Abstract：
In 1781, G. Monge raised the optimal transport problem from the engineering study. In 1940s, L. Kantorovich relaxed the Monge problem and applied his method to study the optimization problems in economics. In 1975, he was awarded the Nobel prize in economics. In 1992, Y. Brenier solved the Monge-Kantorovich optimal transport problem for quadratic cost function. Since then, the optimal transport problem has been intensively studied by many people, including the Fields medalists C. Villani and A. Figalli. On the other hand, entropy, which was introduced in the study of thermodynamics and statistical mechanics, has played very important role in kinetic theory, information theory, PDEs and geometric analysis. In 2012, G. Perelman introduced the mysterious W-entropy for the Ricci flow and proved the non collapsing theorem. In this talk, we will briefly recall the history of the optimal transport problem, and present some recent results on the study of the optimal transport problem and the W-entropy.
Biography:
Xiangdong Li, Hua Loo Keng Chair Professor in Applied Mathematics at Academy of Mathematics and Systems Science, Chinese Academy of Sciences, is an expert in Stochastic Analysis and Stochastic Differential Geometry. He obtained his PhD from the Institute of Applied Mathematics of CAS and the University of Lisbon in 1999. After being a Postdoctoral Researcher at the University of Oxford during 2000-2003, he had worked as a Maitre de Conference and obtained HDR (Habilitation a Diriger de Rechercher) at the University Paul Sabatier in 2007. After one year Full Professorship at Fudan University, he moved to AMSS CAS in 2009 as a Hundred Talent Researcher and has worked there until now.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai