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,...)
preliminary lecture (also to dertermine the dates): Tuesday March 7th, 11 a.m. (Freihaus 7. Floor, green section, Besprechungszimmer)
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.