报告题目：Parabolic and hyperbolic Liouville equations
报告人：Dr. Yuzhao WANG (University of Birmingham)
摘要: We will talk about some stochastic partial differential equations (SPDEs), which arise naturally in the context of Liouville quantum gravity and are proposed to preserve the Liouville measure which has been constructed recently in the work by David-Kupiainen-Rhodes-Vargas. We construct global solutions to these equations and then show the invariance of the Liouville measure under the resulting dynamics. As a by product, we also answer an open problem proposed by Sun-Tzvetkov recently.
Dr Wang is a Lecture at the University of Birmingham, School of Mathematics. His research interests lie in partial differential equations, harmonic analysis, and stochastic analysis. In particular, the study of nonlinear dispersive PDEs such as nonlinear Schrödinger equations, nonlinear wave equations, and the KdV equation by using techniques from PDEs, Harmonic Analysis, and Probability theory. Partial papers are pubilished in "Adv. Math", "SIAM J. Math. Anal.", "J. Funct. Anal.", "Comm. Partial Differential Equations.","Nonlinearity", "Proc. Lond. Math. Soc.", etc.