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BEGIN:VEVENT
SUMMARY:Tanmay Deshpande (TIFR)
DTSTART;VALUE=DATE-TIME:20200408T203000Z
DTEND;VALUE=DATE-TIME:20200408T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/1
DESCRIPTION:Title: C
haracter sheaves on algebraic groups\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;VALUE=DATE-TIME:20200415T203000Z
DTEND;VALUE=DATE-TIME:20200415T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/2
DESCRIPTION:Title: S
hadows of Lie theory in the world of matroids\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;VALUE=DATE-TIME:20200506T203000Z
DTEND;VALUE=DATE-TIME:20200506T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/3
DESCRIPTION:Title: A
rthur packets for G(2) and perverse sheaves on cubics\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;VALUE=DATE-TIME:20200429T203000Z
DTEND;VALUE=DATE-TIME:20200429T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/4
DESCRIPTION:Title: U
nipotent representations of real reductive groups\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;VALUE=DATE-TIME:20200422T203000Z
DTEND;VALUE=DATE-TIME:20200422T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/5
DESCRIPTION:Title: C
anonical bases and coherent sheaves\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;VALUE=DATE-TIME:20200513T203000Z
DTEND;VALUE=DATE-TIME:20200513T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/6
DESCRIPTION:Title: U
nipotent representations\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;VALUE=DATE-TIME:20200909T203000Z
DTEND;VALUE=DATE-TIME:20200909T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/7
DESCRIPTION:Title: S
tructure of Harish-Chandra cells\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;VALUE=DATE-TIME:20200916T203000Z
DTEND;VALUE=DATE-TIME:20200916T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/8
DESCRIPTION:Title: A
strong Henniart identity for reductive groups over finite fields\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;VALUE=DATE-TIME:20200923T203000Z
DTEND;VALUE=DATE-TIME:20200923T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/9
DESCRIPTION:Title: S
pherical varieties\, L-functions\, and crystal bases\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;VALUE=DATE-TIME:20200930T203000Z
DTEND;VALUE=DATE-TIME:20200930T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/10
DESCRIPTION:Title:
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;VALUE=DATE-TIME:20201007T203000Z
DTEND;VALUE=DATE-TIME:20201007T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/11
DESCRIPTION:Title:
Two Dimensional Field Theories and Partial Fractions\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;VALUE=DATE-TIME:20201014T203000Z
DTEND;VALUE=DATE-TIME:20201014T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/12
DESCRIPTION:Title:
Bernstein components for p-adic groups\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;VALUE=DATE-TIME:20201021T203000Z
DTEND;VALUE=DATE-TIME:20201021T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/13
DESCRIPTION:Title:
Compactifying the category of D-modules on the stack of G-bundles\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;VALUE=DATE-TIME:20201028T203000Z
DTEND;VALUE=DATE-TIME:20201028T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/14
DESCRIPTION:Title:
Categorical g-actions for modules over truncated shifted Yangians\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;VALUE=DATE-TIME:20201110T213000Z
DTEND;VALUE=DATE-TIME:20201110T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/15
DESCRIPTION:Title:
Coherent Springer theory and categorical Deligne-Langlands\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;VALUE=DATE-TIME:20201104T213000Z
DTEND;VALUE=DATE-TIME:20201104T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/16
DESCRIPTION:Title:
Monodromic model for Khovanov-Rozansky homology\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;VALUE=DATE-TIME:20201118T213000Z
DTEND;VALUE=DATE-TIME:20201118T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/17
DESCRIPTION:Title:
Elliptic stable envelopes and 3-dimensional mirror symmetry\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;VALUE=DATE-TIME:20201202T230000Z
DTEND;VALUE=DATE-TIME:20201203T000000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/18
DESCRIPTION:Title:
Twisted endoscopic character relation for Kaletha's regular supercuspidal
L-packets\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;VALUE=DATE-TIME:20201209T213000Z
DTEND;VALUE=DATE-TIME:20201209T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/19
DESCRIPTION:Title:
From families in Weyl groups to unipotent elements\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;VALUE=DATE-TIME:20201216T213000Z
DTEND;VALUE=DATE-TIME:20201216T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
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;VALUE=DATE-TIME:20210224T213000Z
DTEND;VALUE=DATE-TIME:20210224T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/21
DESCRIPTION:Title:
Unipotent Harish-Chandra bimodules\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;VALUE=DATE-TIME:20210303T213000Z
DTEND;VALUE=DATE-TIME:20210303T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/22
DESCRIPTION:Title:
From the Hecke Category to the Unipotent Locus\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;VALUE=DATE-TIME:20210310T213000Z
