Student Seminar on Automorphic Forms

Introduction

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.

References

[1] Daniel Bump, Automorphic Forms and Representations, Cambridge Studies in Advanced Mathematics, 1997. Amazon link
[2] Dorian Goldfeld, Automorphic Forms and L-Functions for the Group GL(n,R), Cambridge Studies in Advanced Mathematics, 2006. Amazon link
[3] Henri Darmon, Topics in Number Theory: L-functions and modular forms, Lecture Notes. Link
[4] J.W. Cogdell, Converse Theorem, Functoriality and Applications, Expository Paper. Link
[5] Henryk Iwaniec, Spectral Methods of Automorphic Forms: Second Edition. AMS Store link

Schedule

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

Topics Covered

Serial No.	Date	Speaker	Abstract	Notes
1	16-Sep	Aditya Ghosh	Quick recap of Modular Forms, Hecke Operators, Twisting	[1] Chapters 1.1 - 1.5
2	23-Sep	Aditya Ghosh	Rankin-Selberg Method, Converse Theorems, Langlands Functoriality	[1] Chapters 1.6 - 1.8, [3] Lec 20 - 24 and [4]
3	30-Sep	Aditya Ghosh	Hilbert Modular Forms, Maass Forms and Base Change	[1] Chapters 1.7, 1.9 - 1.10
4	07-Oct	Austin Lei	Discrete group action of SL(n,Z) on SL(n,R): Generalized upper half plane, Siegel sets and Haar Measure. We also look at invariant differential operators and their eigenfunctions.	[2] Chapters 1, 2, Notes
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, Notes
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, [5]
7	28-Oct	Alex Pascadi (Oxford)	(Virtual) Special topic: The dispersion method and beyond: from primes to exceptional Maass forms	Arxiv paper
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	Super-positivity for L-functions associated to modular forms
12	02-Dec	Alan Zhao	Maass Forms and Whittaker Functions for SL(n,Z)	[2] Chapter 5
13	09-Dec	Aditya Ghosh	Tate's Thesis	[1] Chapter 3.1,3.2

Introduction

References

Schedule

Topics Covered

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