An introduction to modular representation theory
For a fixed prime p Richard Brauer introduced, in the 1950's, a theory of "p-modular characters" for a finite group G. Now known as Brauer characters, these are a powerful tool linking the characteristic p representation theory of G with the representation theory in characteristic 0. Some of the deepest problems in group representation theory deal with understanding the nature of this connection. I this talk I will define Brauer characters, describe some of their fundamental properties, and discuss some of the major open problems in the area.
(Bagels and refreshments will be served.)