If you have suggestions or requests email Eugenia at rosu [at] math.berkeley.edu or Shelly at shellym [at] math.berkeley.edu.
In the Fall 2014 semester we will be studying the Langlands program, following various lecture notes.
| Date |
Topic | Speaker |
| 09/18 |
Automorphic forms | Eugenia |
| 09/25 |
Admissible representations | Alex Y. |
| 10/02 |
Automorphic representations and their L-functions | Will |
| 10/09 |
Global and local Langlands for GL_n I | Shelly |
| 10/16 |
Global and local Langlands in characteristic p | Yotam |
| 10/23 |
Langlands L-group | Dylan |
| 10/30 |
Langlands correspondence for G reductive and Langlands L-functions | Alex C. |
| 11/6 |
Langlands over functions fields | |
| 11/13 |
||
| 11/20 |
Geometric Langlands | |
| 12/10 |
||
Syllabus of talks:
Automorphic forms: defining modular forms, classical automorphic forms, space of adelic automorphic forms. Cuspidal automorphic forms. Automorphic forms on general groups. Definition of automorphic representations. Fourier expansion and Whittaker functions.
Admissible representations: defining admissible representations; Smooth (also called class one) representations. Hecke algebra. Principal series representation.
Automorphic representations and their L-functions: representations of GL_n(A); Multiplicity one theorem; Tensor product theorem. L-functions: local, global, functional equation, analytic continuation.
Global and local Langlands for GL_n: Galois representations; L-functions of Galois representations; statements of local and global Langlands, Weil group.
Global and local Langlands for GL_n II: Weil-Deligne group, statements, local-global compatibility.
Langlands L-group: reductive groups; Borel subgroups; root datum; root system; Langlands L-group.
Langlands correspondence for G reductive and Langlands L-functions.
Langlands over function fields
Geometric Langlands