Title: Introduction to the arithmetic of modular forms.

Date: 09/26/2017

Time: 3:00 PM - 3:50 PM

Place: C304 Wells Hall

Speaker: John Bergdall, MSU

This is part of a 3 lecture series. The ultimate purpose of this lecture series is to explain a recent conjecture made jointly with Robert Pollack. The conjecture itself is about coarse p-adic invariants of modular forms called slopes, which are nothing other than the norms of the eigenvalues of a certain operator. By way of motivation, I will start by first discussing modular forms with a bias towards the arithmetic context of the Langlands program. The second talk will be reserved for exposing what one might call p-adic methods for modular forms. These have been around since the 70’s and 80’s and they are central to research on “p-adic Langlands” over the past 15 years. Finally, I will aim to state precisely the conjecture (called the ghost conjecture) Pollack and I have made and explain its numerical and theoretical evidence.