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BEGIN:VEVENT
SUMMARY:Tanmay Deshpande (TIFR)
DTSTART;VALUE=DATE-TIME:20200408T203000Z
DTEND;VALUE=DATE-TIME:20200408T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/1
DESCRIPTION:Title: Character sheaves on algebraic groups\nby Tanmay Deshpa
nde (TIFR) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\n
Abstract\nCharacter sheaves on an algebraic group are supposed to be the g
eometric analogues of irreducible characters of a finite group. In 1980s L
usztig 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 develope
d the theory of character sheaves on unipotent\ngroups. In this talk\, I w
ill describe an approach (due to Drinfeld) towards a theory\nof character
sheaves on general algebraic groups and describe the known results in\nthe
case of solvable algebraic groups.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Mautner (Dartmouth)
DTSTART;VALUE=DATE-TIME:20200415T203000Z
DTEND;VALUE=DATE-TIME:20200415T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/2
DESCRIPTION:Title: Shadows of Lie theory in the world of matroids\nby Carl
Mautner (Dartmouth) as part of MIT Lie groups seminar\n\n\nAbstract\nI wi
ll discuss a program (partly conjectural) exploring analogues of the Schur
\nalgebra and category $\\mathcal O$ for matroids and oriented matroids. T
his program was motivated in large part by work of Braden-Licata-Proudfoot
-Webster. The talk\nwill be based on joint work with Tom Braden and work i
n progress with Jens\nEberhardt and Ethan Kowalenko. I will not assume pri
or knowledge of matroid\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART;VALUE=DATE-TIME:20200506T203000Z
DTEND;VALUE=DATE-TIME:20200506T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/3
DESCRIPTION:Title: Arthur packets for G(2) and perverse sheaves on cubics\
nby Clifton Cunningham (University of Calgary) as part of MIT Lie groups s
eminar\n\n\nAbstract\nThis talk demonstrates a non-invasive procedure that
calculates Arthur packets\, their associated stable distributions and Lan
glands-Shelstad transfers\, without direct use of endoscopy\, using certai
n unipotent representations of the split p-adic exceptional group G(2) as
examples. In the case at hand\, this procedure relies on a study of the ca
tegory of GL(2)-equivariant perverse sheaves on the moduli space of homoge
neous cubics in two variables\, which is perhaps of independent interest.
Specifically\, we find the Fourier transform and the microlocalization of
the simple objects in this category\, and convert that into information ab
out the Aubert involution and stable distributions attached to Arthur pack
ets. This is joint work with Andrew Fiori and Qing Zhang\, based on earlie
r joint work with Andrew Fiori\, Ahmed Moussaoui\, James Mracek and Bin Xu
\, which is based on earlier work by David Vogan\, sadly\, not joint.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (MIT)
DTSTART;VALUE=DATE-TIME:20200429T203000Z
DTEND;VALUE=DATE-TIME:20200429T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/4
DESCRIPTION:Title: Unipotent representations of real reductive groups\nby
Lucas Mason-Brown (MIT) as part of MIT Lie groups seminar\n\n\nAbstract\nL
et $G$ be a real reductive group and let ${\\widehat G}$ be the set of\nir
reducible unitary representations of $G$. The determination of $\\widehat
G$ (for\narbitrary $G$) is one of the fundamental unsolved problems in\nre
presentation theory. In the early 1980s\, Arthur introduced a finite\nset
Unip($G$) of (conjecturally unitary) irreducible representations of\n$G$ c
alled {\\it unipotent representations}. In a certain sense\, these\nrepres
entations form the building blocks of $\\widehat G$. Hence\, the\ndetermin
ation of $\\widehat G$ requires as a crucial ingredient the determination\
nof Unip($G$). In this thesis\, we prove three results on unipotent\nrepre
sentations. First\, 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-s
tanding conjecture of Vogan. Next\, we study the\nunipotent representation
s attached to induced nilpotent orbits. We\nfind that Unip($G$) is ‘gene
rated’ by an even smaller set $\\hbox{Unip}'(G)$\nconsisting of represen
tations attached to rigid nilpotent\norbits. Finally\, we study the unipot
ent representations attached to\nthe principal nilpotent orbit. We provide
a complete classification of\nsuch representations\, including a formula
for their $K$-types.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART;VALUE=DATE-TIME:20200422T203000Z
DTEND;VALUE=DATE-TIME:20200422T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/5
DESCRIPTION:Title: Canonical bases and coherent sheaves\nby Roman Bezrukav
nikov (MIT) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\
