The fifth Takagi Lectures
October 4, 2008 (Sat) 15:00--16:00
October 5, 2008 (Sun) 14:30--15:30
Graduate School of Mathematical Sciences
The University of Tokyo

Ricci curvature and measures
Jean-Pierre Bourguignon
(CNRS - Institut des Hautes Études Scientifiques)


In the last thirty years three a priori very different fields of mathematics, Optimal Transport Theory, Riemannian Geometry and Probability Theory, have come together in a remarkable way, leading to a very substantial improvement of our understanding of what may look like a very specific question, namely the analysis of spaces whose Ricci curvature admits a lower bound.

The purpose of these lectures is, starting from the classical context, to present the basics of the three fields that lead to an interesting generalisation of the concepts, and to highlight some of the most striking new developments.