授课题目： Introduction to Wasserstein spaces

主讲人：方诗赞教授 (University of Burgundy, France)

时间：6月8-18日，2018

授课摘要：

The purpose of this course is to present basic ingredients in the theory of Wasserstein space and perspectives of applications to mean field games or to Fokker-Plank equations. We will begin with long time behavior of a gradient flow generated by a convex function, which will be served as a socle for further developments of analysis on the Wasserstein space. Wasserstein distance will be introduced as well as its dual representation formula, the relation with weak convergence will be discussed. The intrinsic notion of derivative on the Wasserstein space will be introduced with helps of absolutely continuous curves. As application, we will present R. Jordan,D. Kinderlehrer and F. Otto’s Wasserstein space approach to Fokker-Planck equations.

授课地点：华中科技大学东校区恩明楼813室

具体授课时间及主题：

6月8-10日9点 -11点： Long time behavior of gradient flow generated by convex functions, introduction of Wasserstein distance as well as Kantorovich-Rubinstein dual formula.

6月11-13日8点30- 10点30: Verification of three conditions of distance, completeness, relation with weak convergence.

6月14-16日15点 - 17点: Introduction of absolutely continuous curves, continuity equation, intrinsic notion of derivatives on the Wasserstein space.

6月17-18日8点30- 10点30: De Giorgi iteration scheme, R. Jordan,D. Kinderlehrer and F. Otto’s Wasserstein space approach to Fokker-Planck equations.