Working seminar

I am a former co-organizer of the monthly working seminar "Curvature, optimal transport and probability theory" (C-Top) at the Institut Henri Poincaré.
During 2008-2012, I co-organized the seminar with François Bolley and Ivan Gentil and during 2012-2016, I  co-organized  it with Nathaël Gozlan.
The seminar is currently co-organized by Matthieu Fradelizi and Nathaël Gozlan.

The seminar is mainly focused on the notion of dissipative functional inequalities such as logarithmic Sobolev and spectral gap inequalities and their relations with curvature and optimal transport. The original motivation for organizing the seminar in 2008 was the urge for understanding and further developing the newly born LSV theory of a synthetic notion of Ricci curvature on metric measure spaces put forward independently by Karl-Theodor Sturm on one hand and by John Lott and Cédric Villani on the other hand. Here is a photograph of LSV at MSRI. This theory and its extensions gather optimal transport, probability theory, parabolic PDEs, gradient flows and geometry.

There are still many open problems in this active field of research. In particular, the LSV approach works pretty well on geodesic spaces, but much remains to be done on discrete spaces.  Several recents talks at the seminar were about curvature of random walks on discrete graphs.