Séminaire Jeunes chercheurs (Benjamin Capdeville, jeudi 29 janvier 2026)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 29 janvier 2026 à 17h en salle A707. Nous aurons le plaisir d'écouter Benjamin Capdeville (Université Paris-Saclay), qui nous parlera de

Hidden gradient Flow structures for the Moran process and the Kimura equation.

Abstract
Since a significant paper by Jordan, Otto, and Kinderlehrer (98'), it is now well known that some evolution PDEs, such as diffusion and advection PDEs, can be interpreted as gradient flows with respect to the Wasserstein distance. Since then, there have been ongoing efforts to integrate various evolutionary processes into this framework. In this talk, I will introduce the Moran process and its high popuation limit the Kimura equation, and explain how they are related to Wasserstein gradient flows. Indeed, the degeneracy of the diffusion at the boundaries leads to the study of a conditioned version of the dynamics, that can be seen as a Wasserstein gradient flow, with degenerate underlying geometry, involving the Shahshahani metric. Finally, we will see that the dissipation induced by the hidden gradient flow in the continuous setting is a good approximation of the dissipation in the discrete setting in its high population limit.