DTEND;VALUE=DATE-TIME:20210310T223000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/23
DESCRIPTION:Title:
Harmonic analysis and gamma functions on symplectic group\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;VALUE=DATE-TIME:20210317T203000Z
DTEND;VALUE=DATE-TIME:20210317T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/24
DESCRIPTION:Title:
Graded Lie algebras\, character sheaves\, and representations of DAHAs
\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;VALUE=DATE-TIME:20210324T203000Z
DTEND;VALUE=DATE-TIME:20210324T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/25
DESCRIPTION:Title:
Categorified sheaf theory and the spectral Betti Langlands TQFT\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;VALUE=DATE-TIME:20210407T203000Z
DTEND;VALUE=DATE-TIME:20210407T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/26
DESCRIPTION:Title:
Macdonald polynomials and counting parabolic bundles\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;VALUE=DATE-TIME:20210414T203000Z
DTEND;VALUE=DATE-TIME:20210414T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/27
DESCRIPTION:Title:
Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric Satake
equivalence\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;VALUE=DATE-TIME:20210421T203000Z
DTEND;VALUE=DATE-TIME:20210421T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/28
DESCRIPTION:Title:
Hitchin fibration and commuting schemes\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;VALUE=DATE-TIME:20210428T203000Z
DTEND;VALUE=DATE-TIME:20210428T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/29
DESCRIPTION:Title:
What is a unipotent representation?\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;VALUE=DATE-TIME:20210505T203000Z
DTEND;VALUE=DATE-TIME:20210505T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/30
DESCRIPTION:Title:
Finite Howe correspondence and Lusztig classification\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;VALUE=DATE-TIME:20210512T203000Z
DTEND;VALUE=DATE-TIME:20210512T213000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/31
DESCRIPTION:Title:
Quantization and Duality for Spherical Varieties\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;VALUE=DATE-TIME:20210519T173000Z
DTEND;VALUE=DATE-TIME:20210519T183000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/32
DESCRIPTION:Title:
Kac-Moody superalgebras and Duflo-Serganova functors\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;VALUE=DATE-TIME:20210908T200000Z
DTEND;VALUE=DATE-TIME:20210908T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/33
DESCRIPTION:Title:
Constructing unipotent representations\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;VALUE=DATE-TIME:20210915T200000Z
DTEND;VALUE=DATE-TIME:20210915T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/34
DESCRIPTION:Title:
From braids to transverse slices in reductive groups\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;VALUE=DATE-TIME:20210922T200000Z
DTEND;VALUE=DATE-TIME:20210922T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/35
DESCRIPTION:Title:
Total positivity in symmetric spaces\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;VALUE=DATE-TIME:20210929T200000Z
DTEND;VALUE=DATE-TIME:20210929T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/36
DESCRIPTION:Title:
Harish-Chandra modules over quantizations of nilpotent orbits.\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;VALUE=DATE-TIME:20211006T140000Z
DTEND;VALUE=DATE-TIME:20211006T150000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/37
DESCRIPTION:Title:
Frobenius-twisted conjugacy classes of loop groups and Demazure product of
Iwhaori-Weyl groups\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;VALUE=DATE-TIME:20211020T200000Z
DTEND;VALUE=DATE-TIME:20211020T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/38
DESCRIPTION:Title:
Frobenii on Morava E-theoretical quantum groups\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;VALUE=DATE-TIME:20211027T200000Z
DTEND;VALUE=DATE-TIME:20211027T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/39
DESCRIPTION:Title:
Topological realization of rings of quasi-invariants of finite reflection
groups\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;VALUE=DATE-TIME:20211110T210000Z
DTEND;VALUE=DATE-TIME:20211110T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/40
DESCRIPTION:Title:
Quantum symmetric pairs via star products\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;VALUE=DATE-TIME:20211013T200000Z
DTEND;VALUE=DATE-TIME:20211013T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/41
DESCRIPTION:Title:
Derived Chevalley isomorphisms\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;VALUE=DATE-TIME:20211103T200000Z
DTEND;VALUE=DATE-TIME:20211103T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/42
DESCRIPTION:Title:
Universal symplectic quotients via Lie theory\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;VALUE=DATE-TIME:20211117T210000Z
DTEND;VALUE=DATE-TIME:20211117T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/43
DESCRIPTION:Title:
Examples of Hecke eigen-functions for moduli spaces of bundles over local
non-archimedean field and an analog of Eisenstein series\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;VALUE=DATE-TIME:20211201T210000Z