nAbstract\nThe primary application of canonical bases in a Grothendieck gr
oup of\nrepresentations is to computation of characters of (say) irreducib
le\nrepresentations\; however\, it is not their only application. I will\
nreview construction and properties of canonical bases in Grothendieck\ngr
oups of coherent sheaves on the Springer resolution and related\nspaces an
d speculate on possible generalization to a new setting\ninvolving the fix
ed group of an involution. The toolbox includes\nlinear Koszul duality of
Mirkovic-Riche and a version of Soergel\nbimodules theory.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Adams (University of Maryland)
DTSTART;VALUE=DATE-TIME:20200513T203000Z
DTEND;VALUE=DATE-TIME:20200513T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/6
DESCRIPTION:Title: Unipotent representations\nby Jeffrey Adams (University
of Maryland) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\
n\nAbstract\nI will give an overview of the current state of the Atlas of
Lie groups and Representations project\, with an emphasis on computing all
unipotent representations\nof real exceptional groups.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Vogan (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20200909T203000Z
DTEND;VALUE=DATE-TIME:20200909T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/7
DESCRIPTION:Title: Structure of Harish-Chandra cells\nby David Vogan (MIT
Mathematics) as part of MIT Lie groups seminar\n\n\nAbstract\nOne of the f
undamental contributions of Kazhdan and Lusztig's 1979 Inventiones paper w
as the notion of "cells" in Weyl groups. They gave a decomposition of the
left regular representation of W as a direct sum of "left cell" representa
tions\, which encode deep and powerful information about group representat
ions. In the case of the symmetric group S_n=W\, the left cells are irredu
cible representations. In all other cases they are not. Lusztig in his 198
4 book gave a beautiful description of all left cells in terms of the geom
etry of a nilpotent orbit.\n\\\\\nThere is a parallel notion of "Harish-Ch
andra 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) representations. I will formulate a conjecture extending Lusztig
's calculation of left cell representations to this case\, and explain its
connection with Arthur's theory of unipotent representations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20200916T203000Z
DTEND;VALUE=DATE-TIME:20200916T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/8
DESCRIPTION:Title: A strong Henniart identity for reductive groups over fi
nite fields\nby Charlotte Chan (MIT Mathematics) as part of MIT Lie groups
seminar\n\nLecture held in 2-142.\n\nAbstract\nIn 1992\, Henniart proved
that supercuspidal representations for –adic GLn are determined by their
character on so-called very regular elements. This has been useful in m
any ways as it allows for convenient comparison between various constructi
ons of supercuspidal representations for GLn. We describe a version of t
his type of result which holds for (some) representations of reductive gro
ups over finite fields. This is joint work with Masao Oi.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wang (MIT Mathematics)
DTSTART;VALUE=DATE-TIME:20200923T203000Z
DTEND;VALUE=DATE-TIME:20200923T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/9
DESCRIPTION:Title: Spherical varieties\, L-functions\, and crystal bases\n
by Jonathan Wang (MIT Mathematics) as part of MIT Lie groups seminar\n\nLe
cture held in 2-142.\n\nAbstract\nThe program of Sakellaridis and Venkates
h proposes a unified framework to study integral representations of L-func
tions through the lens of spherical varieties. For X an affine spherical v
ariety\, the (hypothetical) IC complex of the infinite-dimensional formal
arc space of X is conjecturally related to special values of local unramif
ied L-functions. We formulate this relation precisely using a new conjectu
ral geometric construction of the crystal basis of a finite-dimensional re
presentation (determined by X) of the dual group. We prove these conjectur
es for a large class of spherical varieties. This is joint work with Yiann
is Sakellaridis.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Dudas (CNRS)
DTSTART;VALUE=DATE-TIME:20200930T203000Z
DTEND;VALUE=DATE-TIME:20200930T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/10
DESCRIPTION:Title: Macdonald polynomials and decomposition numbers for fin
ite unitary groups\nby Olivier Dudas (CNRS) as part of MIT Lie groups semi
nar\n\nLecture held in 2-142.\n\nAbstract\n(work in progress with R. Rouqu
ier) In this talk I will present a computational (yet conjectural) method
to determine some decomposition matrices for finite groups of Lie type. I
will first explain how one can produce a "natural" self-equivalence in the
