**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
SL_{n}(**R**) / SL_{n}(**Z**), which can be identified with the
space of lattices in
**R**^{n} 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.