Speaker: Sean Howe (University of Utah)

Date, time & place: February 4, 2021, 4:45 pm, online

Title: Verma modules and automorphic forms

Abstract: Verma modules for gl_2 arise naturally as the local cohomology of the line bundles O(k) at a point on P^1 (that’s just a fancy way of describing the derivative of the action of linear fractional transforms on meromorphic tails!). In this talk, we explain a few different ways this construction can be used to give rise to canonical Verma modules inside various spaces of automorphic forms (archimedean and p-adic), and speculate vaguely on the possible role of analytic completions of Verma modules in the (p-adic) Langlands program.