This is a weekly student number theory seminar organized by Thomas Browning, Sug Woo Shin, and Bobby Zhang. This webpage is maintained by Bobby Zhang.
We meet every Tuesday from 1:10 pm to 2:00 pm at Evans 939.
The main theme is to study the case of GL(1) and GL(2). Starting with the Tate’s thesis (the GL(1) case), we first see the general construction for general fields (number fields, function fields) and then work out carefully on Q as an example. Then the story of GL(2) begins with a review of modular forms and Hecke theory.
| Lectures | Time | Lecturer | Content | Lecture Notes |
|---|---|---|---|---|
| 1 | 9/7/2021 | Thomas Browning | Tate’s thesis (I) | Lecture 1 |
| 2 | 9/14/2021 | Thomas Browning | Tate’s thesis (II) | Lecture 2 |
| 3 | 9/21/2021 | Bobby Zhang | Tate’s thesis over Q, a motivation | Lecture 3 (i), Lecture 3 (ii) |
| 4 | 9/28/2021 | Xiaoyu Niu | Review of classical modular forms | |
| 5 | 10/5/2021 | Xiaoyu Niu | Hecke theory | |
| 6 | 10/12/2021 | Thomas Browning | Weil’s converse theorem | Lecture 6 |
| 7 | 10/26/2021 | Bobby Zhang | Classical automorphic forms (I) | Lecture 7,8 |
| 8 | 11/2/2021 | Bobby Zhang | Classical automorphic forms (II) | |
| 9 | 11/9/2021 | Fangu Chen | Maass forms and real analytic Eisenstein series (I) | Lecture 9,10 |
| 10 | 11/23/2021 | Fangu Chen | Maass forms and real analytic Eisenstein series (II) | |
| 11 | 11/30/2021 | Rose Lopez | Adelic automorphic forms | Lecture 11 |
| 12 | 12/7/2021 | Thomas Browning | General automorphic forms and representations | Lecture 12 |
Resource/materials
- Textbooks: Gelbart’s book Automorphic Forms on Adele Groups, Goldfeld and Hundley’s book Automorphic Representations and L-Functions for the General Linear Group (I) .
- History of modular/automorphic forms: the first answer of this question, section 1.3 of the first article “A Glimpse at the Genesis of the Langlands Program” in the book The Genesis of the Langlands Program;
- Maass forms and spectral theory “Can you hear the shape of a drum?”: Section 2.6.3 of this;
- Langlands-Shahidi Method: Section 1 of this;
Numberingeometry 