## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** On p-adic families of admissible representations of GL_2(Q_l).

**Speaker:** Professor David Helm

**Speaker Info:** UT Austin

**Brief Description:**

**Special Note**:

**Abstract:**

The local Langlands correspondence for GL_2 associates an admissible
representation of GL_2(Q_l) to every Frobenius-semisimple two-dimensional
representation of the Weil group W of Q_l. It is an interesting question
to try to extend this correspondence to p-adic families of representations
of W- that is, given a p-adic family of representations of W, construct a
corresponding family of admissible representations of GL_2(Q_l). Recent work of Emerton gives a set of
properties that uniquely characterise such
a family. We show how to construct such families using deformation-theoretic arguments.

**Date:** Monday, December 1, 2008

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Florian Herzig

**Contact email:** herzig@math.northwestern.edu

**Contact Phone:** 847-467-1898

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