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BEGIN:VEVENT
SUMMARY:Tanmay Deshpande (TIFR)
DTSTART:20200408T203000Z
DTEND:20200408T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/1/">C
 haracter sheaves on algebraic groups</a>\nby Tanmay Deshpande (TIFR) as pa
 rt of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nCharac
 ter sheaves on an algebraic group are supposed to be the geometric analogu
 es of irreducible characters of a finite group. In 1980s Lusztig developed
  the\ntheory of character sheaves on reductive groups and gave a geometric
  description\nof the character theory of finite reductive groups. Inspired
  by Lusztig’s works\,\nBoyarchenko and Drinfeld developed the theory of 
 character sheaves on unipotent\ngroups. In this talk\, I will describe an 
 approach (due to Drinfeld) towards a theory\nof character sheaves on gener
 al algebraic groups and describe the known results in\nthe case of solvabl
 e algebraic groups.\n
LOCATION:https://researchseminars.org/talk/MITLie/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Mautner (Dartmouth)
DTSTART:20200415T203000Z
DTEND:20200415T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/2/">S
 hadows of Lie theory in the world of matroids</a>\nby Carl Mautner (Dartmo
 uth) as part of MIT Lie groups seminar\n\n\nAbstract\nI will discuss a pro
 gram (partly conjectural) exploring analogues of the Schur\nalgebra and ca
 tegory $\\mathcal O$ for matroids and oriented matroids. This program was 
 motivated in large part by work of Braden-Licata-Proudfoot-Webster. The ta
 lk\nwill be based on joint work with Tom Braden and work in progress with 
 Jens\nEberhardt and Ethan Kowalenko. I will not assume prior knowledge of 
 matroid\n
LOCATION:https://researchseminars.org/talk/MITLie/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART:20200506T203000Z
DTEND:20200506T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/3/">A
 rthur packets for G(2) and perverse sheaves on cubics</a>\nby Clifton Cunn
 ingham (University of Calgary) as part of MIT Lie groups seminar\n\n\nAbst
 ract\nThis talk demonstrates a non-invasive procedure that calculates Arth
 ur packets\, their associated stable distributions and Langlands-Shelstad 
 transfers\, without direct use of endoscopy\, using certain unipotent repr
 esentations 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\, w
 e find the Fourier transform and the microlocalization of the simple objec
 ts in this category\, and convert that into information about the Aubert i
 nvolution and stable distributions attached to Arthur packets. This is joi
 nt work with Andrew Fiori and Qing Zhang\, based on earlier joint work wit
 h Andrew Fiori\, Ahmed Moussaoui\, James Mracek and Bin Xu\, which is base
 d on earlier work by David Vogan\, sadly\, not joint.\n
LOCATION:https://researchseminars.org/talk/MITLie/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (MIT)
DTSTART:20200429T203000Z
DTEND:20200429T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/4/">U
 nipotent representations of real reductive groups</a>\nby Lucas Mason-Brow
 n (MIT) as part of MIT Lie groups seminar\n\n\nAbstract\nLet $G$ be a real
  reductive group and let ${\\widehat G}$ be the set of\nirreducible unitar
 y representations of $G$. The determination of $\\widehat G$ (for\narbitra
 ry $G$) is one of the fundamental unsolved problems in\nrepresentation the
 ory. In the early 1980s\, Arthur introduced a finite\nset Unip($G$) of (co
 njecturally unitary) irreducible representations of\n$G$ called {\\it unip
 otent representations}. In a certain sense\, these\nrepresentations form t
 he building blocks of $\\widehat G$. Hence\, the\ndetermination of $\\wide
 hat G$ requires as a crucial ingredient the determination\nof Unip($G$). I
 n this thesis\, we prove three results on unipotent\nrepresentations.  Fir
 st\, we study unipotent representations by\nrestriction to $K\\subset G$\,
  a maximal compact subgroup. We deduce a formula\nfor this restriction in 
 a wide range of cases\, proving (in these\ncases) a long-standing conjectu
 re of Vogan. Next\, we study the\nunipotent representations attached to in
 duced nilpotent orbits. We\nfind that Unip($G$) is ‘generated’ by an e
 ven smaller set $\\hbox{Unip}'(G)$\nconsisting of representations attached
  to rigid nilpotent\norbits. Finally\, we study the unipotent representati
 ons attached to\nthe principal nilpotent orbit. We provide a complete clas
 sification of\nsuch representations\, including a formula for their $K$-ty
 pes.\n
LOCATION:https://researchseminars.org/talk/MITLie/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20200422T203000Z
DTEND:20200422T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/5/">C
 anonical bases and coherent sheaves</a>\nby Roman Bezrukavnikov (MIT) as p
 art of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nThe p
 rimary application of canonical bases in a Grothendieck group of\nrepresen
 tations is to computation of characters of (say) irreducible\nrepresentati
 ons\; however\, it is not their only application.  I will\nreview construc
 tion and properties of canonical bases in Grothendieck\ngroups of coherent
  sheaves on the Springer resolution and related\nspaces and speculate on p
 ossible generalization to a new setting\ninvolving the fixed group of an i
 nvolution. The toolbox includes\nlinear Koszul duality of Mirkovic-Riche a
 nd a version of Soergel\nbimodules theory.\n
LOCATION:https://researchseminars.org/talk/MITLie/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Adams (University of Maryland)
DTSTART:20200513T203000Z
DTEND:20200513T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/6/">U
 nipotent representations</a>\nby Jeffrey Adams (University of Maryland) as
  part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nI w
 ill give an overview of the current state of the Atlas of Lie groups and R
 epresentations project\, with an emphasis on computing all unipotent repre
 sentations\nof real exceptional groups.\n
LOCATION:https://researchseminars.org/talk/MITLie/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Vogan (MIT Mathematics)
DTSTART:20200909T203000Z
DTEND:20200909T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/7/">S
 tructure of Harish-Chandra cells</a>\nby David Vogan (MIT Mathematics) as 
 part of MIT Lie groups seminar\n\n\nAbstract\nOne of the fundamental contr
 ibutions of Kazhdan and Lusztig's 1979 Inventiones paper was the notion of
  "cells" in Weyl groups. They gave a decomposition of the left regular rep
 resentation of W as a direct sum of "left cell" representations\, which en
 code deep and powerful information about group representations. In the cas
 e of the symmetric group S_n=W\, the left cells are irreducible representa
 tions. In all other cases they are not. Lusztig in his 1984 book gave a be
 autiful description of all left cells in terms of the geometry of a nilpot
 ent orbit.\n\\\\\nThere is a parallel notion of "Harish-Chandra cells" in 
 the representation theory of a real reductive group G(R). Again each cell 
 is a representation of W\, encoding deep information about the G(R) repres
 entations. I will formulate a conjecture extending Lusztig's calculation o
 f left cell representations to this case\, and explain its connection with
  Arthur's theory of unipotent representations.\n
LOCATION:https://researchseminars.org/talk/MITLie/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT Mathematics)
DTSTART:20200916T203000Z
DTEND:20200916T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/8/">A
  strong Henniart identity for reductive groups over finite fields</a>\nby 
 Charlotte Chan (MIT Mathematics) as part of MIT Lie groups seminar\n\nLect
 ure held in 2-142.\n\nAbstract\nIn 1992\, Henniart proved that supercuspid
 al representations for –adic GLn are determined by their character on so
 -called very regular elements.  This has been useful in many ways as it a
 llows for convenient comparison between various constructions of supercusp
 idal representations for GLn.  We describe a version of this type of resu
 lt which holds for (some) representations of reductive groups over finite 
 fields.  This is joint work with Masao Oi.\n
LOCATION:https://researchseminars.org/talk/MITLie/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wang (MIT Mathematics)
DTSTART:20200923T203000Z
DTEND:20200923T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/9/">S
 pherical varieties\, L-functions\, and crystal bases</a>\nby Jonathan Wang
  (MIT Mathematics) as part of MIT Lie groups seminar\n\nLecture held in 2-
 142.\n\nAbstract\nThe program of Sakellaridis and Venkatesh proposes a uni
 fied framework to study integral representations of L-functions through th
 e lens of spherical varieties. For X an affine spherical variety\, the (hy
 pothetical) IC complex of the infinite-dimensional formal arc space of X i
 s conjecturally related to special values of local unramified L-functions.
