Speaker: Elon Lindenstrauss (NYU/Clay Mathematics Institute)
Title: Dynamics on the Space of Lattices and Number Theory
Abstract: A very active area of current research is dynamics on locally homogeneous spaces. The simplest, and arguably the most important example is SLn(R) / SLn(Z), which can be identified with the space of lattices in Rn which have a fundamental domain of volume 1. I will discuss how this is related to many number theoretic questions, including Littlewood's conjecture on simultaneous Diophantine approximations.