After successful completion of the course, students are able to:

• Formulate the optimal transportation problem according to Monge resp. Kantorovich.
• Solve the 1-dimensional optimal transportation problem.
• Formulate the dual problem according to Kantorovich and prove the existence of maximizers.
• Define the Wasserstein space and Wasserstein distance.
• Prove classical geometric inequalities using optimal transportation.

Optimal Transport formulation according to Monge resp. Kantorovich; Kantorovich Duality; solution of the 1-dimensional problem; theory of convex functions, in particular the Legendre transform; Wasserstein distances and Wasserstein spaces; geometric inequalites (Brunn-Minkowski, Prékopa-Leindler,...)

Mathematical definitions and proves.

Lecture Friday 10h-12h at Zeichensaal 1 (FH 8th floor, green section).

Additional literature:

• Cédric Villani, "Topics in Optimal Transportation", Graduate Studies in Mathematics Volume 58, American Mathematical Society, 2003.
• Cédric Villani, "Optimal transport: old and new",  Grundlehren der mathematischen Wissenschaften 338, Springer-Verlag, 2009.

oral exam

Ein Skriptum ist verfügbar.