Title:	Self dual perverse sheaves on certain unitary Shimura varieties
Speaker:	Rajesh Kulkarni (Michigan State University)
Abstract:	The Galois group of the rational numbers is an important object in number theory and is an active area of research. One way to understand this complicated group is to study its representations. These representations can be realized as cohomology of some spaces arising out of algebraic groups defined over the rational numbers. In order for this machine to work, one needs a self-dual cohomology theory on compactifications of these spaces. We prove that such a cohomology theory exists for certain unitary Shimura varieties. The talk will be a leisurely introduction to the circle of ideas.