Summer Graduate School
|Location:||MSRI: Simons Auditorium, Atrium|
- Kevin Buzzard (Imperial College, London)
The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.
- For an introduction to the p-adic numbers there is Cassels: "Lectures on elliptic curves" -- chapter 2
- One may also enjoy reading Cassels' "Local fields" book for a more complete treatment, or Serre's "Local Fields" / "Corps Locaux" which is better suited for readers familiar with the subject
- For an introduction to modular forms there is Serre: "A Course in Arithmetic" / "Cours d'Arithmetique", last chapter
- Another very natural place to read about modular forms is "Modular Forms" by Diamond and Shurman. As general preparation for the course, Bump's book "Automorphic forms and representations" might be a good thing to look over, although our approach will be more algebraic and less analytic.
For eligibility and how to apply, see the Summer Graduate Schools homepage
Class Field Theory