Modular forms and arithmetic, II

Seminar: 
Lang Lecture
Event time: 
Thursday, April 13, 2017 - 12:15pm to 1:15pm
Location: 
215 LOM
Speaker: 
Jack Thorne
Speaker affiliation: 
University of Cambridge
Event description: 

Modular forms are holomorphic functions which admit symmetries under arithmetic groups (such as subgroups of $SL_2(Z)$). They are the key to our understanding of some of the deepest results in algebraic number theory.

In my first lecture, I will introduce some famous (and classical) Diophantine equations and explain how modular forms can be used to study their solutions. In my second lecture, I will introduce the notion of potential modularity, and discuss its role in our understanding of L-functions and Galois groups.