic fields that bind electrons.
• April 2022 - Isabelle Gallagher (Ecole Normale Supérieure de Paris). Sur la dynamique des gaz dilués.
• December 2021 - Elisabeth Gassiat (Université Paris-Saclay). Quand la dépendance ouvre des possibles.
• October 2021 - Nicolas Curien (Université Paris-Saclay). Surfaces aléatoires en tous genres.