Events

Arthur-Packets for real classical groups

Speaker: Nicolás Arancibia Robert

Room: MS337 and Zoom (Join URL: https://zoom.us/j/846139176)

For classical real groups we can list three important constructions of A(rthur)-packets. We can begin by mentioning the definition due to Arthur that appears in his work on the classification of the discrete automorphic spectrum of classical groups, and that relies on techniques from harmonic analysis. A second and radically different definition is due to Adams, Barbasch and Vogan. Their approach to A-packets is by means of sophisticated geometrical methods, using the theory of perverse sheaf,
D-modules and some others tools from microlocal geometry. A third construction in the context of unitary representations with cohomology, is due to Adams and Johnson. The aim of this talk is to explain why in this latter context the three constructions coincide. If time permits, I will report on work in progress, joint with P. Mezo, in proving the more general problem that the definitions of A-packets due to Arthur and the one due to ABV are equivalent for real classical groups.

Event Date: 
Tuesday, August 20, 2019 - 11:00 to 12:30
Event Type: 

Focused Research Group: The Voganish Project (19frg277) Banff International Research Station (BIRS) for Mathematical Research and Innovation

Participants:
Clifton Cunningham, University of Calgary
Sarah Dijols, Tsinghua University
Andrew Fiori, University of Lethbridge
Ahmed Moussaoui, Université Versailles Saint Quentin
Kam-Fai Tam (Geo), Radboud University Nijmegen
Bin Xu, Yau Mathematical Sciences Center, Tsinghua University
Qing Zhang, PIMS Postdoctoral Scholar, University of Calgary
Geoff Vooys, Graduate Student, University of Calgary

http://www.birs.ca/events/2019/focussed-research-groups/19frg277

Event Date: 
Sunday, July 21, 2019 - 09:00 to Sunday, July 28, 2019 - 17:00
Event Type: 
Project: 
Voganish Project

Summation Formulas and Beyond Endoscopy

Tian An Wong (UBC)

Abstract: In this talk, I will outline the basic ideas in Langlands’ Beyond Endoscopy proposal, and the role of summation formulas and the nontempered automorphic spectrum. I will discuss the various approaches of Frenkel-Langlands-Ngô, Altug, and Ngô to the geometric side of the trace formula, and propose an alternate approach beginning on the spectral side instead.

Location: MS 337 + https://zoom.us/j/171589529

Event Date: 
Tuesday, May 14, 2019 - 11:00 to 12:30
Event Type: 

The geometry of Arthur packets

Venue: Representation Theory Seminar at University of Alberta

https://sites.ualberta.ca/~kkoziol/sem/NTRT.html

Title: The geometry of Arthur packets

Abstract: This talk uses two examples to show how Arthur parameters determine a category of equivariant perverse sheaves and how the microlocal perspective on this category reveals the Arthur packet attached to the Arthur parameter. The full picture is explained in Arthur packets for p-adic groups by way of microlocal vanishing cycles, with examples, joint with Andrew Fiori, Ahmed Moussaoui, James Mracek and Bin Xu, to appear in Memoirs of the American Mathematical Society. The talk includes some remarks on an emerging categorical local Langlands correspondence.

Event Date: 
Friday, March 22, 2019 - 14:30 to 16:00
Event Type: 
Project: 
Voganish Project

Compactification of Vogan varieties

On the compactification of mini-Vogan varieties V and the restriction functor D_P(G/P) --> D_H(V).

Clifton and Qing in Calgary, Geo in Radboud and Andrew in Lethbridge

Location: Zoom

Event Date: 
Thursday, March 21, 2019 - 07:00 to 09:00
Event Type: 
Project: 
Voganish Project

Quiver Categories

Speakers: James Steele and André de Waal

We continue our study of the quiver category A_n and the four functors

J^* : A_n --> A_0,
J_* : A_0 --> A_n,
J_! : A_0 --> A_n and
J_{!*} : A_0 --> A_n.

The goal of the talk is to prove Propositions 3.3, 3.5 and 3.6 of Section 3.2 of Tom Braden's thesis.

Event Date: 
Wednesday, March 20, 2019 - 09:00 to 10:00
Event Type: 
Project: 
Voganish Project

Update on the G(2) project

Speaker: Qing Zhang

Qing and Clifton have now computed all ABV-packets for all unipotent Arthur parameters of the exceptional group G(2). The results are summarized in this talk.

Event Date: 
Wednesday, March 13, 2019 - 09:00
Event Type: 
Project: 
Voganish Project

The Bernstein Centre and the Bernstein Decomposition

Speaker: Geoff Vooys

In this talk we will introduce the Bernstein Decomposition and describe the Bernstein Centre of the category of smooth representations of the F-rational points of a p-adic group G. We will then describe how to realize the Bernstein Centre as a ring of sections of a variety, and, time permitting, use this to explain the parametrization of the Bernstein Decomposition.

Event Date: 
Wednesday, February 6, 2019 - 09:00 to 10:30
Event Type: 

Verification of the Kazhdan-Lusztig conjecture for the subregular unipotent infinitesimal parameter for G(2)

Clifton will make a small correction to the geometric multiplicity matrix for the admissible representations of G(2) with “subregular unipotent” infinitesimal parameter.
Qing will explain that he’s found all the admissible representations and standard modules of G(2) with “subregular unipotent” infinitesimal parameter and that the multiplicity matrix matches the geometric calculation. This concludes the proof of the Kazhdan-Lusztig conjecture (as it appears in the Voganish book) for the subregular unipotent infinitesimal parameter of G(2).

Event Date: 
Wednesday, January 16, 2019 - 09:00 to 10:30
Event Type: 
Project: 
Voganish Project

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