BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Oscar Kivinen (Caltech)
DTSTART:20200623T140000Z
DTEND:20200623T143000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/2
DESCRIPTION:Title: Z-algebras from Coulomb branches\nby Oscar Kivinen (Caltech) a
s part of Geometric Representation Theory conference\n\n\nAbstract\nI will
explain how to obtain the Gordon-Stafford construction and some related c
onstructions of $Z$-algebras in the literature\, using certain mathematica
l avatars of line defects in 3d $\\mathcal N$=$4$ theories. Time permit
ting\, I will discuss the $K$-theoretic and elliptic cases as well.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (Harvard/Aarhus)
DTSTART:20200624T140000Z
DTEND:20200624T143000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/3
DESCRIPTION:Title: Elliptic stable envelopes via loop spaces\nby Michael McBreen
(Harvard/Aarhus) as part of Geometric Representation Theory conference\n\n
\nAbstract\nElliptic stable envelopes\, introduced by Aganagic and Okounko
v\, are a key ingredient in the study of quantum integrable systems attach
ed to a symplectic resolution. I will describe a relation between elliptic
stable envelopes on a hypertoric variety and a certain 'loop space' of th
at variety. Joint with Artan Sheshmani and Shing-Tung Yau.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Bozec (Université de Montpeilier)
DTSTART:20200625T151500Z
DTEND:20200625T154500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/4
DESCRIPTION:Title: Relative critical loci\, quiver moduli\, and new lagrangian subvar
ieties\nby Tristan Bozec (Université de Montpeilier) as part of Geome
tric Representation Theory conference\n\n\nAbstract\nThe preprojective alg
ebra of a quiver naturally appears when computing\nthe cotangent to the qu
iver moduli\, via the moment map. When considering\nthe derived setting\,
it is replaced by its differential graded (dg)\nvariant\, introduced by Gi
nzburg. This construction can be generalized\nusing potentials\, so that o
ne retrieves critical loci when considering\nmoduli of perfect modules.\nO
ur idea is to consider some relative\, or constrained critical loci\,\ndef
ormations of the above\, and study Calabi--Yau structures on the\nunderlyi
ng relative versions of Ginzburg's dg-algebras. It yields for\ninstance so
me new lagrangian subvarieties of the Hilbert schemes of\npoints on the pl
ane.\n\nThis reports a joint work with Damien Calaque and Sarah Scherotzke
\narxiv.org/abs/2006.01069\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (MPIM Bonn)
DTSTART:20200626T151500Z
DTEND:20200626T154500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/5
DESCRIPTION:Title: K-Motives and Koszul Duality\nby Jens Eberhardt (MPIM Bonn) as
part of Geometric Representation Theory conference\n\n\nAbstract\nKoszul
duality\, as conceived by Beilinson-Ginzburg-Soergel\, describes a remarka
ble symmetry in the representation theory of Langlands dual reductive grou
ps. Geometrically\, Koszul duality can be stated as an equivalence of cate
gories of mixed (motivic) sheaves on flag varieties. In this talk\, I will
argue that there should be an an 'ungraded' version of Koszul duality bet
ween monodromic constructible sheaves and equivariant $K$-motives on flag
varieties. For this\, I will explain what $K$-motives are and present prel
iminary results.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Scherotzke (Université du Luxembourg)
DTSTART:20200622T144500Z
DTEND:20200622T154500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/6
DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg algebras\
nby Sarah Scherotzke (Université du Luxembourg) as part of Geometric Repr
esentation Theory conference\n\n\nAbstract\nWe give an introduction to the
notion of moduli stack of a dg category. \nWe explain what shifted symple
ctic structures are and how they are connected to Calabi-Yau structures on
dg categories. More concretely\, we will show that the cotangent complex
to the moduli stack of a dg category $A$ admits a modular interpretation:
namely\, it is isomorphic to the moduli stack of the Calabi-Yau completion
of $A$. This answers a conjecture of Keller-Yeung. \n \nThis is joint wor
k with Damien Calaque and Tristan Bozec arxiv.org/abs/2006.01069\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (Université de Paris-Sud ORSAY)
DTSTART:20200622T160000Z
DTEND:20200622T170000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/7
DESCRIPTION:Title: Yangians and cohomological Hall algebras of Higgs sheaves on curve
s\nby Olivier Schiffmann (Université de Paris-Sud ORSAY) as part of G
eometric Representation Theory conference\n\n\nAbstract\nWe will review a
set of conjectures related to the structure of cohomological Hall algebras
(COHA) of categories of Higgs sheaves on curves. We then focus on the cas
e of $\\mathbb P^1$\, and relate its COHA to the affine Yangian of $\\math
frak{sl}_2$\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Raskin (University of Texas at Austin)
DTSTART:20200622T180000Z
DTEND:20200622T190000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/11
DESCRIPTION:Title: Tate's thesis in the de Rham setting\nby Sam Raskin (Universi
ty of Texas at Austin) as part of Geometric Representation Theory conferen
ce\n\n\nAbstract\nThis is joint work with Justin Hilburn. We will explain
a theorem showing that $D$-modules on the Tate vector space of Laurent ser
ies are equivalent to ind-coherent sheaves on the space of rank 1 de Rham
local systems on the punctured disc equipped with a flat section. Time per
mitting\, we will also describe an application of this result in the globa
l setting. Our results may be understood as a geometric refinement of Tate
's ideas in the setting of harmonic analysis. They also may be understood
as a proof of a strong form of the 3d mirror symmetry conjectures: our res
ults amount to an equivalence of A/B-twists of the free hypermultiplet and
a $U(1)$-gauged hypermultiplet.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Stanford University)
DTSTART:20200622T191500Z
DTEND:20200622T194500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/12
DESCRIPTION:Title: Fundamental local equivalences in quantum geometric Langlands
\nby Gurbir Dhillon (Stanford University) as part of Geometric Representat
ion Theory conference\n\n\nAbstract\nIn quantum geometric Langlands\, the
Satake equivalence plays a less prominent role than in the classical theor
y. Gaitsgory-Lurie proposed a conjectural substitute\, later termed the fu
ndamental local equivalence\, relating categories of arc-integrable Kac-Mo
ody representations and Whittaker $D$-modules on the affine Grassmannian.
