Orateur : Aymeric Martin
Établissement : IMB – Université de Bordeaux (France)
Dates : 2025-11-27 – 2025-11-27
Heures : 14:00 – 15:00
Lieu : Salle 0-3
Résumé :
Titre de la conférence : About stochastic differential equations on the Wasserstein space over a Riemannian manifoldAfter presenting the basics about stochastic calculus on Riemannian manifolds, we introduce the notion of SDEs on the Wasserstein space over a Riemannian manifold $M$. Then, we will endow the group of diffeomorphisms $mathrm{Diff}(M,M)$ with a structure of Riemannian submersion onto the Wasserstein space. This point of view will allows us to construct a stochastic parallel transport along diffusions on the Wasserstein space. If time permits, we will come back to the finite-dimensional case in order the discuss some conditions that leads to stability properties of diffusions, namely, the Bakry-Emery curvature-dimension condition and the Half-Concavity condition of Cattiaux and Guillin. We will then discuss possible extensions of these condition to our infinite-dimensional setting.