Speaker: Geoff Vooys
Abstract: There are (at least) four known approaches to the equivariant bounded derived category (EDC) known in the literature that people have used in various works. One is due to BernsteinLunts in the topological case and was extended rigorously to the scheme case by Pramod Achar.. A second approach to the EDC is the one presented by Lusztig in Cuspidal Local Systems and Graded Hecke Algebras II, which has the benefit of being intimately related to graded Hecke algebra. The third EDC we consider is the equivariant derived category of simplicial sheaves on the simplicial scheme approximating the quotient G \ X (cf., for instance, Deligne's Théorie de Hodge : III). Finally, the last EDC we consider is the one (essentially) defined by Kai Behrend in Derived $\ell$adic Categories for Algebraic Stacks as a certain 2colimit of constructible derived categories of $\ell$adic sheaves on the quotient stack [G/X].
In this talk we will discuss not just what these objects are, but also sketch (emphasis on sketch here; there are a lot of ``no one wants to see this done live'' type details) how they can all be seen to be equivalent. In particular, I will discuss some notions of 2coskeletal simplicial schemes that may be of interest to anyone interested in higher category theory or other areas of math that use simplicial techniques.
Zoom: 846139176
Event Date: Thursday, January 28, 2021  08:00 to 09:00

Speaker: Nicole Kitt
Abstract: It is known that not all ABVpackets are Arthur packets, and in particular, that Arthur packets for general linear groups are singletons. This talk concerns, what is believed to be, the smallest known example of an ABVpacket for a general linear group that is not a singleton, and hence is not of Arthur type. Specifically, we have shown that there is an irreducible admissible representation $\pi_{KS}$ of padic GL(16) with the property that its ABVpacket contains exactly one other irreducible representation, $\pi_{\psi}$.
The main tool that we use to calculate the ABVpacket for padic GL(16) is the functor Ev. In this talk, I will illustrate the geometric methods used to compute this functor. In particular, I will provide a sketch computation of the ABVpacket for GL(16). Before doing so, I will review ABVpackets and Vogan varieties for GL(n). This is joint work with Clifton Cunningham, based on prior joint work with Clifton and Reginald Lybbert; both of which included several enlightening conversations with Andrew Fiori.
Zoom link: 846139176
Event Date: Thursday, January 21, 2021  08:00 to 09:00

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
