## Introduction to Modular Forms and Congruence Primes

### Huixi Li – Clemson University

Modular forms are interesting objects in number theory. In this presentation I will first go over the proof of the Lagrange’s four squares theorem using elliptic modular forms. Second I will introduce Hilbert modular forms and Siegel modular forms, with the motivation of generalizing the four squares theorem to totally real fields. Finally I will talk about our recent result on congruence primes for Hilbert Siegel eigenforms. This is joint work with Jim Brown.