This is a joint Pure Mathematics Seminar/Number Theory Seminar venture.

Abstract: A finite group of Lie type is the group of elements of a reductive algebraic groups defined over a finite field. For example, all finite simple groups are finite groups of Lie type except for a finite list of exceptions. We will begin by describing the basic elements of the theory of characters of finite groups of Lie type, and how Springer theory plays a role. If time permits, we will proceed to discuss their possible affine generalization.