Road to the Langlands Program
The Langlands Program is a collection of ideas, theorems, and conjectures on the connection between geometry, representation theory, and number theory. The program and its underlying philosophy have played a starring role in modern research. Unfortunately one needs a huge amount of background knowledge just to understand the basic ideas of the program. The goal of this seminar series is to learn a little bit about the program. We hope that by the end, participants will have the background necessary to understand Langlands's original letter to Weil, as well as some of the work that's been done since then.
We will assume participants will have a decent familiarity with basic notions from algebraic number theory (e.g. number fields, class group), as well as a decent familiarity with basic notions from modern algebraic geometry (e.g. schemes, sheaves).
Time & Place
S. Gelbart, An Elementary Introduction to the Langlands Program
D. Garbanati, Class Field Theory Summarized
J. S. Milne, Class Field Theory