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Time: M,W, F at 11am (twice a week among these).
Location: 381-U.
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, 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.
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:
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December 5, 3-4pm
Introduction (Alessandro Carlotto)
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January 9
c-concave functions, Rockafellar's theorem.
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January 18
Brenier's theorem and optimal maps.
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January 23
Examples. Polar factorization.
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January 27
McCann's theorem.
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January 30
Wasserstein space, I (Otis Chodosh).
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February 3
Wasserstein space, II (Otis Chodosh).
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February 6
Wasserstein space, III.
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February 10
Wasserstein space, IV.
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February 13
Wasserstein space, V.
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February 15
Gradient flows (basic existence and uniqueness) (Ehsan Kamalinejad).
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February 17
Gradient flows, I (Alessandro Carlotto).
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February 22
Gradient flows, II (Alessandro Carlotto).
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February 24
Gradient flows and Wasserstein space, I.
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February 27
The Riemannian structure on Wasserstein space, I.
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March 2
Gradient flows and Wasserstein space, II.
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March 5
The Riemannian structure on Wasserstein space, II.
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March 9
Analytic applications:
Isoperimetric, Sobolev, and Brunn-Minkowski inequalities.
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