Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)
Introduction to Optimal Transport with Application to Geometric Inequalities
Kai-Hsiang Wang (Northwestern University)
Abstract
In this talk, I will first give an introduction to optimal transport (OT) theory and recall some fundamental results. This will then be illustrated by the common scenario where the cost function is given by distance squared and the measures are absolutely continuous. Under these assumptions, I will show the classical theorems of Brenier and McCann about OT maps for Euclidean spaces and manifolds, respectively, as well as the connection to the Monge-Amp\'ere equation and some geometric inequalities. After that, I will mention my previous work generalizing McCann's theorem to a submanifold setting and its application to the Michael-Simon inequality.
WebEx Link: TAB
Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chung-Jun Tsai (NTU)
