Speaker: Clifton Cunningham (University of Calgary)

Abstract: This talk demonstrates a non-invasive procedure that calculates Arthur packets, their associated stable distributions and Langlands-Shelstad transfers, without direct use of endoscopy, using certain unipotent representations of the split p-adic exceptional group G(2) as examples. In the case at hand, this procedure relies on a study of the category of GL(2)-equivariant perverse sheaves on the moduli space of homogeneous cubics in two variables, which is perhaps of independent interest. Specifically, we find the Fourier transform and the microlocalization of the simple objects in this category, and convert that into information about the Aubert involution and stable distributions attached to Arthur packets. This is joint work with Andrew Fiori and Qing Zhang, based on earlier joint work with Andrew Fiori, Ahmed Moussaoui, James Mracek and Bin Xu, which is based on earlier work by David Vogan, sadly, not joint.

This is one of Lie group seminar event of MIT, see https://researchseminars.org/seminar/MITLie

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.

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

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

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.

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

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.

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.