  We formulate this relation precisely using a new conjectural geometric co
 nstruction of the crystal basis of a finite-dimensional representation (de
 termined by X) of the dual group. We prove these conjectures for a large c
 lass of spherical varieties. This is joint work with Yiannis Sakellaridis.
 \n
LOCATION:https://researchseminars.org/talk/MITLie/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Dudas (CNRS)
DTSTART:20200930T203000Z
DTEND:20200930T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/10/">
 Macdonald polynomials and decomposition numbers for finite unitary groups<
 /a>\nby Olivier Dudas (CNRS) as part of MIT Lie groups seminar\n\nLecture 
 held in 2-142.\n\nAbstract\n(work in progress with R. Rouquier) In this ta
 lk I will present a computational (yet conjectural) method to determine so
 me decomposition matrices for finite groups of Lie type. I will first expl
 ain how one can produce a "natural" self-equivalence in the case of $\\mat
 hrm{GL}_n(q)$ coming from the topology of the Hilbert scheme of $\\mathbb{
 C}^2$. The combinatorial part of this equivalence is related to Macdonald'
 s theory of symmetric functions and gives $(q\,t)$-decomposition numbers. 
 The evidence suggests that the case of finite unitary groups is obtained b
 y taking a suitable square root of that equivalence.\n
LOCATION:https://researchseminars.org/talk/MITLie/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20201007T203000Z
DTEND:20201007T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/11/">
 Two Dimensional Field Theories and Partial Fractions</a>\nby Victor Ostrik
  (University of Oregon) as part of MIT Lie groups seminar\n\nLecture held 
 in 2-142.\n\nAbstract\nThis talk is based on joint work with M.Khovanov an
 d Y.Kononov. By evaluating a topological field theory in dimension 2 on su
 rfaces of genus 0\,1\,2 etc we get a sequence. We investigate which sequen
 ces occur in this way depending on the assumptions on the target category.
 \n\n\n\n\n\nPlease become a member of our email list to receive announceme
 nts of upcoming MIT Lie Groups seminars as well as related information:\n\
 nhttps://mailman.mit.edu:444/mailman/listinfo/liegroups\n
LOCATION:https://researchseminars.org/talk/MITLie/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit)
DTSTART:20201014T203000Z
DTEND:20201014T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/12/">
 Bernstein components for p-adic groups</a>\nby Maarten Solleveld (Radboud 
 Universiteit) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
 n\nAbstract\nSuppose that one has a supercuspidal representation of a Levi
  subgroup of some reductive $p$-adic group $G$. Bernstein associated to th
 is a block Rep$(G)^s$ in the category of smooth $G$-representations. We ad
 dress the question: what does Rep$(G)^s$ look like?\n\nUsually this is inv
 estigated with Bushnell--Kutzko types\, but these are not always available
 . Instead\, we approach it via the endomorphism algebra of a progenerator 
 of Rep$(G)^s$. We will show that Rep$(G)^s$ is "almost" equivalent with th
 e module category of an affine Hecke algebra -- a statement that will be m
 ade precise in several ways.\n\nIn the end\, this leads to a classificatio
 n of the irreducible representations in Rep$(G)^s$ in terms of the complex
  torus and the finite groups that are canonically associated to this Berns
 tein component.\n
LOCATION:https://researchseminars.org/talk/MITLie/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (University of Wisconsin)
DTSTART:20201021T203000Z
DTEND:20201021T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/13/">
 Compactifying the category of D-modules on the stack of G-bundles</a>\nby 
 Dima Arinkin (University of Wisconsin) as part of MIT Lie groups seminar\n
 \nLecture held in 2-142.\n\nAbstract\nLet X be a projective curve\, G a re
 ductive group. Let Bun be the stack of G-bundles over X\, and consider the
  category of D-modules on Bun. (This category appears on the “automorphi
 c” side of the geometric Langlands correspondence.) Drinfeld and Gaitsgo
 ry prove that\, despite the “unbounded” (non-quasi compact) nature of 
 Bun\, the category of D-modules is well-behaved (compactly generated).\n\n
 In this talk\, we will “compactify” this category in a stronger sense\
 ; this can be viewed as compactifying the quantized cotangent bundle to Bu
 n. While the basic idea of such compactification goes back to ideas of Del
 igne and Simpson\, its construction relies on non-trivial properties of th
 e geometry of Bun (similar to the Drinfeld-Gaitsgory Theorem).\n
LOCATION:https://researchseminars.org/talk/MITLie/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20201028T203000Z
DTEND:20201028T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/14/">
 Categorical g-actions for modules over truncated shifted Yangians</a>\nby 
 Joel Kamnitzer (University of Toronto) as part of MIT Lie groups seminar\n
 \nLecture held in 2-142.\n\nAbstract\nGiven a representation V of a reduct
 ive group G\, Braverman-Finkelberg-Nakajima defined a Poisson variety call
 ed the Coulomb branch\, using a convolution algebra construction. This var
 iety comes with a natural deformation quantization\, called a Coulomb bran
 ch algebra. Important cases of these Coulomb branches are (generalized) af
 fine Grassmannian slices\, and their quantizations are truncated shifted Y
 angians.\n\nMotivated by the geometric Satake correspondence and the theor
 y of symplectic duality/3d mirror symmetry\, we expect a categorical g-act
 ion on modules for these truncated shifted Yangians. I will explain three 
 results in this direction. First\, we have an indirect realization of this
  action\, using equivalences with KLRW-modules. Second\, we have a geometr
 ic relation between these generalized slices by Hamiltonian reduction. Fin
 ally\, we have an algebraic version of this Hamiltonian reduction which we
  are able to relate to the first realization.\n\nThis seminar will take pl
 ace entirely online. Please email Andre Dixon (aldixon@mit.edu) for the Zo
 om meeting Link.\n
LOCATION:https://researchseminars.org/talk/MITLie/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harrison Chen (Cornell University)
DTSTART:20201110T213000Z
DTEND:20201110T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/15/">
 Coherent Springer theory and categorical Deligne-Langlands</a>\nby Harriso
 n Chen (Cornell University) as part of MIT Lie groups seminar\n\nLecture h
 eld in 2-142.\n\nAbstract\nKazhdan and Lusztig proved the Deligne-Langland
 s conjecture\, a bijection between irreducible representations of unipoten
 t principal block representations of a p-adic group with certain unipotent
  Langlands parameters in the Langlands dual group (plus the data of certai
 n representations).  We lift this bijection to a statement on the level o
 f categories.  Namely\, we define a stack of unipotent Langlands paramete
 rs and a coherent sheaf on it\, which we call the coherent Springer sheaf\
 , which generates a subcategory of the derived category equivalent to modu
 les for the affine Hecke algebra (or specializing at q\, unipotent princip
 al block representations of a p-adic group).  Our approach involves categ
 orical traces\, Hochschild homology\, and Bezrukavnikov's Langlands dual r
 ealizations of the affine Hecke category.  This is a joint work with Davi
 d Ben-Zvi\, David Helm and David Nadler.\n
LOCATION:https://researchseminars.org/talk/MITLie/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostiantyn Tolmachov (University of Toronto)
DTSTART:20201104T213000Z
DTEND:20201104T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/16/">
 Monodromic model for Khovanov-Rozansky homology</a>\nby Kostiantyn Tolmach
 ov (University of Toronto) as part of MIT Lie groups seminar\n\nLecture he
 ld in 2-142.\n\nAbstract\nKhovanov-Rozansky homology is a knot invariant w
 hich\, by the result of Khovanov\, can be computed as the Hochschild cohom
 ology functor applied Rouquier complexes of Soergel bimodules. I will desc
 ribe a new geometric model for the Hochschild cohomology of Soergel bimodu
 les\, living in the monodromic Hecke category. I will also explain how it 
 allows to identify objects representing individual Hochsсhild cohomology 
 groups as images of explicit character sheaves.\n\nBased on the joint work
  with Roman Bezrukavnikov.\n
LOCATION:https://researchseminars.org/talk/MITLie/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Kononov (Columbia University)
DTSTART:20201118T213000Z
DTEND:20201118T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/17/">
 Elliptic stable envelopes and 3-dimensional mirror symmetry</a>\nby Yakov 
 Kononov (Columbia University) as part of MIT Lie groups seminar\n\nLecture
  held in 2-142.\n\nAbstract\nThe action of quantum groups on the K-theory 
 of Nakajima varieties takes the simplest form in the stable bases\, invent
 ed by D.Maulik and A.Okounkov\, and in their most advanced (elliptic) vers
 ion by M.Aganagic and A.Okounkov. In collaboration with A.Smirnov we disco
 vered and proved the factorization property of elliptic stable envelopes. 
