Time: M,W, F at 11am (twice a week among these).
Y. A. Rubinstein
This will be an introductory graduate level course on Optimal Transportation theory.
We will study Monge's problem, Kantorovich's problem, c-concave functions
(also in the Riemannian setting), Wasserstein distance and geodesics
(including a PDE formulation), applications to inequalities in convex
analysis, as well as other topics, time permitting.
Participating graduate students will be required to present
some of the topics.
L. Ambrosio, N. Gigli,
A user's guide to optimal transport, 2011.
C. Villani, Topics in Optimal Transportation, AMS, 2003.
C. Villani, Optimal Transport: Old and New, Springer, 2008.
December 5, 3-4pm
Introduction (Alessandro Carlotto)
c-concave functions, Rockafellar's theorem.
Brenier's theorem and optimal maps.
Examples. Polar factorization.
Wasserstein space, I (Otis Chodosh).
Wasserstein space, II (Otis Chodosh).
Wasserstein space, III.
Wasserstein space, IV.
Wasserstein space, V.
Gradient flows (basic existence and uniqueness) (Ehsan Kamalinejad).
Gradient flows, I (Alessandro Carlotto).
Gradient flows, II (Alessandro Carlotto).
Gradient flows and Wasserstein space, I.
The Riemannian structure on Wasserstein space, I.
Gradient flows and Wasserstein space, II.
The Riemannian structure on Wasserstein space, II.
Isoperimetric, Sobolev, and Brunn-Minkowski inequalities.