MATH 6140: Topics in Analysis (spring 2009)

Instructor: John Smillie

This course will serve as the second semester of ergodic theory following Seonhee Lim's course. We will study the ergodic theory and topological dynamics of group actions on homogeneous space and some of its analogs. Topics will include Ratner's theorems on the horocycle flow, the Oppenheim conjecture and the asymptotics of closed geodesics on polygonal billiard tables.

Lectures will come from some combination of the following sources: the book by Bekka and Mayer on "Ergodic theory and topological dynammics of group actions"; the book by David Morris, "Ratner's theorems on unipotent flows" and lecture notes by Eskin, Einsiedler and Kleinbock.