 As a consequence\, we proved the conjectures of E.Gorsky and A.Negut. Also
  it gives a new interesting description of the operators of quantum differ
 ence equations\, shift operators and other quantities in enumerative geome
 try. The talk is based on joint works with A.Smirnov.\n
LOCATION:https://researchseminars.org/talk/MITLie/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masao OI (University of Kyoto)
DTSTART:20201202T230000Z
DTEND:20201203T000000Z
DTSTAMP:20260422T212553Z
UID:MITLie/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/18/">
 Twisted endoscopic character relation for Kaletha's regular supercuspidal 
 L-packets</a>\nby Masao OI (University of Kyoto) as part of MIT Lie groups
  seminar\n\nLecture held in 2-142.\n\nAbstract\nRecently Kaletha construct
 ed the local Langlands correspondence (i.e.\, L-packets and their L-parame
 ters) for a wide class of supercuspidal representations.  In this talk\, 
 I would like to discuss my ongoing work on the twisted endoscopic characte
 r relation for Kaletha's supercuspidal L-packets.\n\nThe strategy is to im
 itate Kaletha's proof of the standard endoscopic character relation in the
  setting of twisted endoscopy.  Thus first I am going to review Kaletha's
  construction of supercuspidal L-packets and his proof of the standard end
 oscopic character relation.  Then I will explain a few key points in the 
 twisting process with an emphasis on Waldspurger's philosophy "l'endoscopi
 c tordue n'est pas si tordue".\n
LOCATION:https://researchseminars.org/talk/MITLie/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Lusztig (MIT)
DTSTART:20201209T213000Z
DTEND:20201209T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/19/">
 From families in Weyl groups to unipotent elements</a>\nby George Lusztig 
 (MIT) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstr
 act\nIn geometric representation theory one tries to understand group repr
 esentations using geometry. But sometimes one can try to go in the opposit
 e direction. In this talk we will illustrate this by showing that a number
  of features in geometry (such as Springer correspondence attached to unip
 otent classes) can be recovered from pure algebra (such as the generic deg
 rees of representations of Weyl groups).\n
LOCATION:https://researchseminars.org/talk/MITLie/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erez Lapid (Weizmann Institute)
DTSTART:20201216T213000Z
DTEND:20201216T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/20
DESCRIPTION:by Erez Lapid (Weizmann Institute) as part of MIT Lie groups s
 eminar\n\nLecture held in 2-142.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITLie/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale Universiy)
DTSTART:20210224T213000Z
DTEND:20210224T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/21/">
 Unipotent Harish-Chandra bimodules</a>\nby Ivan Losev (Yale Universiy) as 
 part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nUnip
 otent representations of semisimple Lie groups is a very important and som
 ewhat conjectural class of unitary representations. Some of these represen
 tations for complex groups (equivalently\, Harish-Chandra bimodules) were 
 defined in the seminal paper of Barbasch and Vogan from 1985 based on idea
 s of Arthur. From the beginning it was clear that the Barbasch-Vogan const
 ruction doesn't cover all unipotent representations. The main construction
  of this talk is a geometric construction of Harish-Chandra bimodules that
  should exhaust all unipotent bimodules. A nontrivial result is that all u
 nipotent bimodules in the sense of Barbasch and Vogan are also unipotent i
 n our sense. The proof of this claim is based on the so called symplectic 
 duality that in our case upgrades a classical duality for nilpotent orbits
  in the version of Barbasch and Vogan. Time permitting I will explain how 
 this works. The talk is based on a joint work with Lucas Mason-Brown and D
 mytro Matvieievskyi.\n
LOCATION:https://researchseminars.org/talk/MITLie/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh-Tam Trinh (MIT Mathematics)
DTSTART:20210303T213000Z
DTEND:20210303T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/22/">
 From the Hecke Category to the Unipotent Locus</a>\nby Minh-Tam Trinh (MIT
  Mathematics) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
 n\nAbstract\nWhen W is the Weyl group of a reductive group G\, we can cate
 gorify its Hecke algebra by means of equivariant sheaves on the double fla
 g variety of G. We will define a functor from the resulting category to a 
 certain category of modules over a polynomial extension of C[W]. We will p
 rove that\, on objects called Rouquier complexes\, our functor yields the 
 equivariant Borel-Moore homology of a generalized Steinberg variety attach
 ed to a positive element in the braid group of W. Some reasons this may be
  interesting: (1) In type A\, the triply-graded Khovanov-Rozansky homology
  of the link closure of the braid is a summand of the weight-graded equiva
 riant homology of this variety. This extends previously-known results for 
 the top and bottom "a-degrees" of KR homology. (2) The "Serre duality" of 
 KR homology under insertion of full twists leads us to conjecture a myster
 ious homeomorphism between pieces of different Steinbergs. (3) We find evi
 dence for a rational-DAHA action on the (modified) homology of the Steinbe
 rgs of periodic braids. It seems related to conjectures of Broué-Michel a
 nd Oblomkov-Yun in rather different settings.\n
LOCATION:https://researchseminars.org/talk/MITLie/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhilin Luo (University of Minnesota)
DTSTART:20210310T213000Z
DTEND:20210310T223000Z
DTSTAMP:20260422T212553Z
UID:MITLie/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/23/">
 Harmonic analysis and gamma functions on symplectic group</a>\nby Zhilin L
 uo (University of Minnesota) as part of MIT Lie groups seminar\n\nLecture 
 held in 2-142.\n\nAbstract\nWe develop a new type of harmonic analysis on 
 an extended symplectic group $G=\\BG_m\\times \\Sp_2n$ over $p$-adic field
 s. It is associated with the Langlands $\\gamma$-functions attached to irr
 educible admissible representations of $G(F)$ and the standard representat
 ion of the dual group. Our work can be viewed as an extension of the work 
 of Godement-Jacquet (which is a generalization of Tate's thesis). We confi
 rm a series of conjectures in the local theory of the Braverman-Kazhdan pr
 oposal in this setting. This is a joint work with D. Jiang and L. Zhang.\n
LOCATION:https://researchseminars.org/talk/MITLie/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ting Xue (University of Melbourne)
DTSTART:20210317T203000Z
DTEND:20210317T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/24/">
 Graded Lie algebras\, character sheaves\, and representations of DAHAs</a>
 \nby Ting Xue (University of Melbourne) as part of MIT Lie groups seminar\
 n\nLecture held in 2-142.\n\nAbstract\nWe describe a strategy for classify
 ing character sheaves in the setting of graded Lie algebras. Via a nearby 
 cycle construction we show that irreducible representations of Hecke algeb
 ras of complex reflection groups at roots of unity enter the description o
 f character sheaves. We will explain connection to the work of Lusztig and
  Yun where (Fourier transforms of) character sheaves are parametrized by i
 rreducible representations of trigonometric double affine Hecke algebras (
 DAHA). We will discuss some conjectures arising from this connection\, whi
 ch relate finite dimensional irreducible representations of trigonometric 
 DAHAs to irreducible representations of Hecke algebras. This is based on j
 oint work with Kari Vilonen and partly with Misha Grinberg.\n
LOCATION:https://researchseminars.org/talk/MITLie/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:German Stefanich (UC Berkeley)
DTSTART:20210324T203000Z
DTEND:20210324T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/25/">
 Categorified sheaf theory and the spectral Betti Langlands TQFT</a>\nby Ge
 rman Stefanich (UC Berkeley) as part of MIT Lie groups seminar\n\nLecture 
 held in 2-142.\n\nAbstract\nIt is expected that the Betti form of the geom
 etric Langlands equivalence will ultimately fit into an equivalence of fou
 r dimensional topological field theories. In this talk I will give an over
 view of ongoing work in the theory of sheaves of higher categories in deri
 ved algebraic geometry\, and explain how it can be used to define a candid
 ate four dimensional theory for the spectral side.\n
LOCATION:https://researchseminars.org/talk/MITLie/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20210407T203000Z
