Speaker: Professor Ouyang Cheng
Topic: Parabolic Anderson Model on Compact Manifolds
Date: August 13th, 2024 (Tuesday)
Time: 3.00 p.m.
Venue: Academic Lecture Hall 1709, Jingyuan Building
Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology
Biography:
Ouyang Cheng is a professor at the University of Illinois at Chicago. He received his Ph.D. from Northwestern University in 2009, his supervisor is the famous probabilist Professor Elton P. Hsu. He conducted postdoctoral research at Purdue University from 2009 to 2011, and has worked in the Department of Mathematics at the University of Illinois at Chicago since 2011. He is mainly engaged in the research of stochastic analysis on manifolds, rough path theory and fractional Brownian motion. He has published more than 20 papers in authoritative journals such as AOP, TAMS, JFA, etc.
Abstract:
We introduce a family of intrinsic Gaussian noises on compact manifolds that we call “colored noise” on manifolds. With this noise, we study the parabolic Anderson model (PAM) on manifolds. Under some curvature conditions, we show the well-posedness of the PAM and provide some preliminary (but sharp) bounds on the second moment of the solution.