Seminar series
Date
Fri, 14 Mar 2025
16:00
16:00
Location
L1
Speaker
Glenn Stevens
Organisation
Boston University
This will be an expository lecture intended for a general mathematical audience to illustrate, through examples, the theme of $p$-adic variation in the classical theory of modular forms. Classically, modular forms are complex analytic objects, but because their Fourier coefficients are typically integral, it is possible to also do elementary arithmetic with them. Early examples arose already in the work of Ramanujan. Today one knows that modular forms encode deep arithmetic information about elliptic curves and Galois representations. Our main goal will be to illustrate these ideas through simple concrete examples.