DTEND:20210407T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/26/">
 Macdonald polynomials and counting parabolic bundles</a>\nby Anton Mellit 
 (University of Vienna) as part of MIT Lie groups seminar\n\nLecture held i
 n 2-142.\n\nAbstract\nIt is well known that Hall-Littlewood polynomials na
 turally arise from the problem of counting partial flags preserved by a ni
 lpotent matrix over a finite field. I give an explicit interpretation of t
 he modified Macdonald polynomials in a similar spirit\, via counting parab
 olic bundles with nilpotent endomorphism over a curve over finite field. T
 he result can also be interpreted as a formula for a certain truncated wei
 ghted counting of points in the affine Springer fiber over a constant nilp
 otent matrix. This leads to a confirmation of a conjecture of Hausel\, Let
 ellier and Rodriguez-Villegas about Poincare polynomials of character vari
 eties. On the other hand\, it naturally leads to interesting expansions of
  Macdonald polynomials and related generating functions that appear in the
  shuffle conjecture and its generalizations.\n
LOCATION:https://researchseminars.org/talk/MITLie/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (MIT Mathematics)
DTSTART:20210414T203000Z
DTEND:20210414T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/27/">
 Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric Satake
  equivalence</a>\nby Vasily Krylov (MIT Mathematics) as part of MIT Lie gr
 oups seminar\n\nLecture held in 2-142.\n\nAbstract\nThis talk is based on 
 the paper (joint with M. Finkelberg and I. Mirković).\n\nLet G be a reduc
 tive complex algebraic group. Recall that a geometric Satake isomorphism i
 s an equivalence between the category of G(O)-equivariant perverse sheaves
  on the affine Grassmannian for G and the category of finite dimensional r
 epresentations of the Langlands dual group \\hat{G}. It follows that for a
 ny G(O)-equivariant perverse sheaf P there exists an action of the dual Li
 e algebra \\hat{\\mathfrak{g}} on the global cohomology of P.\n\nWe will e
 xplain one possible approach to constructing this action. To do so\, we wi
 ll describe a new geometric construction of the universal enveloping algeb
 ra of the positive nilpotent subalgebra of the Langlands dual Lie algebra 
 \\hat{\\mathfrak{g}} based on certain one-parametric deformation of zastav
 a spaces. We will introduce the so-called Drinfeld-Gaitsgory-Vinberg inter
 polation Grassmannian that is a one-parametric deformation of the affine G
 rassmannian Gr_G. We will discuss the case G=SL_2 as an example.\n
LOCATION:https://researchseminars.org/talk/MITLie/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsao-Hsien Chen (University of Minnesota)
DTSTART:20210421T203000Z
DTEND:20210421T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/28/">
 Hitchin fibration and commuting schemes</a>\nby Tsao-Hsien Chen (Universit
 y of Minnesota) as part of MIT Lie groups seminar\n\nLecture held in 2-142
 .\n\nAbstract\nThe commuting scheme has always been of great interest in i
 nvariant theory but it was only recent that it appears as a primordial obj
 ect in the study of the Hitchin fibration for higher dimensional varieties
 . I will explain how the invariant theory for the commuting scheme\, in pa
 rticular the Chevalley restriction theorem for the commuting scheme\, is u
 sed in the study of Hitchin fibration and the proof of the Chevalley restr
 iction theorem in the case of symplectic Lie algebras. The talk is based o
 n joint work with Ngo Bao Chau.\n
LOCATION:https://researchseminars.org/talk/MITLie/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (University of Oxford)
DTSTART:20210428T203000Z
DTEND:20210428T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/29/">
 What is a unipotent representation?</a>\nby Lucas Mason-Brown (University 
 of Oxford) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\n
 Abstract\nThe concept of a unipotent representation has its origins in the
  representation theory of finite Chevalley groups. Let G(Fq) be the group 
 of Fq-rational points of a connected reductive algebraic group G. In 1984\
 , Lusztig completed the classification of irreducible representations of G
 (Fq). He showed:\n\n1) All irreducible representations of G(Fq) can be con
 structed from a finite set of building blocks -- called `unipotent represe
 ntations.'\n\n2) Unipotent representations can be classified by certain ge
 ometric parameters related to nilpotent orbits for a complex group associa
 ted to G(Fq).\n\nNow\, replace Fq with C\, the field of complex numbers\, 
 and replace G(Fq) with G(C). There is a striking analogy between the finit
 e-dimensional representation theory of G(Fq) and the unitary representatio
 n theory of G(C). This analogy suggests that all unitary representations o
 f G(C) can be constructed from a finite set of building blocks -- called `
 unipotent representations' -- and that these building blocks are classifie
 d by geometric parameters related to nilpotent orbits. In this talk I will
  propose a definition of unipotent representations\, generalizing the Barb
 asch-Vogan notion of `special unipotent'. The definition I propose is geom
 etric and case-free. After giving some examples\, I will state a geometric
  classification of unipotent representations\, generalizing the well-known
  result of Barbasch-Vogan for special unipotents.\n\nThis talk is based on
  forthcoming joint work with Ivan Loseu and Dmitryo Matvieievskyi.\n
LOCATION:https://researchseminars.org/talk/MITLie/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shu-Yen Pan (National Tsinghua University (Taiwan))
DTSTART:20210505T203000Z
DTEND:20210505T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/30/">
 Finite Howe correspondence and Lusztig classification</a>\nby Shu-Yen Pan 
 (National Tsinghua University (Taiwan)) as part of MIT Lie groups seminar\
 n\nLecture held in 2-142.\n\nAbstract\nLet $(G\,G')$ be a reductive dual p
 air inside a finite symplectic group. By restricting the Weil representati
 on to the dual pair\, there exists a relation (called the finite Howe corr
 espondence) between the irreducible representations of the two groups $G\,
 G'$. In this talk\, we would like to discuss some progress on the understa
 nding of the correspondence by using Lusztig's classification on the repre
 sentations of finite classical groups.\n\nIn particular\, we will focus on
  the following three subjects:\n1. the decomposition of the uniform projec
 tion of the Weil character\n2. the commutativity between the Howe correspo
 ndence and the Lusztig correspondence\n3. the description of the Howe corr
 espondence on unipotent characters in terms of the symbols by Lusztig.\n
LOCATION:https://researchseminars.org/talk/MITLie/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ben-Zvi (University of Texas - Austin)
DTSTART:20210512T203000Z
DTEND:20210512T213000Z
DTSTAMP:20260422T212553Z
UID:MITLie/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/31/">
 Quantization and Duality for Spherical Varieties</a>\nby David Ben-Zvi (Un
 iversity of Texas - Austin) as part of MIT Lie groups seminar\n\nLecture h
 eld in 2-142.\n\nAbstract\nI will present joint work with Yiannis Sakellar
 idis and Akshay Venkatesh\, in which we apply a perspective from topologic
 al field theory to the relative Langlands program. To a spherical variety 
 one can assign two quantization problems\, automorphic and spectral\, both
  resulting in structures borrowed from QFT. The automorphic quantization (
 or A-side) organizes objects such as periods\, Plancherel measure\, theta 
 series and relative trace formula\, while the spectral quantization (or B-
 side) organizes L-functions and Langlands parameters. Our conjectures desc
 ribe a duality operation on spherical varieties\, which exchanges automorp
 hic and spectral quantizations (and may be seen as Langlands duality for b
 oundary conditions in 4d TFT\, a refined form of symplectic duality / 3d m
 irror symmetry).\n
LOCATION:https://researchseminars.org/talk/MITLie/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (Weizmann Institute of Science)
DTSTART:20210519T173000Z
DTEND:20210519T183000Z
DTSTAMP:20260422T212553Z
UID:MITLie/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/32/">
 Kac-Moody superalgebras and  Duflo-Serganova functors</a>\nby Maria Goreli
 k (Weizmann Institute of Science) as part of MIT Lie groups seminar\n\nLec
 ture held in 2-142.\n\nAbstract\nThe central characters of the finite-dime
 nsional Kac-Moody superalgebras can be described by their "cores"\; this n
 otion can be nicely interpreted in terms of the Duflo-Serganova functors. 
