Student Seminar on Automorphic Forms

Introduction

Welcome to the Learning Seminar on Automorphic Forms. This seminar aims to provide an introduction to automorphic forms, continuing on the seminar last semester. 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: TBD

Time: TBD

Location: TBD

Topics Covered

Serial No.	Date	Speaker	Abstract	Notes
1	27-Jan	Austin Lei	Maass forms and Whittaker functions for SL(n, Z): We will discuss Maass forms and their Fourier expansions for SL(n, Z). We will also discuss the construction of the Jacquet Whittaker function and their functional equation.	[2] Chapter 5
2	3-Feb	Alan Zhao	Vogan diagrams for real semisimple Lie groups: The existence of a Cartan involution distinguishes compact and non-compact Lie groups simply yet precisely. Whereas these adjectives are usually placed as assumptions at the outset, the classification of real Lie groups depends on how they intertwine, i.e. the Cayley transform. This talk will further realize these details.	TBD
3	10-Feb	Austin Lei	Automorphic forms and L-functions for SL(3, Z)	[2] Chapter 6
4	17-Feb	Aditya Ghosh	TBD	[1] Chapter 2.5 - 2.6
5	24-Feb	Austin Lei	The Godement-Jacquet L-function	[2] Chapter 9
6	3-Mar	Alan Zhao	TBD	TBD
7	10-Mar	Austin Lei	Langlands Eisenstein Series	[2] Chapter 10
8	17-Mar	-	Spring Break, no seminar	-
9	24-Mar	Austin Lei	Langlands Eisenstein Series (Part 2)	[2] Chapter 10
10	31-Mar	Aditya Ghosh	TBD	[1] Chapter 2.7 - 2.9
11	7-Apr	Aditya Ghosh	TBD	TBD
12	14-Apr	Alan Zhao	TBD	TBD
13	21-Apr	Aditya Ghosh	TBD	TBD
14	28-Apr	Alan Zhao	TBD	TBD
15	5-May	Aditya Ghosh	TBD	TBD

Introduction

References

Schedule

Topics Covered

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