# $p$-adic aspects of $L$-functions and automorphic forms

### Ellen Eischen (University of Oregon)

Fri Aug 7, 00:20-01:10 (2 days ago)

Abstract: I will discuss recent developments for $p$-adic aspects of $L$-functions and automorphic forms, especially in the setting of unitary groups. With a viewpoint that encompasses several settings, including modular forms (GL$_2$) and automorphic forms on higher rank (namely, unitary and symplectic) groups, I will give a recipe for constructing $p$-adic $L$-functions that relies strongly on the behavior of associated automorphic forms. Recent developments will be put in the context of more familiar constructions of Serre, Katz, and Hida. I will also describe some challenges unique to the higher rank setting, as well as recent attempts to overcome them.

number theoryrepresentation theory

Audience: researchers in the discipline

Series comments: The Eighth Pacific Rim Conference in Mathematics will be a high profile mathematical event that will cover a wide range of exciting research in contemporary mathematics. It will be held online between Monday, August 3rd and Tuesday, August 11th, featuring nine plenary speakers and ten discipline-specific sessions.

Very brief registration for livestream info: wp.math.berkeley.edu/pacificrim2020/registration-for-sessions/

 Organizers: Erik Bates*, Alan Hammond, Fraydoun Rezakhanlou, Milind Hegde *contact for this listing

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