 I will discuss an extension of these results to affine Lie superalgebras.\
 n
LOCATION:https://researchseminars.org/talk/MITLie/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Vogan (MIT)
DTSTART:20210908T200000Z
DTEND:20210908T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/33/">
 Constructing unipotent representations</a>\nby David Vogan (MIT) as part o
 f MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nIn the 195
 0s\, Mackey began a systematic analysis of unitary representations of grou
 ps in terms of "induction" from normal subgroups. Ultimately this led to a
  fairly good reduction of unitary representation theory to the case of sim
 ple groups\, which lack interesting normal subgroups. At about the same ti
 me\, Gelfand and Harish-Chandra understood that many representations of si
 mple groups could be constructed using induction from parabolic subgroups.
  After many refinements and extensions of this work\, there still remain a
  number of interesting representations of simple groups that are often not
  obtained by parabolic induction.\n\nFor the case of real reductive groups
 \, I will discuss a certain (finite) family of representations\, called un
 ipotent\, whose existence was conjectured by Arthur in the 1980s. Some uni
 potent representations can in fact be obtained by parabolic induction\; I 
 will talk about when this ought to happen\, and about the (rather rare) ca
 ses in which Arthur's unipotent representations are not induced. (A lot of
  what I will say is meaningful and interesting over local or finite fields
 \, but I know almost nothing about those cases.)\n
LOCATION:https://researchseminars.org/talk/MITLie/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wicher Malten (Oxford University)
DTSTART:20210915T200000Z
DTEND:20210915T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/34/">
 From braids to transverse slices in reductive groups</a>\nby Wicher Malten
  (Oxford University) as part of MIT Lie groups seminar\n\nLecture held in 
 2-142.\n\nAbstract\nWe explain how group analogues of Slodowy slices arise
  by interpreting certain Weyl group elements as braids. Such slices origin
 ate from classical work by Steinberg on regular conjugacy classes\, and di
 fferent generalisations recently appeared in work by Sevostyanov on quantu
 m group analogues of W-algebras and in work by He-Lusztig on Deligne-Luszt
 ig varieties. Also building upon recent work of He-Nie\, our perspective f
 urnishes a common generalisation and a simple geometric criterion for Weyl
  group elements to yield strictly transverse slices.\n
LOCATION:https://researchseminars.org/talk/MITLie/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Lusztig (MIT)
DTSTART:20210922T200000Z
DTEND:20210922T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/35/">
 Total positivity in symmetric spaces</a>\nby George Lusztig (MIT) as part 
 of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nThe theor
 y of total positive matrices in GL_n(R) was initiated by Schoenberg (1930)
  and Gantmacher-Krein (1935) and extended to reductive groups in my 1994 p
 aper. It turns out that much of the theory makes sense also for symmetric 
 spaces although some new features arise.\n
LOCATION:https://researchseminars.org/talk/MITLie/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale)
DTSTART:20210929T200000Z
DTEND:20210929T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/36/">
 Harish-Chandra modules over quantizations of nilpotent orbits.</a>\nby Iva
 n Losev (Yale) as part of MIT Lie groups seminar\n\nLecture held in 2-142.
 \n\nAbstract\nLet O be a nilpotent orbit in a semisimple Lie algebra over 
 the complex numbers. Then it makes sense to talk about filtered quantizati
 ons of O\, these are certain associative algebras that necessarily come wi
 th a preferred homomorphism from the universal enveloping algebra. Assume 
 that the codimension of the boundary of O is at least 4\, this is the case
  for all birationally rigid orbits (but six in the exceptional type)\, for
  example. In my talk I will explain a geometric classification of faithful
  irreducible Harish-Chandra modules over quantizations of O\, concentratin
 g on the case of canonical  quantizations -- this gives rise to modules th
 at could be called unipotent. The talk is based on a joint paper with Shil
 in Yu (in preparation).\n
LOCATION:https://researchseminars.org/talk/MITLie/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuhua He (Chinese U. Hong Kong)
DTSTART:20211006T140000Z
DTEND:20211006T150000Z
DTSTAMP:20260422T212553Z
UID:MITLie/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/37/">
 Frobenius-twisted conjugacy classes of loop groups and Demazure product of
  Iwhaori-Weyl groups</a>\nby Xuhua He (Chinese U. Hong Kong) as part of MI
 T Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nThe affine Del
 igne-Lusztig varieties\, roughly speaking\,\ndescribe the intersection of 
 Iwahori-double cosets and Frobenius-twisted\nconjugacy classes in a loop g
 roup. For each fixed Iwahori-double coset\n$I w I$\, there exists a unique
  Frobenius-twisted conjugacy class whose\nintersection with $I w I$ is ope
 n dense in $I w I$. Such\nFrobenius-twisted conjugacy class $[b_w]$ is cal
 led the generic\nFrobenius-twisted conjugacy class with respect to the ele
 ment $w$.\nUnderstanding $[b_w]$ leads to some important consequences in t
 he study\nof affine Deligne-Lusztig varieties. In this talk\, I will give 
 an\nexplicit description of $[b_w]$ in terms of Demazure product of the\nI
 wahori-Weyl groups. It is worth pointing out that a priori\, $[b_w]$ is\nr
 elated to the conjugation action on $I w I$\, and it is interesting that\n
 $[b_w]$ can be described using Demazure product instead of conjugation\nac
 tion. This is based on my preprint arXiv:2107.14461.\n\nIf time allows\, I
  will also discuss an interesting application. Lusztig\nand Vogan recently
  introduced a map from the set of translations to the\nset of dominant tra
 nslations in the Iwahori-Weyl group. As an\napplication of the connection 
 between $[b_w]$ and Demazure product\, we\nwill give an explicit formula f
 or the map of Lusztig and Vogan.\n
LOCATION:https://researchseminars.org/talk/MITLie/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaping Yang (U. Melbourne)
DTSTART:20211020T200000Z
DTEND:20211020T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/38/">
 Frobenii on Morava E-theoretical quantum groups</a>\nby Yaping Yang (U. Me
 lbourne) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAb
 stract\nIn this talk\, I will explain a connection between stable homotopy
  theory and representation theory. I will focus on one application of this
  idea to a problem arising from the modular representation theory. More ex
 plicitly\, we study a family of new quantum groups labelled by a prime num
 ber and a positive integer constructed using the Morava E-theories. Those 
 quantum groups are related to Lusztig's 2015 reformulation of his conjectu
 re from 1979 on character formulas for algebraic groups over a field of po
 sitive characteristic. This talk is based on my joint work with Gufang Zha
 o.\n
LOCATION:https://researchseminars.org/talk/MITLie/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Berest (Cornell)
DTSTART:20211027T200000Z
DTEND:20211027T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/39/">
 Topological realization of rings of quasi-invariants of finite reflection 
 groups</a>\nby Yuri Berest (Cornell) as part of MIT Lie groups seminar\n\n
 \nAbstract\nQuasi-invariants are natural geometric generalizations of clas
 sical invariant polynomials of finite reflection groups. They first appear
 ed in mathematical physics in the early 1990s\, and since then have found 
 applications in a number of other areas (most notably\, representation the
 ory\, algebraic geometry and combinatorics).\n\nIn this talk\, I will expl
 ain how the algebras of quasi-invariants can be realized topologically: as
  (equivariant) cohomology rings of certain spaces naturally attached to co
 mpact connected Lie groups. Our main result can be viewed as a generalizat
 ion of a well-known theorem of A. Borel that realizes the algebra of invar
 iant polynomials of a Weyl group W as the cohomology ring of the classifyi
 ng space BG of the corresponding Lie group G. Replacing equivariant cohomo
 logy with equivariant K-theory gives a multiplicative (exponential) analog
 ues of quasi-invariants of Weyl groups. But perhaps more interesting is th
