Convexity Seminar

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Regularity theory for optimal transport maps IV

Speaker: Nestor Guillen, Texas State University, NYU Courant

Location: Warren Weaver Hall 1302

Date: Tuesday, November 18, 2025, 11 a.m.

Synopsis:

We will continue our study of the question of regularity for optimal transport maps via their corresponding Monge-Ampère equation. In the last part in this series we introduced the framework of c-convex geometry in order to study the regularity of optimal transport maps for general costs, particularly costs given by the geodesic distance in a Riemannian manifold. This week we will go into the deeper aspects of this framework, explaining the geometric significance of the Ma-Trudinger-Wang tensor of a cost function and how it governs the regularity (or lack of it) for the problem.