case of $\\mathrm{GL}_n(q)$ coming from the topology of the Hilbert schem
e of $\\mathbb{C}^2$. The combinatorial part of this equivalence is relate
d to Macdonald's theory of symmetric functions and gives $(q\,t)$-decompos
ition numbers. The evidence suggests that the case of finite unitary group
s is obtained by taking a suitable square root of that equivalence.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART;VALUE=DATE-TIME:20201007T203000Z
DTEND;VALUE=DATE-TIME:20201007T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/11
DESCRIPTION:Title: Two Dimensional Field Theories and Partial Fractions\nb
y 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 wit
h M.Khovanov and Y.Kononov. By evaluating a topological field theory in di
mension 2 on surfaces of genus 0\,1\,2 etc we get a sequence. We investiga
te which sequences occur in this way depending on the assumptions on the t
arget category.\n\n\n\n\n\nPlease become a member of our email list to rec
eive announcements of upcoming MIT Lie Groups seminars as well as related
information:\n\nhttps://mailman.mit.edu:444/mailman/listinfo/liegroups\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten Solleveld (Radboud Universiteit)
DTSTART;VALUE=DATE-TIME:20201014T203000Z
DTEND;VALUE=DATE-TIME:20201014T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/12
DESCRIPTION:Title: Bernstein components for p-adic groups\nby Maarten Soll
eveld (Radboud Universiteit) as part of MIT Lie groups seminar\n\nLecture
held in 2-142.\n\nAbstract\nSuppose that one has a supercuspidal represent
ation of a Levi subgroup of some reductive $p$-adic group $G$. Bernstein a
ssociated to this a block Rep$(G)^s$ in the category of smooth $G$-represe
ntations. We address the question: what does Rep$(G)^s$ look like?\n\nUsua
lly this is investigated with Bushnell--Kutzko types\, but these are not a
lways 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" equ
ivalent with the module category of an affine Hecke algebra -- a statement
that will be made precise in several ways.\n\nIn the end\, this leads to
a classification of the irreducible representations in Rep$(G)^s$ in terms
of the complex torus and the finite groups that are canonically associate
d to this Bernstein component.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (University of Wisconsin)
DTSTART;VALUE=DATE-TIME:20201021T203000Z
DTEND;VALUE=DATE-TIME:20201021T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
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 g
roups seminar\n\nLecture held in 2-142.\n\nAbstract\nLet X be a projective
curve\, G a reductive group. Let Bun be the stack of G-bundles over X\, a
nd consider the category of D-modules on Bun. (This category appears on th
e “automorphic” side of the geometric Langlands correspondence.) Drinf
eld and Gaitsgory prove that\, despite the “unbounded” (non-quasi comp
act) nature of Bun\, the category of D-modules is well-behaved (compactly
generated).\n\nIn this talk\, we will “compactify” this category in a
stronger sense\; this can be viewed as compactifying the quantized cotange
nt bundle to Bun. While the basic idea of such compactification goes back
to ideas of Deligne and Simpson\, its construction relies on non-trivial p
roperties of the geometry of Bun (similar to the Drinfeld-Gaitsgory Theore
m).\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201028T203000Z
DTEND;VALUE=DATE-TIME:20201028T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/14
DESCRIPTION:Title: Categorical g-actions for modules over truncated shifte
d Yangians\nby Joel Kamnitzer (University of Toronto) as part of MIT Lie g
roups seminar\n\nLecture held in 2-142.\n\nAbstract\nGiven a representatio
n V of a reductive group G\, Braverman-Finkelberg-Nakajima defined a Poiss
on variety called the Coulomb branch\, using a convolution algebra constru
ction. This variety comes with a natural deformation quantization\, called
a Coulomb branch algebra. Important cases of these Coulomb branches are (
generalized) affine Grassmannian slices\, and their quantizations are trun
cated shifted Yangians.\n\nMotivated by the geometric Satake correspondenc
e and the theory of symplectic duality/3d mirror symmetry\, we expect a ca
tegorical g-action on modules for these truncated shifted Yangians. I will
explain three results in this direction. First\, we have an indirect real
ization of this action\, using equivalences with KLRW-modules. Second\, we
have a geometric relation between these generalized slices by Hamiltonian
reduction. Finally\, we have an algebraic version of this Hamiltonian red
uction which we are able to relate to the first realization.\n\nThis semin
ar will take place entirely online. Please email Andre Dixon (aldixon@mit.