 e fact that one can also realize topologically the quasi-invariants of som
 e non-Coxeter groups: our `spaces of quasi-invariants' can be constructed 
 in a purely homotopy-theoretic way\, and this construction extends natural
 ly to (p-adic) pseudoreflection groups. In this last case\, the compact Li
 e groups are replaced by p-compact groups (a.k.a. homotopy Lie groups). Th
 e talk is based on joint work with A. C. Ramadoss.\n
LOCATION:https://researchseminars.org/talk/MITLie/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern University)
DTSTART:20211110T210000Z
DTEND:20211110T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/40/">
 Quantum symmetric pairs via star products</a>\nby Milen Yakimov (Northeast
 ern University) as part of MIT Lie groups seminar\n\nLecture held in 2-142
 .\n\nAbstract\nThe systematic study of quantum symmetric pairs (QSPs) was 
 initiated by Gail Letzter in 1999. The area has been greatly developed in 
 recent years. We will present a new approach to the theory of quantum symm
 etric pairs for symmetrizable Kac-Moody algebras based on star products on
  noncommutative graded algebras. It will be used to give solutions to two 
 main problems in the area: (1) determine the defining relations of QSPs an
 d (2) find a Drinfeld type formula for universal $K$-matrices as sums of t
 ensor products over dual bases. This is a joint work with Stefan Kolb.\n
LOCATION:https://researchseminars.org/talk/MITLie/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT)
DTSTART:20211013T200000Z
DTEND:20211013T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/41/">
 Derived Chevalley isomorphisms</a>\nby Tony Feng (MIT) as part of MIT Lie 
 groups seminar\n\nLecture held in 2-142.\n\nAbstract\nFor a reductive grou
 p G\, the classical Chevalley isomorphism identifies conjugation-invariant
  functions on G with Weyl-invariant functions on its maximal torus. Berest
 -Ramadoss-Yeung have conjectured a derived upgrade of this statement\, whi
 ch predicts that the conjugation-invariant functions on the derived commut
 ing variety of G identify with the Weyl-invariant functions on the derived
  commuting variety of its maximal torus. In joint work with Dennis Gaitsgo
 ry we deduce this conjecture for G = GL_n from investigations into derived
  aspects of the local Langlands correspondence. I’ll explain this story\
 , assuming no background in derived algebraic geometry.\n
LOCATION:https://researchseminars.org/talk/MITLie/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART:20211103T200000Z
DTEND:20211103T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/42/">
 Universal symplectic quotients via Lie theory</a>\nby Peter Crooks (Northe
 astern University) as part of MIT Lie groups seminar\n\nLecture held in 2-
 142.\n\nAbstract\nIn its most basic form\, symplectic geometry is a mathem
 atically rigorous framework for classical mechanics. Noether's perspective
  on conserved quantities thereby gives rise to quotient constructions in s
 ymplectic geometry. The most classical such construction is Marsden-Weinst
 ein-Meyer reduction\, while more modern variants include Ginzburg-Kazhdan 
 reduction\, Kostant-Whittaker reduction\, Mikami-Weinstein reduction\, sym
 plectic cutting\, and symplectic implosion.\n\nI will provide a simultaneo
 us generalization of the quotient constructions mentioned above. This gene
 ralization will be shown to have versions in the smooth\, holomorphic\, co
 mplex algebraic\, and derived symplectic contexts. As a corollary\, I will
  derive a concrete and Lie-theoretic construction of "universal" symplecti
 c quotients.\n\nThis represents joint work with Maxence Mayrand.\n
LOCATION:https://researchseminars.org/talk/MITLie/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto)
DTSTART:20211117T210000Z
DTEND:20211117T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/43/">
 Examples of Hecke eigen-functions for moduli spaces of bundles over local 
 non-archimedean field and an analog of Eisenstein series</a>\nby Alexander
  Braverman (University of Toronto) as part of MIT Lie groups seminar\n\nLe
 cture held in 2-142.\n\nAbstract\nLet X be a smooth projective curve over 
 a finite field $k$\, and let $G$ be a reductive group. The unramified part
  of the theory of automorphic forms for the group G and the field $k(X)$ s
 tudies functions on the $k$-points on the moduli space of $G$-bundles on $
 X$ and the eigen-functions of the Hecke operators (to be reviewed in the t
 alk!) acting there. The spectrum of the Hecke operators has continuous and
  discrete parts and it is described by the global Langlands conjectures (w
 hich in the case of functional fields are essentially proved by V.Lafforgu
 e).\n\nAfter recalling the above notions and constructions I will discuss 
 what happens when $k$ is replaced by a local field. The corresponding Heck
 e operators were essentially defined by myself and Kazhdan about 10 years 
 ago\, but the systematic study of eigen-functions has begun only recently.
  It was initiated several years ago by Langlands when $k$ is archimedean a
 nd then Etingof\, Frenkel and Kazhdan formulated a very precise conjecture
  describing the spectrum in terms of the dual group. Contrary to the class
 ical case only discrete spectrum is expected to exist. I will discuss what
  is is known in the case when $k$ is a local non-archimedean field $K$. In
  particular\, I will talk about some version of the Eisenstein series oper
 ator which allows to construct a Hecke eigen-function over $K$ starting fr
 om a cuspidal Hecke eigen-function over finite field  (joint work in progr
 ess with D.Kazhdan and A.Polishchuk).\n
LOCATION:https://researchseminars.org/talk/MITLie/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20211201T210000Z
DTEND:20211201T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/44/">
 Seminar Cancelled</a>\nby Tasho Kaletha (University of Michigan) as part o
 f MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nSeminar Ca
 ncelled\n
LOCATION:https://researchseminars.org/talk/MITLie/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Ciubotaru (Oxford University)
DTSTART:20211208T210000Z
DTEND:20211208T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/45/">
 A nonabelian Fourier transform for tempered unipotent representations of p
 -adic groups</a>\nby Dan Ciubotaru (Oxford University) as part of MIT Lie 
 groups seminar\n\nLecture held in The Simons Building in Room: 2-142.\n\nA
 bstract\nIn the representation theory of finite reductive groups\, an esse
 ntial role is played by Lusztig's nonabelian Fourier transform\, an involu
 tion on the space of unipotent characters the group. This involution is th
 e change of bases matrix between the basis of irreducible characters and t
 he basis of `almost characters'\, certain class functions attached to char
 acter sheaves. For reductive p-adic groups\, the unipotent local Langlands
  correspondence gives a natural parametrization of irreducible smooth repr
 esentations with unipotent cuspidal support. However\, many questions abou
 t the characters of these representations are still open. Motivated by the
  study of the characters on compact elements\, we introduce in joint work 
 with A.-M. Aubert and B. Romano (arXiv:2106.13969) an involution on the sp
 aces of elliptic and compact tempered unipotent representations of pure in
 ner twists of a split simple p-adic group. This generalizes a construction
  by Moeglin and Waldspurger (2003\, 2016) for elliptic tempered representa
 tions of split orthogonal groups\, and potentially gives another interpret
 ation of a Fourier transform for p-adic groups introduced by Lusztig (2014
 ). We conjecture (and give supporting evidence) that the restriction to re
 ductive quotients of maximal compact open subgroups intertwines this invol
 ution with a disconnected version of Lusztig's nonabelian Fourier transfor
 m for finite reductive groups.\n
LOCATION:https://researchseminars.org/talk/MITLie/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kari Vilonen (Melbourne)
DTSTART:20220209T210000Z
DTEND:20220209T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/46/">
 Mixed Hodge modules and representation theory of real groups</a>\nby Kari 
 Vilonen (Melbourne) as part of MIT Lie groups seminar\n\nLecture held in 2
 -142.\n\nAbstract\n\\noindent I will explain how mixed Hodge modules can b
 e utilized to understand representation theory of real groups. In particul
 ar\, we obtain a refinement of the Lusztig-Vogan polynomials in this setti
 ng. Adams\, van Leeuwen\, Trapa\, and Vogan (ALTV) have given an algorithm
