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Monday, January 25, 2010

Mathematics Colloquium - Special Lecture 2009-10
4:00 pm   in 245 Altgeld Hall,  Monday, January 25, 2010
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Submitted by seminar.
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.

Please join us for refreshments at 3:30 p.m. in the Common Room, 321 Altgeld Hall.