## Number Theory - Peng-Jie Wong

### Wednesday, November 15th, 2017

**Time:** 1:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Peng-Jie Wong

**Title:** Base change and the Langlands reciprocity conjecture

**Abstract:** In light of Artin reciprocity, Langlands enunciated a reciprocity conjecture asserting that any complex Galois representation is automorphic. Around 1980, Langlands established certain cyclic base change and proved his reciprocity conjecture for 2-dimensional Galois representations with projective image isomorphic to $A_4$. In this talk, we will try to give a motivation of the Langlands reciprocity conjecture and discuss its relation to base change. If time permits, we will explain how the conjectural base change leads to Langlands reciprocity for all 3-dimensional Galois representations with solvable image.

This is a joint work with M. Ram Murty and V. Kumar Murty