  to determine the unitary dual of a real reductive group. As a corollary o
 f our results we obtain a proof of a key result of (ALTV) on signature pol
 ynomials. \\\\\n\\vspace{2ex}\n\\noindent This is joint work with Dougal D
 avis.\n
LOCATION:https://researchseminars.org/talk/MITLie/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emile Okada (University of Oxford)
DTSTART:20220216T210000Z
DTEND:20220216T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/47/">
 The wavefront set and Arthur packets of p-adic groups</a>\nby Emile Okada 
 (University of Oxford) as part of MIT Lie groups seminar\n\nLecture held i
 n 2-142.\n\nAbstract\nThe wavefront set is a powerful harmonic analytic in
 variant attached to representations of p-adic groups that is expected to p
 lay an important role in the construction of Arthur packets. In this talk 
 I will present new results relating it to the local Langlands corresponden
 ce for representations in the principal block. In the process I will intro
 duce a natural refinement of the (geometric) wavefront set with many nicer
  properties and use it to construct some unipotent Arthur packets of arbit
 rary split groups. The results are based on joint work with Dan Ciubotaru 
 and Lucas Mason-Brown.\n
LOCATION:https://researchseminars.org/talk/MITLie/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Fu (Harvard University)
DTSTART:20220223T210000Z
DTEND:20220223T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/48/">
 Kazhdan-Lusztig Equivalence at the Iwahori Level</a>\nby Yuchen Fu (Harvar
 d University) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
 n\nAbstract\nWe construct an equivalence between Iwahori-integrable repres
 entations of affine Lie algebras and representations of the "mixed" quantu
 m group\, thus confirming a conjecture by Gaitsgory. Our proof utilizes fa
 ctorization methods: we show that both sides are equivalent to algebraic/t
 opological factorization modules over a certain factorization algebra\, wh
 ich can then be compared via Riemann-Hilbert. On the quantum group side th
 is is achieved via general machinery of homotopical algebra\, whereas the 
 affine side requires inputs from the theory of (renormalized) ind-coherent
  sheaves as well as compatibility with global Langlands over P1.\n\nThis i
 s joint work with Lin Chen.\n
LOCATION:https://researchseminars.org/talk/MITLie/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20220302T210000Z
DTEND:20220302T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/49/">
 Characterization and construction of the local Langlands correspondence fo
 r supercuspidal parameters</a>\nby Tasho Kaletha (University of Michigan) 
 as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nW
 e will formulate a list of properties that uniquely characterize the local
  Langlands correspondence for discrete Langlands parameters with trivial m
 onodromy. Suitably interpreted\, this characterization holds for any local
  field\, but requires an assumption on p in the non-archimedean case. We w
 ill then discuss an explicit construction of this correspondence\, as a re
 alization of functorial transfer from double covers of elliptic maximal to
 ri.\n
LOCATION:https://researchseminars.org/talk/MITLie/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cedric Bonnafe (CNRS)
DTSTART:20220309T210000Z
DTEND:20220309T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/50/">
 Calogero-Moser spaces vs unipotent representations</a>\nby Cedric Bonnafe 
 (CNRS) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbst
 ract\nTitle to be shared\n
LOCATION:https://researchseminars.org/talk/MITLie/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT)
DTSTART:20220316T200000Z
DTEND:20220316T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/51/">
 On the trace of the affine Hecke category</a>\nby Andrei Negut (MIT) as pa
 rt of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nWe pro
 pose a connection between the horizontal trace of the affine Hecke categor
 y and the elliptic Hall algebra\, mirroring known constructions for the fi
 nite Hecke category. Explicitly\, we construct a family of generators of t
 he affine Hecke category\, compute certain categorified commutators betwee
 n them\, and show that their K-theoretic shadows match certain commutators
  in the elliptic Hall algebra. Joint work with Eugene Gorsky.\n
LOCATION:https://researchseminars.org/talk/MITLie/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Gannon (University of Texas)
DTSTART:20220330T200000Z
DTEND:20220330T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/52/">
 Categorical Representation Theory and the Coarse Quotient</a>\nby Tom Gann
 on (University of Texas) as part of MIT Lie groups seminar\n\nLecture held
  in 2-142.\n\nAbstract\nThe main theorem of this talk will be that one can
  understand a "dense open" subset of DG categories with an action of a spl
 it reductive group G over a field of characteristic zero entirely in terms
  of its root datum. We will start by introducing the notion of a categoric
 al representation of G and discuss some motivation. Then\, we will discuss
  some of the main technical tools involved in making the statement of the 
 main theorem precise\, including discussion of the "coarse quotient" of th
 e dual maximal Cartan by the affine Weyl group. We will also discuss how s
 heaves on this coarse quotient can be identified with bi-Whittaker sheaves
  on G\, obtaining symmetric monoidal upgrade of a result of Ginzburg and L
 onergan\, and then give an outline of the proof of the main theorem. Time 
 permitting\, we will discuss some applications of these categorical repres
 entation theoretic ideas which prove a modified version of a conjecture of
  Ben-Zvi and Gunningham on the essential image of parabolic restriction.\n
LOCATION:https://researchseminars.org/talk/MITLie/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (Caltech)
DTSTART:20220406T200000Z
DTEND:20220406T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/53/">
 Perverse mod p sheaves on affine flag varieties</a>\nby Robert Cass (Calte
 ch) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstrac
 t\nPerverse sheaves have important applications in representation theory a
 nd number theory. In this talk we will consider the case of mod p étale s
 heaves on affine flag varieties over a field of characteristic p. Despite 
 the pathological behavior of such sheaves\, they encode the structure of m
 od p Hecke algebras. We will primarily focus on a version of the geometric
  Satake equivalence for the affine Grassmannian. Time permitting\, we may 
 also discuss central sheaves on the Iwahori affine flag variety. Part of t
 his is joint work with Cédric Pépin.\n
LOCATION:https://researchseminars.org/talk/MITLie/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Michigan)
DTSTART:20220504T200000Z
DTEND:20220504T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/54/">
 Title to be announced</a>\nby Peter Dillery (University of Michigan) as pa
 rt of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nTitle 
 to be shared\n
LOCATION:https://researchseminars.org/talk/MITLie/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramod Achar (LSU)
DTSTART:20220511T200000Z
DTEND:20220511T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/55/">
 Co-t-structures on coherent sheaves and the Humphreys conjecture</a>\nby P
 ramod Achar (LSU) as part of MIT Lie groups seminar\n\nLecture held in 2-1
 42.\n\nAbstract\nLet G be a connected reductive group over an algebraicall
 y closed field\, and let C be a nilpotent orbit for G.  If L is an irreduc
 ible G-equivariant vector bundle on C\, then one can define a "coherent in
 tersection cohomology complex" IC(C\,L). These objects play an important r
 ole in various results related to the local geometric Langlands program. \
 n\nWhen G has positive characteristic\, instead of an irreducible bundle L
 \, one might consider a tilting bundle T on C.  I will explain a new const
 ruction that associates to the pair (C\,T) a complex of coherent sheaves S
 (C\,T) with remarkable Ext-vanishing properties.  This construction leads 
 to a proof of a conjecture of Humphreys on (relative) support varieties fo
 r tilting modules\, and hints at a kind of "recursive" structure in the te
 nsor category of tilting G-modules.  This work is joint with W. Hardesty (
 and also partly with S. Riche).\n
LOCATION:https://researchseminars.org/talk/MITLie/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Ionov (MIT)
