MIT Lie Groups Seminar
2022  2023
Meetings: 4:00pm on Wednesdays
This seminar will take place either inperson or online. For inperson seminars, it will be held at 2142. You are welcome to join inperson seminars by Zoom. For remote participation, the Zoom link is the same as last year's. You can email Andre Dixon or JuLee Kim for the Zoom meeting Link. To access videos of talks, please email Andre Dixon for the password.
Spring 2022

Sept 7
2142
Local geometric langlands and affine BeilinsonBernstein localization
Abstract: We will exposit some tenets of the local geometric Langlands philosophy with concrete representationtheoretic consequences. In particular, we will focus on the problem of affine BeilinsonBernstein localization at the critical level. Then, we will explain how to actually prove some of these statements. Some of this work is joint with Sam Raskin.

Sept 14
(10am)ChengChiang Tsai
(Taiwan)Zoom
Wavefront set and graded Springer theory
Abstract: For characters of padic reductive groups there is the notion of wavefront set, which is a set of nilpotent orbits that describes the asymptotic behavior of a character near the identity. (Maybe one can think of the closure of wavefront set as singular support.) There is a longstanding conjecture that any wavefront set is contained in a single geometric orbit, as worked out by many authors for several types of depth0 representations. In this talk, we explain how the above conjecture cannot hold in general, because an analogous assertion does not hold for graded Lie algebras. We will discuss this last statement in the context of graded Springer theory.

Sept 21
2142
Wavefront sets and unipotent representations of padic groups
Abstract: An important invariant for admissible representations of reductive padic groups is the wavefront set, the collection of the maximal nilpotent orbits in the support of the orbital integrals that occur in the HarishChandraHowe local character expansion. We compute the geometric and Okada's canonical unramified wavefront sets for representations in Lusztig's category of unipotent reduction for a split group in terms of the KazhdanLusztig parameters. We use this calculation to give a new characterisation of the antitempered unipotent Arthur packets. Another interesting consequence is that the geometric wavefront set of a unipotent supercuspidal representation uniquely determines the nilpotent part of the Langlands parameter; this is an extension to padic groups of Lusztig's result for unipotent representations of finite groups of Lie type. The talk is based on joint work with Lucas MasonBrown and Emile Okada.

Sept 23
Miller, Adams
Achar, Lusztig2190

Sept 24
MasonBrown
Nevins, Trapa2190

Sept 28
(3pm)Raphael BeuzartPlessis (Marseille)
Zoom
On the formal degree conjecture for classical groups
Abstract: A conjecture of Hiraga, Ichino and Ikeda expresses the formal degree of a discrete series of a (algebraic) reductive group over a local field in terms of the adjoint gamma factor of its Langlands parameter. It can be checked for real reductive groups using work of Harish Chandra and the explicit form of the Langlands correspondence in this case. For classical groups over a padic field, the conjecture was established for odd orthogonal groups as well as unitary groups by two completely different methods. In this talk, I will explain a proof for symplectic and even orthogonal padic groups based on properties of twisted endoscopy and ideas originating from Shahidi relating residue of intertwining operators to twisted orbital integrals. This method can actually be readily adapted to treat odd orthogonal and unitary groups as well.

Oct. 5
2142
Affine Springer fibers and sheaves on Hilbert scheme of points on the plane.
Abstract: My talk is based on the joint work with E. Gorsky and O. Kivinen. I will explain a construction that associates a coherent sheaf on the Hilbert scheme of points on the plane to plane curve singularity. The global sections of the sheaf are equal to cohomology of the corresponding Affine (type A) Springer fiber. The construction categorifies HOMFLYPT homology/cohomogy of compactified Jacobian conjecture if combined with Soergel bimodule/ Sheaves of Hilbert scheme theorem of OblomkovRozansky. I will also discuss generalizations outside of type A.

Oct. 12
Dennis Gaitsgory
(Bonn)2142

Oct. 19
2142

Oct. 26
2142
On some Hecke algebra modules arising from theta correspondence and it’s deformation
Abstract: This talk is based on the joint work with Jiajun Ma and Congling Qiu on theta correspondence of type I dual pairs over a finite field F_q. We study the Hecke algebra modules arising from theta correspondence between certain HarishChandra series for these dual pairs. We first show that the normalization of the corresponding Hecke algebra is related to the first occurrence index, which leads to a proof of the conservation relation. We then study the deformation of this Hecke algebra module at q=1 and generalize the results of AubertMichelRouquier and Pan on theta correspondence between unipotent representations along this way.

Nov. 2
Alexander Bertoloni Meli
(U. Michigan)2142

Nov. 9
Asilata Bapat
Zoom

Nov. 16
Carl Mautner
2142

Nov. 23
2142

Nov. 30
2142

Dec. 7
2142
Archive
Contact: Andre Dixon