A-packets for quasisplit GSp(2n) and GSO(2n) over a p-adic field

Speaker: Bin Xu,

Arthur (1989) conjectured that the discrete spectrum of automorphic representations of a connected reductive group over a number field can be decomposed into global A-packets, in terms of which he also conjectured a multiplicity formula. Arthur (2013) proved his conjectures for symplectic and orthogonal groups, in which case the global A-packets are parametrized by self-dual automorphic representations of general linear groups. In this talk, I will give a construction of the local A-packets for general symplectic and general even orthogonal groups in the nonarchimedean case. This is based on our earlier works in the tempered case, and it follows a construction by Moeglin for symplectic and orthogonal groups.

Zoom: 846139176

Event Date: 
Thursday, September 24, 2020 - 08:30 to 10:00
Event Type: 

Quivers and their representations

Speaker: James Steele

Abstract: In this talk, we will give an introduction to quivers and their representations.

Talk on Zoom: 846139176.

Event Date: 
Thursday, September 17, 2020 - 08:30 to 09:30
Event Type: 

Distinguished Arthur parameters and relative discrete series

Speaker: Jerrod Smith,

Abstract: In this talk, we will report the recent progress on representations of GL(2n) distinguished by symplectic group Sp(2n) and those representations distinguished by unitary groups.

Reference: Jerrod Smith, Speh representations are relatively discrete, to appear in Representation Theory (2020).

Zoom Link: 846139176

Event Date: 
Thursday, July 30, 2020 - 08:30 to 09:30
Event Type: 

Endoscopic transfer from PGL(3) to G_2

Speaker: Qing Zhang,

Abstract: In this talk, we will give an introduction of the unipotent representations of PGL_3 and its pure inner forms and the transfer of these representations, following work by Gan & Savin.

Talk via Zoom: 846139176

Event Date: 
Wednesday, June 17, 2020 - 08:30 to 09:30
Event Type: 

Arthur packets for G(2) and perverse sheaves on cubics

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

Event Date: 
Thursday, May 7, 2020 - 16:30 to 17:30

Arthur-Packets for real classical groups

Speaker: Nicolás Arancibia Robert

Room: MS337 and Zoom (Join URL:

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

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

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