Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Some arithmetic and geometric problems in complex ball quotients

Sai Kee Yeung (Purdue University)

Abstract:  The purpose of the talk is to explain several instances in which  arithmetics are used to understand geometry or vice versa, mainly on  complex ball quotients.  The first is the use of arithmetics in the classification  of fake projective planes.  The second is on finiteness of integral points on  complex two ball quotients of finite volume.  The last is to explain some examples  for a problem of Lang on transcendence of the uniformizing radius of a hyperbolic Riemann surface.