Number Theory Seminar

Speaker: Ian Kiming (KU)

Title: Eisenstein series and overconvergence

Abstract: I will talk about recent work with Nadim Rustom on the rate of overconvergence of certain modular functions that arise from classical Eisenstein series. Knowledge of this kind can be put to use to understand the finer structure of the Coleman-Mazur eigencurve, in concrete terms, this knowledge has implications for the study of Coleman families passing through classical forms. Among other things we prove a theorem that is a direct generalization of a theorem of Coleman-Wan that was instrumental in Wan's celebrated work regarding the Coleman-Mazur conjecture. Other of our theorems are general versions for p≥5 of statements that were proved for p=2 and p=3 by Buzzard-Kilford and Roe, respectively, in their work on what is now known as the 'halo conjecture'.
I will start the talk very lightly with an introduction to overconvergent modular forms for the benefit of those in the audience who might not know about it or need to be reminded a bit.

The talk will take place on Zoom. If you would like to receive the Zoom link and are not part of our current NT Seminar mailing list, please contact the organizer.