p-adic Afternoon

Get ready for a p-adic (representation theory) afternoon! On October 3rd, we're hosting three talks by distinguished mathematicians: Claus Sorensen (UC San Diego), Justin Trias (University of East Anglia), Mishty Ray (UBC).

Mishty Ray
Title: Geometric analogues to local Arthur packets for p-adic groups
Abstract: Local Arthur packets are sets of representations of p-adic groups that help us realize an important classes of automorphic representations. Vogan’s geometric perspective on the local Langlands correspondence establishes a bijection between equivalence classes of smooth irreducible representations of $G$, along with its pure inner forms, and simple equivariant perverse sheaves on a moduli space of Langlands parameters. This gives us the notion of an ABV-packet attached to a Langlands parameter. Conjecturally, ABV-packets are generalized A-packets; we call this Vogan's conjecture. I will set up the geometric perspective on the local Langlands correspondence with examples, and establish the statement of the main conjecture. I will report on the progress of the conjecture and, time permitting, sketch the main ingredients of the proof in the case of general linear groups and odd special orthogonal groups.

Justin Trias
Title: The universal Harish-Chandra j-function
Abstract: The Harish–Chandra μ-function plays a central role in the explicit Plancherel formula for a p-adic group G. It arises as the normalising factor for the Plancherel measure on the unitary dual of G, and is defined through the theory of intertwining operators. In this talk, we show how to extend the construction of the μ-function—or more precisely its inverse, the j-function—to all finitely generated representations, and over general coefficient rings such as Z[1/p]. This leads to a universal j-function with values in the Bernstein centre, which specialises to the classical j-function. Beyond its role in harmonic analysis, the universal j-function also encodes arithmetic information: it reflects aspects of the local Langlands correspondence for classical groups, via Mœglin’s criterion and its connection to reducibility points of parabolically induced representations. Time permitting, we will illustrate how this perspective applies to the study of the local Langlands correspondence in families. This is joint work with Gil Moss.

Claus Sorensen
Title: Support theories 
Abstract: I will give an overview of various notions of localization and support in the context of the derived category of smooth mod p representations of a p-adic Lie group. 

Join Us for Lunch

Before the talks, we are organizing a lunch in the PIMS lounge starting at noon. It's a great opportunity to connect with fellow researchers and students. To help us get a headcount for lunch, please fill out this quick survey in the button below:

REGISTER

Please submit your response by Friday at 3:00 PM, or no later than Monday, September 29th, at 2:00 PM.

Everyone is welcome!