Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Julia Gordon

Contact: lior

math.ubc.ca

MATX 1112

604-827-3031

Fall 2023: Modular Forms

This will be an introductory course in modular forms.

Meetings: Fridays 11:00-13:00 at MATH 126.
Graduate students can take the seminar for credit by signing up for MATH 592A, section 101.
Organizational meeting: Friday September 9th, 12:30 at MATH 126.

Agenda

Section references are to [1] unless noted otherwise.

Meeting	Title	Speaker	Material	Notes
0. 8/9	Organization	n/a	n/a
1. 15/9	Introduction	Lior Silberman		notes
2. 22/9	Riemann surfaces	Simone Maletto	[2] Ch. 1	Also [1] Ch. 2
3. 29/9	Modular forms	Shubhrajit Bhattacharya	[1] Ch. 1	Also [2] Ch. 2 & 4
4. 6/10	Interlude: some algebraic geometry	Souptik Mudi
5. 13/10	(continued)
6. 20/10	Hecke operators	Tam Nguyen	[1] §§5.1-5.5	also [2] §§2.7-8, 4.5
7. 27/10	(continued)
8. 3/11	Newforms & L-functions	Ethan Armitage	[1] §§5.6-5.10	also [2] §§4.3,4.6
9. 10/11	Weil's Converse Theorem	Zhengheng Bao	[2] §4.3
10. 17/11	(continued)
11. 24/11	Modular curves	Nicky Priebe	[1] Ch. 7
12. 1/12	The Eichler-Shimura relation	Atonu Mukherjee	[3] Ch. XI
13. 8/12	(continued)

References

	Author(s)	Title	Data
[1]	Diamond & Shurman	A First Couse in Modular Forms	Springer, 2005
[2]	Miyake	Modular Forms	Springer, 1989
[3]	Knapp	Elliptic curves	Princeton Univeristy Press, 1992

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