MAI0140 Topics in Optimal Transport/Optimal TransportThis course will treat some central topics in optimal transport theory. It will consist of five compulsory lectures, with a rough plan as follows:
Lecture 1: Some measure theoretic preliminaries and formulations of the Monge and Kantorovich minimization problems.
Lecture 2: Properties of c-cyclical monotonic sets and c-convex functions.
Lecture 3: Kantorovich-Koopmans duality.
Lecture 4: A game-theoretic approach to the duality. Existence of optimal maps.
Lecture 5: An overview of some known results in Euclidean spaces. Brenier's theorem, regularity properties...
Examination: Apart from the attendance to the compulsory lectures each student should make a small presentation on a topic relevant to the course. Some suggested topics can be found here.
We will follow the Lecture Notes on Optimal Transport written by myself.
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Last updated: 2019-11-29