Speaker: James Steele

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

Talk on Zoom: 846139176.

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

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

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

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

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

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.