On the Ma-Trudinger-Wang condition

Alessio Figalli, University of Texas-Austin
Fine Hall 314

The Ma-Trudinger-Wang condition, first introduced to prove regularity of optimal transport maps for general cost functions, has turned out to be a useful tool for: - Obtaining geometric informations on the underlying manifold. - Making the principal-agent problem theoretically and computationally tractable, allowing to derive uniqueness and stability of the principal's optimum strategy. In this expository talk I'll give an overview of these results.