Valid Until: 2027-01-31 23:59
Abstract: The study of the dynamics of Teichmuller flows has in large part been inspired by the analogy with homogeneous flows, e.g an analog of Ratner's theorems for unipotent flows attained for the SL(2,R)-action on the moduli space of holomorphic differentials in the celebrated work of Eskin-Mirzakhani-Mohammadi. Interestingly, some results about homogeneous flows and the behavior of their trajectories were inspired by investigations of dynamical properties of foliations of surfaces and Teichmuller geodesic rays. In this talk, I will describe some contributions in this direction pertaining to various concepts in Diophantine approximation such as singular vectors and Khintchine-Levy constant.
Bio: Yitwah Cheung received his PhD in Mathematics in 2000 from the University of Illinois at Chicago under the direction of Howard A. Masur. After holding the position of Ralph Boas Assistant Professor at Northwestern University, he joined San Francisco State University in 2005, where he became Associate Professor in 2010 and Full Professor in 2015. He is a recipient of the Clay Mathematician Liftoff Award (2000) and NSF CAREER Award (2010-2016) and has published research articles that have appeared in Annals of Mathematics (2003,2011), Inventiones (2011) and Duke (2016) and Ann. Ecole Normale Superior (2024, to appear) on a variety of topics, including the ergodic theory of rational billiards, Teichmuller dynamics and Diophantine approximation. In 2018, he joined Tsinghua University as a member of the Yau Mathematical Sciences Center and the Mathematics Department.