勷勤数学•专家报告

题      目：On Well-posedness of Mean Field Game Master Equations: A Unified Approach

报  告  人：牟宸辰 助理教授  (邀请人：杨舟)

                                      香港城市大学

时      间： 12月23日  10：00-11:00

地     点：数科院东楼401

报告人简介:

       牟宸辰，香港城市大学助理教授，国家青年人才，于2016年获得美国佐治亚理工学院的数学博士学位，2016-2020年间在加州大学洛杉矶分校做博士后，主要从事平均场博弈理论的研究工作，已在JEMS, Memoirs of the AMS, Ann. Probab., Ann. Appl. Probab., Anal. PDE, Comm. Math. Phys., Trans. Amer. Math. Soc.等国际权威期刊上发表论文数篇。

摘      要：

       It is well known that the global (in time) well-posedness of mean field game master equations relies on certain monotonicity conditions, and there have been several types of conditions proposed in the literature. In this talk we intend to provide a unified understanding on the role of monotonicity conditions in the theory. Inspired by Lyapunov functions for dynamical systems, we propose a general type of monotonicity condition, which covers all the existing ones as special cases and is essentially necessary for the existence of Lipschitz continuous classical solutions. Our approach works for very general mean field games, including extended mean field games and mean field games with volatility control. In particular, for the latter a new notion of second order monotonicity condition is required. The talk is based on some ongoing joint works with Jianfeng Zhang and Jianjun Zhou.

          欢迎老师、同学们参加、交流！