Convexity Seminar

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An Introduction to Optimal Transport, Part 2

Speaker: Nestor Guillen, Texas State University, NYU Courant

Location: Warren Weaver Hall 1302

Date: Tuesday, September 30, 2025, 11 a.m.

Synopsis:

(It is not necessary to have attended part 1 in order to follow part 2)

In part 1 we went over the historical motivation for and several important applications of optimal transport. In part 2 we will continue our study by going over the proof of existence of optimal transport maps for general costs. To achieve this we will discuss the dual problem, the elements of c-convex functions, and maps admitting a c-convex potential — the latter being the same as the class of optimal maps for a given cost.