|Location:||MSRI: Simons Auditorium|
We start with preliminaries on the optimal transportation problem and the Monge-Ampere equation. We will focus on transportation of the log-concave measures and regularity results for the corresponding MA equation with potential applications in probability and convex analysis, such as the Caffarelli contraction principle. In the second part of the talk it will be explained how certain tools from Riemannian geometry (Laplacians acting on tensors) can be used in analysis of the Monge-Ampere operator. We discuss various applications, in particular, higher-order generalizations of the Caffarelli theorem, applications in Gaussian analysis, the Kaehler-Einstein equation and moment measures. The talk will be finished with an open question on extremal metrics associated with the Kaehler-Einstein equation on convex bodies (the solution is known only in dimension 2).
The talk is partially based on joint works with Bo'az Klartag.