London Heilbronn Colloquia - London Heilbronn Colloquiua. Online registration by Cvent

The London Heilbronn Colloquia are a series of triannunal lectures by distinguished mathematicians and theoretical physicists at the forefront of current research. They are aimed at a general mathematical audience and informal interaction with the speaker is invited.

The lectures are normally accompanied by a reception. The lectures rotate between Imperial College London, King's College London and University College London. Attendence is free, but registration is usually required.

The London Heilbronn Colloquia are supported by funding from the Heilbronn Institute for Mathematical Research.

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.