I co-organize 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.
Since 2012, I still co-organize it with 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