Time: M,W, F at 11am (twice a week among these).
Location: 381U.
Teacher:
Y. A. Rubinstein
This will be an introductory graduate level course on Optimal Transportation theory.
We will study Monge's problem, Kantorovich's problem, cconcave 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.
Main references:
L. Ambrosio, N. Gigli,
A user's guide to optimal transport, 2011.
(Older version)
C. Villani, Topics in Optimal Transportation, AMS, 2003.
C. Villani, Optimal Transport: Old and New, Springer, 2008.
Schedule:

December 5, 34pm
Introduction (Alessandro Carlotto)

January 9
cconcave functions, Rockafellar's theorem.

January 18
Brenier's theorem and optimal maps.

January 23
Examples. Polar factorization.

January 27
McCann's theorem.

January 30
Wasserstein space, I (Otis Chodosh).

February 3
Wasserstein space, II (Otis Chodosh).

February 6
Wasserstein space, III.

February 10
Wasserstein space, IV.

February 13
Wasserstein space, V.

February 15
Gradient flows (basic existence and uniqueness) (Ehsan Kamalinejad).

February 17
Gradient flows, I (Alessandro Carlotto).

February 22
Gradient flows, II (Alessandro Carlotto).

February 24
Gradient flows and Wasserstein space, I.

February 27
The Riemannian structure on Wasserstein space, I.

March 2
Gradient flows and Wasserstein space, II.

March 5
The Riemannian structure on Wasserstein space, II.

March 9
Analytic applications:
Isoperimetric, Sobolev, and BrunnMinkowski inequalities.
