Wednesday, March 1st, 2006
11:00am - 12:00pm, in Science 3-028

Alistair Savage

University of Toronto

Quiver Varieties and Geometric Representation Theory

Abstract: Recently, there has been considerable interest in the field of geometric representation theory. In this talk, we will begin with an overview of the area, paying special attention to the method of quiver varieties. This method involves constructing Kac-Moody Lie algebras and their representations in the homology of varieties attached to quivers, or oriented graphs. We will discuss the connections to several branches of representation theory. In particular, we will describe a recent result using the theory of quiver varieties to give a geometric realization of the important boson-fermion correspondence. We will also discuss recent work on geometric realizations of crystal graphs, which can be viewed as the q=0 limit of quantum groups.