number theory seminar

[William Stein]

Hi,

Rob Harron will give the next Number Theory Seminar:

Speaker: Rob Harron (University of Wisconsin)

Title: Computing Hida families

Date: Thursday, October 18 at 10:30am in Padelford C401.

Abstract: I will report on joint work with Rob Pollack, Evan Dummit,
Marton Hablicsek, Lalit Jain, and Daniel Ross on explicitly computing
Hida families using overconvergent modular symbols. This grew out of a
project at the Arizona Winter School and the basic idea is to study
p-adic families of overconvergent modular symbols. I will go over the
basic definitions starting from modular symbols themselves and explain
how one goes about encoding these objects on a computer. Aside from
being able to compute formal q-expansions of Hida families, we can
also compute the structure of the ordinary p-adic Hecke algebra,
L-invariants, two-variable p-adic L-functions, etc. Several examples
will be provided. The code is implemented in Sage.