MIT Lie Groups Seminar

2022 - 2023

Meetings: 4:00pm on Wednesdays

This seminar will take place either in-person or online. For in-person seminars, it will be held at 2-142. You are welcome to join in-person seminars by Zoom. For remote participation, the Zoom link is the same as last year's. You can email Andre Dixon or Ju-Lee Kim for the Zoom meeting Link. To access videos of talks, please email Andre Dixon for the password.




Spring 2022

  • Sept 7

    David Yang
    (MIT)

    2-142

    Local geometric langlands and affine Beilinson-Bernstein localization

    Abstract: We will exposit some tenets of the local geometric Langlands philosophy with concrete representation-theoretic consequences. In particular, we will focus on the problem of affine Beilinson-Bernstein 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.

    Video

  • Sept 14
    (10am)

    Cheng-Chiang Tsai
    (Taiwan)

    Zoom

    Wave-front set and graded Springer theory

    Abstract: For characters of p-adic reductive groups there is the notion of wave-front 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 wave-front set as singular support.) There is a long-standing conjecture that any wave-front set is contained in a single geometric orbit, as worked out by many authors for several types of depth-0 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.

    Slides

    Video

  • Sept 21

    Dan Ciubotaru
    (Oxford)

    2-142

    Wavefront sets and unipotent representations of p-adic groups

    Abstract: An important invariant for admissible representations of reductive p-adic groups is the wavefront set, the collection of the maximal nilpotent orbits in the support of the orbital integrals that occur in the Harish-Chandra-Howe 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 Kazhdan-Lusztig parameters. We use this calculation to give a new characterisation of the anti-tempered 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 p-adic groups of Lusztig's result for unipotent representations of finite groups of Lie type. The talk is based on joint work with Lucas Mason-Brown and Emile Okada.

    Video

  • Sept 23

    Miller, Adams
    Achar, Lusztig

    2-190

    Special Lie Groups Day

  • Sept 24

    Mason-Brown
    Nevins, Trapa

    2-190

    Special Lie Groups Day

  • Sept 28
    (3pm)

    Raphael Beuzart-Plessis (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 p-adic 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 p-adic 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.

    Slides

    Video

  • Oct. 5

    Alexei Oblomkov
    (U. Mass)

    2-142

    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 Oblomkov-Rozansky. I will also discuss generalizations outside of type A.

  • Oct. 12

    Dennis Gaitsgory
    (Bonn)

    2-142

  • Oct. 19

    Xiao Wang
    (U. Chicago)

    2-142

  • Oct. 26

    Jialiang Zou
    (U. Michigan)

    2-142

    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 Harish-Chandra 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 Aubert-Michel-Rouquier and Pan on theta correspondence between unipotent representations along this way.

  • Nov. 2

    Alexander Bertoloni Meli
    (U. Michigan)

    2-142

  • Nov. 9

    Asilata Bapat

    Zoom

  • Nov. 16

    Carl Mautner

    2-142

  • Nov. 23


    2-142

  • Nov. 30


    2-142

  • Dec. 7


    2-142




Archive

Contact: Andre Dixon

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