## Spring 2016: Optimal transportation

Welcome back to the stochastic analysis seminar! We resume our informal lectures this semester on the topic of *optimal transportation*.

Optimal transportation is the problem of coupling probability measures in an optimal manner (in the sense that a certain expected cost functional is minimized.) The rich theory that arises from this problem has had far-reaching consequences in probability theory, geometry, PDEs, interacting particle systems, etc. The aim of these informal lectures is to introduce some of the basic ingredients of this theory and to develop some probabilistic applications. Potential topics include: Wasserstein distances and Kantorovich duality; the Brenier map; the Monge-Ampere equation; displacement interpolation; Caffarelli’s theorem; applications to functional inequalities, measure concentration, dissipative PDEs, and/or interacting particle systems.

**Time and location:** Thursdays, 4:30-6:00 PM, Bendheim Center classroom 103 (note different location than last year). The first lecture will be on February 4.

Schedule changes and any other announcements will be posted on this blog. Unfortunately, we will probably not have the resources to post lecture notes this semester as was done in previous semesters.

**References:**

- C. Villani, “Topics in Optimal Transportation“, AMS (2003).
- L. Ambrosio and N. Gigli, “A User’s Guide to Optimal Transport“, lecture notes.
- K. Ball, “An Elementary Introduction to Monotone Transportation“, lecture notes.
- D. Cordero-Erausquin, “Some Applications of Mass Transport to Gaussian-Type Inequalities“, Arch. Rational Mech. Anal. 161 (2002) 257–269.
- D. Bakry, I. Gentil, and M. Ledoux, “Analysis and Geometry of Markov Diffusion Operators“, Springer (2014), Chapter 9.