DTSTART:20220413T200000Z
DTEND:20220413T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/56/">
 Tilting sheaves for real groups and Koszul duality</a>\nby Andrei Ionov (M
 IT) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstrac
 t\nFor a real form of an algebraic group acting on the flag variety we def
 ine a t-structure on the category of equivariant-monodromic sheaves and de
 velop the theory of tilting sheaves. In case of a quasi-split real form we
  construct an analog of a Soergel functor\, which full-faithfully embeds t
 he subcategory of tilting objects to the category of coherent sheaves on a
  block variety. We apply the results to give a new\, purely geometric\, pr
 oof of the Soergel's conjecture for quasi-split groups.\n
LOCATION:https://researchseminars.org/talk/MITLie/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Sommers (UMass)
DTSTART:20220420T200000Z
DTEND:20220420T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/57/">
 Hessenberg varieties and the geometric modular law</a>\nby Eric Sommers (U
 Mass) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstr
 act\nHessenberg varieties are fibers of certain proper maps to a simple Li
 e algebra. These maps are generalizations of the Springer and Grothendieck
 -Springer resolutions. In this talk\, we describe some new properties of n
 ilpotent Hessenberg varieties. In particular\, we show that their cohomolo
 gy satisfies a modular law as we vary the maps. This law generalizes one o
 f De Concini\, Lusztig\, and Procesi and coincides with a combinatorial la
 w of Guay-Paquet and Abreu-Nigro in type A. We also study the push-forward
  of the constant sheaf of these maps and show that only intersection cohom
 ology sheaves with local systems coming from the Springer correspondence a
 ppear in the decomposition\, resolving a conjecture of Brosnan. This is jo
 int work with Martha Precup.\n
LOCATION:https://researchseminars.org/talk/MITLie/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Ciubotaru (University of Oxford)
DTSTART:20220921T200000Z
DTEND:20220921T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/58/">
 Wavefront sets and unipotent representations of p-adic groups</a>\nby Dan 
 Ciubotaru (University of Oxford) as part of MIT Lie groups seminar\n\nLect
 ure held in 2-142.\n\nAbstract\nAn important invariant for admissible repr
 esentations of reductive p-adic groups is the wavefront set\, the collecti
 on of the maximal nilpotent orbits in the support of the orbital integrals
  that occur in the Harish-Chandra-Howe local character expansion. We compu
 te the geometric and Okada's canonical unramified wavefront sets for repre
 sentations in Lusztig's category of unipotent reduction for a split group 
 in terms of the Kazhdan-Lusztig parameters. We use this calculation to giv
 e a new characterisation of the anti-tempered unipotent Arthur packets. An
 other interesting consequence is that the geometric wavefront set of a uni
 potent supercuspidal representation uniquely determines the nilpotent part
  of the Langlands parameter\; this is an extension to p-adic groups of Lus
 ztig'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.\n
LOCATION:https://researchseminars.org/talk/MITLie/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Beuzart-Plessis (Marseille)
DTSTART:20220928T200000Z
DTEND:20220928T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/59/">
 Title to be announced</a>\nby Raphael Beuzart-Plessis (Marseille) as part 
 of MIT Lie groups seminar\n\nLecture held in 2-142.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITLie/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Oblomkov (U. Mass)
DTSTART:20221005T200000Z
DTEND:20221005T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/60/">
 Affine Springer fibers and sheaves on Hilbert scheme of points on the plan
 e.</a>\nby Alexei Oblomkov (U. Mass) as part of MIT Lie groups seminar\n\n
 Lecture held in 2-142 in the Simons building.\n\nAbstract\nMy talk is base
 d on the joint work with E. Gorsky and O. Kivinen.\nI will explain a const
 ruction that associates a coherent sheaf on the\nHilbert scheme of points 
 on the plane to plane curve singularity. The\nglobal sections of the sheaf
  are equal to cohomology of the\ncorresponding Affine  (type A) Springer f
 iber. The construction\ncategorifies  HOMFLYPT homology/cohomogy of compac
 tified Jacobian\nconjecture if combined with Soergel bimodule/ Sheaves of 
 Hilbert\nscheme theorem of Oblomkov-Rozansky. I will also discuss\ngeneral
 izations outside of type A.\n
LOCATION:https://researchseminars.org/talk/MITLie/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Bonn)
DTSTART:20221012T200000Z
DTEND:20221012T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/61/">
 From geometric Langlands to classical via the trace of Frobenius</a>\nby D
 ennis Gaitsgory (Bonn) as part of MIT Lie groups seminar\n\nLecture held i
 n 2-142.\n\nAbstract\nI'll start by summarizing the main results of the se
 ries [AGKRRV]\, where it is shown that the trace of Frobenius on the categ
 ory of automorphic sheaves with nilpotent singular support identifies with
  the space of unramified automorphic functions. We'll then discuss conject
 ural counterparts of this statement in the local and global ramified setti
 ngs.\n
LOCATION:https://researchseminars.org/talk/MITLie/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Wang (University of Chicago)
DTSTART:20221019T200000Z
DTEND:20221019T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/62/">
 Title to be announced</a>\nby Xiao Wang (University of Chicago) as part of
  MIT Lie groups seminar\n\nLecture held in 2-142.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MITLie/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jialiang Zou (University of Michigan)
DTSTART:20221026T200000Z
DTEND:20221026T210000Z
DTSTAMP:20260422T212553Z
UID:MITLie/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/63/">
 On some Hecke algebra modules arising from theta correspondence and it’s
  deformation</a>\nby Jialiang Zou (University of Michigan) as part of MIT 
 Lie groups seminar\n\nLecture held in 2-142 in the Simons building.\n\nAbs
 tract\nThis talk is based on the joint work with Jiajun Ma and Congling Qi
 u on theta correspondence of type I dual pairs over a finite field $F_q$. 
  We study the Hecke algebra modules arising from theta correspondence betw
 een certain Harish-Chandra series for these dual pairs. We first show that
  the normalization of the corresponding Hecke algebra is  related to the f
 irst occurrence index\, which leads to a  proof of the conservation relati
 on. 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 correspo
 ndence between unipotent representations along this way.\n
LOCATION:https://researchseminars.org/talk/MITLie/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20221109T210000Z
DTEND:20221109T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/64/">
 Moduli space of flower curves</a>\nby Joel Kamnitzer (University of Toront
 o) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract
 \nThe Deligne-Mumford moduli space of genus 0 curves plays many roles in r
 epresentation theory. For example\, the fundamental group of its real locu
 s is the cactus group which acts on tensor products of crystals.  I will d
 iscuss a variant on this space which parametrizes "flower curves". The fun
 damental group of the real locus of this space is the virtual cactus group
 . This moduli space of flower curves is also the parameter space for inhom
 ogeneous Gaudin algebras.\n
LOCATION:https://researchseminars.org/talk/MITLie/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Mautner (UC Riverside)
DTSTART:20221116T210000Z
DTEND:20221116T220000Z
DTSTAMP:20260422T212553Z
UID:MITLie/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/65/">
 Perverse sheaves on symmetric products of the plane</a>\nby Carl Mautner (
 UC Riverside) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
 n\nAbstract\nIn joint work with Tom Braden we give a purely algebraic desc
 ription of the category of perverse sheaves (with coefficients in any fiel
 d) on $S^n(C^2)$\, the n-fold symmetric product of the plane.  In particul
 ar\, using the geometry of the Hilbert scheme of points\, we relate this c
 ategory to the symmetric group and its representation ring.  Our work is m
 otivated by analogous structure appearing in the Springer resolution and H
 ilbert-Chow morphism.\n
LOCATION:https://researchseminars.org/talk/MITLie/65/
END:VEVENT
END:VCALENDAR