Gergen Lectures
Tuesday, May 6, 2008, 4:00pm, 119 Physics
Cedric Villani
Optimal transport and Riemannian geometry: Monge meets Riemann

Abstract:

Monge, Boltzmann and Ricci: Starting from works of Otto and Villani, it was understood that Ricci curvature bounds are intimately linked with the behavior of Boltzmann's entropy functional along geodesics (in the space of probability measures on the manifold of interest) induced by the optimal transport problem. This observation can be exploited to give a new point of view of Ricci curvature, with probabilistic and geometric applications (one is the weak stability of Ricci curvature bounds, which was proven independently by Lott and Villani, and by Sturm)

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