##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Ana Caraiani

#### Princeton University

## Patching and the $p$-adic local Langlands program for $\mathrm{GL}_2(\mathbb{Q}_p)$

##### Abstract:

I will explain a new construction and characterization of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$. This is joint work with Emerton, Gee, Geraghty, Pa\v{s}k\={u}nas and Shin and relies on the Taylor-Wiles patching method and on the notion of projective envelope. Please note the unusual time for this week's seminar (10:00 am).

Host: Kiran Kedlaya

### January 14, 2016

### 9:00 AM

### AP&M 7321

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