DTEND;VALUE=DATE-TIME:20211201T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/44
DESCRIPTION:Title:
Seminar Cancelled\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;VALUE=DATE-TIME:20211208T210000Z
DTEND;VALUE=DATE-TIME:20211208T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/45
DESCRIPTION:Title:
A nonabelian Fourier transform for tempered unipotent representations of p
-adic groups\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;VALUE=DATE-TIME:20220209T210000Z
DTEND;VALUE=DATE-TIME:20220209T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/46
DESCRIPTION:Title:
Mixed Hodge modules and representation theory of real groups\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;VALUE=DATE-TIME:20220216T210000Z
DTEND;VALUE=DATE-TIME:20220216T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/47
DESCRIPTION:Title:
The wavefront set and Arthur packets of p-adic groups\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;VALUE=DATE-TIME:20220223T210000Z
DTEND;VALUE=DATE-TIME:20220223T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/48
DESCRIPTION:Title:
Kazhdan-Lusztig Equivalence at the Iwahori Level\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;VALUE=DATE-TIME:20220302T210000Z
DTEND;VALUE=DATE-TIME:20220302T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/49
DESCRIPTION:Title:
Characterization and construction of the local Langlands correspondence fo
r supercuspidal parameters\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;VALUE=DATE-TIME:20220309T210000Z
DTEND;VALUE=DATE-TIME:20220309T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/50
DESCRIPTION:Title:
Calogero-Moser spaces vs unipotent representations\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;VALUE=DATE-TIME:20220316T200000Z
DTEND;VALUE=DATE-TIME:20220316T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/51
DESCRIPTION:Title:
On the trace of the affine Hecke category\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;VALUE=DATE-TIME:20220330T200000Z
DTEND;VALUE=DATE-TIME:20220330T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/52
DESCRIPTION:Title:
Categorical Representation Theory and the Coarse Quotient\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;VALUE=DATE-TIME:20220406T200000Z
DTEND;VALUE=DATE-TIME:20220406T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/53
DESCRIPTION:Title:
Perverse mod p sheaves on affine flag varieties\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;VALUE=DATE-TIME:20220504T200000Z
DTEND;VALUE=DATE-TIME:20220504T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/54
DESCRIPTION:Title:
Title to be announced\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;VALUE=DATE-TIME:20220511T200000Z
DTEND;VALUE=DATE-TIME:20220511T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/55
DESCRIPTION:Title:
Co-t-structures on coherent sheaves and the Humphreys conjecture\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;VALUE=DATE-TIME:20220413T200000Z
DTEND;VALUE=DATE-TIME:20220413T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/56
DESCRIPTION:Title:
Tilting sheaves for real groups and Koszul duality\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;VALUE=DATE-TIME:20220420T200000Z
DTEND;VALUE=DATE-TIME:20220420T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/57
DESCRIPTION:Title:
Hessenberg varieties and the geometric modular law\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;VALUE=DATE-TIME:20220921T200000Z
DTEND;VALUE=DATE-TIME:20220921T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/58
DESCRIPTION:Title:
Wavefront sets and unipotent representations of p-adic groups\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;VALUE=DATE-TIME:20220928T200000Z
DTEND;VALUE=DATE-TIME:20220928T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/59
DESCRIPTION:Title:
Title to be announced\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;VALUE=DATE-TIME:20221005T200000Z
DTEND;VALUE=DATE-TIME:20221005T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/60
DESCRIPTION:Title:
Affine Springer fibers and sheaves on Hilbert scheme of points on the plan
e.\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;VALUE=DATE-TIME:20221012T200000Z
DTEND;VALUE=DATE-TIME:20221012T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/61
DESCRIPTION:Title:
From geometric Langlands to classical via the trace of Frobenius\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;VALUE=DATE-TIME:20221019T200000Z
DTEND;VALUE=DATE-TIME:20221019T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/62
DESCRIPTION:Title:
Title to be announced\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;VALUE=DATE-TIME:20221026T200000Z
DTEND;VALUE=DATE-TIME:20221026T210000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/63
DESCRIPTION:Title:
On some Hecke algebra modules arising from theta correspondence and it’s
deformation\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;VALUE=DATE-TIME:20221109T210000Z
DTEND;VALUE=DATE-TIME:20221109T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/64
DESCRIPTION:Title:
Moduli space of flower curves\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;VALUE=DATE-TIME:20221116T210000Z
DTEND;VALUE=DATE-TIME:20221116T220000Z
DTSTAMP;VALUE=DATE-TIME:20230202T134221Z
UID:MITLie/65
DESCRIPTION:Title:
Perverse sheaves on symmetric products of the plane\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