From Representations of P-Adic Groups to Congruences of Automorphic Forms

Explore a lecture on the connections between p-adic group representations and automorphic form congruences. Delve into the Global Language Correspondence, Algebraic Automorphic Forms, and the theory of types as presented by Jessica Fintzen from Duke University and the University of Cambridge. Examine general representations, compact open subgroups, and the construction of theoretical data. Gain insights into the omni supercast concept and its examples. Follow the exhaustion proof and understand its implications in this advanced mathematical discourse, part of the 2021 Fields Medal Symposium honoring Peter Scholze.

Introduction
Remarks
Setup
Global Language Correspondence
Algebraic Automorphic Forms
representations of padic groups
general representations
theorem
theory of type
example
omni supercast
omni supercast example
compact open subgroups
input
compact open
exhaustion proof
construction of theoretical data