Informal working seminar on pure Arthur packets for twisted groups, and ABV/micropackets for twisted groups.

Location: Calgary and Bonn and Lethbridge and https://zoom.us/j/804455137

Speakers: Clifton and Andrew

Locations: Calgary and Hamilton and online at https://zoom.us/j/331313516

Speakers: Bin and Clifton

Locations: Calgary and Paris and online at https://zoom.us/j/331313516

Title: Arthur packets and Adams-Barbash-Vogan packets for p-adic groups

Speakers: Bin Xu and Clifton Cunningham

https://www.mfo.de/occasion/1721/www_view

Title: Applications of algebraic microlocal analysis in symplectic geometry and representation theory
Location: BA6183, Bahen Center, 40 St. George St.
Speaker: James Mracek
Speaker URL: http://blog.math.toronto.edu/GraduateBlog/files/2017/01/ut-thesis-002.pdf
Institution: University of Toronto

PhD Advisors: Lisa Jeffrey – Clifton Cunningham

***

This thesis investigates applications of microlocal geometry in both representation theory and symplectic geometry. Accordingly, there are two bodies of work contained herein.

The first part of this thesis investigates a conjectural geometrization of local Arthur packets. These packets of representations of a p-adic group were invented by Arthur for the purpose of classifying the automorphic discrete spectrum of special orthogonal and symplectic groups. While their existence has been established, an explicit construction of Arthur packets remains difficult. In the case of real groups, Adams, Barbasch, and Vogan showed how one can use a geometrization of the local Langlands correspondence to construct packets of equivariant D-modules that satisfy similar endoscopic transfer properties as the ones defining Arthur packets. We classify the contents of these “microlocal” packets in the analogue of these varieties for p-adic groups, under certain restrictions, for a plethora of split classical groups.

The goal of the second part of this thesis is to find a way to make sense of the Duistermaat-Heckman function for a Hamiltonian action of a compact torus on an infinite dimensional symplectic manifold. We show that the Duistermaat-Heckman theorem can be understood in the language of hyperfunction theory, then apply this generalization to study the Hamiltonian T×S1 action on ΩSU(2). The essential reason for introducing hyperfunction theory is that the local contribution to the Duistermaat-Heckman polynomial near the image of a fixed point is a Green's function for an infinite order differential equation. Since infinite order differential operators do not act on Schwarz distributions, we are forced to use this more general theory.

https://seminars.math.toronto.edu/seminars/list/events.py/process?action...

Speaker: Clifton Cunningham

Title: Arthur packets packets for p-adic groups and vanishing cycles of perverse sheaves

Abstract: This talk will explain how to adapt the approach developed by Adams-Barbasch-Vogan to Arthur packets from Real groups to p-adic groups, and will illustrate this adaptation with several examples. We will also sketch a proof showing that Arthur packets are p-adic ABV packets for unipotent representations of p-adic special orthogonal groups.

Joint with: Bin Xu, Ahmed Moussaoui, Andrew Fiori, James Mracek

https://www-math.umd.edu/research/seminars/lie-groups-and-rep-theory-sem...

Speaker: Lassina Dembélé, Max Planck Institut für Mathematik

Abstract: In this talk, we discuss the existence of certain lifts of Hilbert modular forms. We then use those lifts to provide theoretical evidence for a conjecture of Dick Gross on the modularity of abelian varieties not of GL_type.
(This is joint work with Clifton Cunningham.)

Location: MS 337 and https://zoom.us/j/344804314

https://zoom.us/j/344804314

Update on the paper.
Sketch of the proof of Conjecture 1.
Cuspidal support decomposition, revisited.