## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** A p-adic Jacquet-Langlands Correspondence

**Speaker:** Erick Knight

**Speaker Info:** Harvard University

**Brief Description:**

**Special Note**:

**Abstract:**

I will construct a $p$-adic Jacquet-Langlands correspondence, which is a correspondence between Banach space representations of $\text{GL}_2(\mathbb{Q}_p)$ and Banach space representations of the unit group of the quaternion algebra $D$ over $\mathbb{Q}_p$. The correspondence satisfies local-global compatibility with the completed cohomology of Shimura curves, as well as a compatibility with the classical Langlands correspondence, in the sense that the $D^\times$ representations can often be shown to have the expected locally algebraic vectors.

**Date:** Monday, October 26, 2015

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Yifeng LIu

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

**Contact Phone:**

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