Colloquium

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.