Convexity Seminar

---

Regularity theory for optimal transport maps III

Speaker: Nestor Guillen, Texas State University, NYU Courant

Location: Warren Weaver Hall 1302

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

Synopsis:

Up until now we have focused on the regularity theory for transport maps when the cost is the quadratic cost in Euclidean space. In this talk we will give a broad overview of the situation for a general cost, covering the important case of the quadratic cost in a Riemannian manifold. We will discuss a crucial curvature-condition discovered by Ma-Trudinger-Wang, and how it guarantees the validity of analogues of the Blashke-Santalo and reverse Blahske-Santalo inequalities in the setting of c-convex geometry.