February 07, 2020
11:00 AM - 12:00 AM
Math Tower 5-127
|Brandon Gontmacher, Stony Brook University|
Modular Forms and Modular Curves
We will define modular forms with respect to congruence subgroups and introduce modular curves, which are Riemann surfaces associated to each congruence subgroup, defining cusps and elliptic points along the way. The goal of the talk is to find a formula for the genus of the modular curve. The material will mostly follow up to section 3.1 in Diamond and Shurman's A First Course in Modular Forms but other good references include the books by Shimura and Lang and Serre's Course in Arithmetic.