edu) for the Zoom meeting Link.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harrison Chen (Cornell University)
DTSTART;VALUE=DATE-TIME:20201110T213000Z
DTEND;VALUE=DATE-TIME:20201110T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/15
DESCRIPTION:Title: Coherent Springer theory and categorical Deligne-Langla
nds\nby Harrison Chen (Cornell University) as part of MIT Lie groups semin
ar\n\nLecture held in 2-142.\n\nAbstract\nKazhdan and Lusztig proved the D
eligne-Langlands conjecture\, a bijection between irreducible representati
ons of unipotent principal block representations of a p-adic group with ce
rtain unipotent Langlands parameters in the Langlands dual group (plus the
data of certain representations). We lift this bijection to a statement
on the level of categories. Namely\, we define a stack of unipotent Lan
glands parameters and a coherent sheaf on it\, which we call the coherent
Springer sheaf\, which generates a subcategory of the derived category equ
ivalent to modules for the affine Hecke algebra (or specializing at q\, un
ipotent principal block representations of a p-adic group). Our approach
involves categorical traces\, Hochschild homology\, and Bezrukavnikov's L
anglands dual realizations of the affine Hecke category. This is a joint
work with David Ben-Zvi\, David Helm and David Nadler.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostiantyn Tolmachov (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201104T213000Z
DTEND;VALUE=DATE-TIME:20201104T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/16
DESCRIPTION:Title: Monodromic model for Khovanov-Rozansky homology\nby Kos
tiantyn Tolmachov (University of Toronto) as part of MIT Lie groups semina
r\n\nLecture held in 2-142.\n\nAbstract\nKhovanov-Rozansky homology is a k
not invariant which\, by the result of Khovanov\, can be computed as the H
ochschild cohomology functor applied Rouquier complexes of Soergel bimodul
es. I will describe a new geometric model for the Hochschild cohomology of
Soergel bimodules\, living in the monodromic Hecke category. I will also
explain how it allows to identify objects representing individual Hochsсh
ild cohomology groups as images of explicit character sheaves.\n\nBased on
the joint work with Roman Bezrukavnikov.\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Kononov (Columbia University)
DTSTART;VALUE=DATE-TIME:20201118T213000Z
DTEND;VALUE=DATE-TIME:20201118T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/17
DESCRIPTION:by Yakov Kononov (Columbia University) as part of MIT Lie grou
ps seminar\n\nLecture held in 2-142.\nAbstract: TBA\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masao OI (University of Kyoto)
DTSTART;VALUE=DATE-TIME:20201202T230000Z
DTEND;VALUE=DATE-TIME:20201203T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/18
DESCRIPTION:by Masao OI (University of Kyoto) as part of MIT Lie groups se
minar\n\nLecture held in 2-142.\nAbstract: TBA\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Lusztig (MIT)
DTSTART;VALUE=DATE-TIME:20201209T213000Z
DTEND;VALUE=DATE-TIME:20201209T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
UID:MITLie/19
DESCRIPTION:by George Lusztig (MIT) as part of MIT Lie groups seminar\n\nL
ecture held in 2-142.\nAbstract: TBA\n
LOCATION:Lecture held in 2-142
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erez Lapid (Weizmann Institute)
DTSTART;VALUE=DATE-TIME:20201216T213000Z
DTEND;VALUE=DATE-TIME:20201216T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050945Z
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:Lecture held in 2-142
END:VEVENT
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