110.618: Number Theory II

Spring 2020

This course will focus on automorphic L-functions. "All" L-functions (e.g., those associated to diophantine equations or Galois representations) are conjecturally — by Langlands reciprocity — equal to automorphic L-functions, so the goal of this course will be to discuss how we define those, and how we study them. The course will meet on TTh 12:00PM - 1:15PM, at Krieger 204. Contents:
1) The automorphic quotient space
2) Local harmonic analysis
3) Global harmonic analysis
4) Automorphic L-functions
5) Period integrals
6) The L-function of a spherical variety
We will finish with some discussion of ongoing work in the geometric Langlands setting.

Course notes are available on the nascent Automorphic project. Unfortunately, for technical reasons, this is only available within the JHU network, for now. (If the server is down, please send me an email.)