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 Apackets, 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 Apackets are parametrized by selfdual automorphic representations of general linear groups. In this talk, I will give a construction of the local Apackets 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

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

Speaker: Sarah Dijols,
Abstract: In this talk, we will report some recent progress on SO(4)distinguished representations of G2. This is a joint work with Jerrod Smith.
Zoom Link: 846139176
Event Date: Thursday, August 20, 2020  08:30 to 09:30

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

Speaker: Clifton Cunningham,
Abstract: In this talk, we will explain how to realize the theta correspondence geometrically in the case of G2, it’s relation to endoscopy, and a cool thing that happens when you include pure inner forms.
Zoom link: 846139176
Event Date: Wednesday, July 8, 2020  10:00 to 11:00

Speaker: Andrew Fiori,
Abstract: In this talk, we will consider the geometric induction from perverse sheaves of PGL(3) to G_2 and then compare it with the endoscopic transfer from PGL(3) to G_2.
Zoom link: 846139176
Event Date: Wednesday, June 24, 2020  08:30 to 09:30

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

Speaker: Clifton Cunningham (University of Calgary)
Abstract: This talk demonstrates a noninvasive procedure that calculates Arthur packets, their associated stable distributions and LanglandsShelstad transfers, without direct use of endoscopy, using certain unipotent representations of the split padic 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
Event Date: Thursday, May 7, 2020  16:30 to 17:30

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 Apackets is by means of sophisticated geometrical methods, using the theory of perverse sheaf,
Dmodules 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 Apackets 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

Participants:
Clifton Cunningham, University of Calgary
Sarah Dijols, Tsinghua University
Andrew Fiori, University of Lethbridge
Ahmed Moussaoui, Université Versailles Saint Quentin
KamFai 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/focussedresearchgroups/19frg277
Event Date: Sunday, July 21, 2019  09:00 to Sunday, July 28, 2019  17:00
