## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Local deformation rings when \(l \neq p\)

**Speaker:** Jack Shotton

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

Given a mod p representation of the absolute Galois group of \(Q_l\), consider the universal framed deformation ring R parametrising its lifts. When l and p are distinct I will explain a relation between the mod p geometry of R and the mod p representation theory of \(GL_n(Z_l)\), that is parallel to the Breuil-Mézard conjecture in the \(l = p\) case. I will give examples and say something about the proof, which uses automorphy lifting techniques.

**Date:** Monday, February 29, 2016

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Yifeng Liu

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

**Contact Phone:**

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