Speaker: 汪徐家教授，西湖大学

Inviter: 流体力学方程研究中心

Title: Optimal transportation and the Monge-Amp`ere equation

Language: Chinese

Time & Venue: 2025.05.15 10:30-11:30 南楼N204

Abstract: Optimal transportation has found many applications in modern science and technology, such as optical imaging and machine learning. It has been extensively studied in the last three decades. The existence of optimal mappings can be obtained by Kantorovich’s duality. The regularity can be obtained by studying the associated Monge- Ampere type equation, which is a class of fully nonlinear partial differential equation with strong singularity. In this lecture, we will introduce optimal transportation and Kantorovich’s duality, and review the regularity theory of the Monge-Amp`ere equation. We will also present a fast and stable computational approach to its numerical solutions.