# UBC Mathematics Colloquium

## Modular representations of p-adic groups

### Mon., Jan. 18, 2010, 4:00pm, MATX 1100

Abstract:

The Langlands program relates complex representations of GL_n(Q_p) to
Galois representations. For n = 1 this is explained by class field
theory and for n = 2 this is closely related to the theory of modular
forms. For general n, this is now understood by the work of
Harris-Taylor and Henniart. In the last decade, a mod-p (as well as a
p-adic) version of the Langlands program have been emerging, and they
have already played an important role in some recent progress in number
theory. But so far understanding has been limited to n = 1 and 2. We
survey some of the known story in the classical and in the mod p case,
and then discuss some recent progress on the classification of mod p
representations of GL_n(Q_p), as time permits.