Welcome to the Learning Seminar on Automorphic Forms. This seminar aims to provide an introduction to automorphic forms. We'll follow the books by Bump (Automorphic Forms and Representations) and Goldfeld (Automorphic Forms and L-Functions for the Group GL(n,R)) . We'll also have some guest lectures from other universities on more specialised topics like: Sieve methods for Automorphic forms and Hida Families.
Organisers: Aditya Ghosh, Alan Zhao, Austin Lei
Date: Mondays, 16th September - 9th December 2024
Time: 4 PM - 5:15 PM
Location: Room 507, Mathematics Hall
| Serial No. | Date | Speaker | Abstract | Notes |
|---|---|---|---|---|
| 1 | 16-Sep | Aditya Ghosh | Quick recap of Modular Forms, Hecke Operators, Twisting, Rankin-Selberg Method | [1] Chapters 1.1 - 1.6 |
| 2 | 23-Sep | Aditya Ghosh | Introduction to Hilbert Modular Forms, Langlands Functoriality | [1] Chapters 1.6 - 1.8 |
| 3 | 30-Sep | Aditya Ghosh | Maass Forms and Base Change. Introduction to the discrete group action of SL(n,Z) on SL(n,R) and Iwasawa decomposition. | [1] Chapters 1.8 - 1.10, [2] Chapter 1 |
| 4 | 07-Oct | Austin Lei | Properties of the discrete group action introduced before: generalized upper half plane, Siegel sets and Haar Measure. We also look at invariant differential operators and their eigenfunctions. | [2] Chapters 1, 2 |
| 5 | 14-Oct | Austin Lei | Automorphic Forms and L-functions for SL(2,Z). Fourier-Whittaker Expansion, Selberg Eigenvalue Conjecture, Hecke operators, L functions for Eisenstein series and Maass forms. | [2] Chapter 3 |
| 6 | 21-Oct | Alan Zhao | Automorphic Forms and Representations of GL(2,R): Spectral Problem, quick recap of Lie Theory, Discreteness of the Spectrum | [1] Chapters 2.1 - 2.4 |
| 7 | 28-Oct | Alex Pascadi (Oxford) | (Virtual) Special topic: Automorphic Forms and Sieve Methods | |
| 8 | 04-Nov | - | (no seminar today) | - |
| 9 | 11-Nov | Alan Zhao | Automorphic Forms and Representations of GL(2,R): Unitaricity and Intertwining Integrals, Representations and the Spectral Problem, Whittaker Models | [1] Chapters 2.5 - 2.9 |
| 10 | 18-Nov | Austin Lei | Existence of Maass Forms | [2] Chapter 4 |
| 11 | 25-Nov | Prof. Dorian Goldfeld | TBD | |
| 12 | 02-Dec | Alan Zhao | Maass Forms and Whittaker Functions for SL(n,Z) | [2] Chapter 5 |
| 13 | 09-Dec | Rohit Kumar (Duke) | (Virtual) Special topic: Introduction to Hida Theory |
Aditya Ghosh: ag4794 (at) columbia (dot) edu
Alan Zhao: asz2115 (at) columbia (dot) edu
Austin Lei: ayl2158 (at) columbia (dot) edu