Special Colloquium
Florian Herzig
Northwestern University
Modular representations of p-adic groups
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.
Tuesday December 8, 2009 at 3:00 PM in SEO 636