With a few exceptions\, we verified this conjecture non-factorizably\, as
well as its extension to the affine flag variety. This is a report on join
t work with Justin Campbell and Sam Raskin.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Lanini (Università di Roma Tor Vergata)
DTSTART:20200623T144500Z
DTEND:20200623T154500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/13
DESCRIPTION:Title: Singularities of Schubert varieties within a right cell\nby M
artina Lanini (Università di Roma Tor Vergata) as part of Geometric Repre
sentation Theory conference\n\n\nAbstract\nWe describe an algorithm which
takes as input any pair of\npermutations and gives as output two permutati
ons lying in the same\nKazhdan-Lusztig right cell. There is an isomorphism
between the\nRichardson varieties corresponding to the two pairs of permu
tations\nwhich preserves the singularity type. This fact has applications
in the\nstudy of $W$-graphs for symmetric groups\, as well as in finding e
xamples\nof reducible associated varieties of sln-highest weight modules\,
and\ncomparing various bases of irreducible representations of the symmet
ric\ngroup or its Hecke algebra. This is joint work with Peter McNamara.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20200624T160000Z
DTEND:20200624T170000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/14
DESCRIPTION:Title: Modular representations and perverse sheaves on affine flag varie
ties\nby Roman Bezrukavnikov (MIT) as part of Geometric Representation
Theory conference\n\n\nAbstract\nI will give an overview of a joint proje
ct with Simon Riche and Laura Rider and another one\nwith Dima Arinkin aim
ed at a modular version of the equivalence between two geometric realizati
on of the affine Hecke algebra and derived Satake equivalence respectively
. As a byproduct we obtain a proof of the Finkelberg-Mirkovic conjecture a
nd a possible approach to understanding cohomology of higher Frobenius ker
nels with coefficients in a $G$-module.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenna Rajchgot (University of Saskatchewan)
DTSTART:20200623T180000Z
DTEND:20200623T190000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/15
DESCRIPTION:Title: Type D quiver representation varieties\, double Grassmannians\, a
nd symmetric varieties\nby Jenna Rajchgot (University of Saskatchewan)
as part of Geometric Representation Theory conference\n\n\nAbstract\nSinc
e the 1980s\, mathematicians have found connections between orbit closures
in type $A$ quiver representation varieties and Schubert varieties in typ
e $A$ flag varieties. For example\, singularity types appearing in type $A
$ quiver orbit closures coincide with those appearing in Schubert varietie
s in type $A$ flag varieties (Bobinski-Zwara)\; combinatorics of type $A$
quiver orbit closure containment is governed by Bruhat order on the symmet
ric group (follows from work of Zelevinsky\, Kinser-R.)\; and multiple res
earchers have produced formulas for classes of type $A$ quiver orbit closu
res in equivariant cohomology and $K$-theory in terms of Schubert polynomi
als\, Grothendieck polynomials\, and related objects.\n \nAfter recalling
some of this type $A$ story\, I will discuss joint work with Ryan Kinser o
n type $D$ quiver representation varieties. I will describe explicit embed
dings which completes a circle of links between orbit closures in type $D$
quiver representation varieties\, $B$-orbit closures (for a Borel subgrou
p $B$ of $GL_n$) in certain symmetric varieties $GL_n/K$\, and $B$-orbit c
losures in double Grassmannians $Gr(a\, n) \\times Gr(b\, n)$. I will end
with some geometric and combinatorial consequences\, as well as a brief di
scussion of joint work in progress with Zachary Hamaker and Ryan Kinser on
formulas for classes of type $D$ quiver orbit closures in equivariant coh
omology.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (MIT)
DTSTART:20200623T191500Z
DTEND:20200623T194500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/16
DESCRIPTION:Title: K-theoretic Hall algebras\nby Tudor Padurariu (MIT) as part o
f Geometric Representation Theory conference\n\n\nAbstract\nGiven a quiver
with potential\, Kontsevich-Soibelman constructed a Hall algebra on the c
ohomology of the stack of representations of $(Q\,W)$. In particular cases
\, one recovers positive parts of Yangians as defined by Maulik-Okounkov.
For general $(Q\,W)$\, the Hall algebra has nice structure properties\, fo
r example Davison-Meinhardt proved a PBW theorem for it using the decompos
ition theorem.\n\nOne can define a $K$-theoretic version of this algebra u
sing certain categories of singularities that depend on the stack of repre
sentations of $(Q\,W)$. In particular cases\, these Hall algebras are posi
tive parts of quantum affine algebras. We show that some of the structure
properties in cohomology\, such as the PBW theorem\, can be lifted to $K$-
theory\, replacing the use of the decomposition theorem with semi-orthogon
al decompositions.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (HSE Moscow)
DTSTART:20200624T144500Z
DTEND:20200624T154500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/17
DESCRIPTION:Title: Global Demazure modules\nby Michael Finkelberg (HSE Moscow) a
s part of Geometric Representation Theory conference\n\n\nAbstract\nThe Be
ilinson-Drinfeld Grassmannian of a simple complex algebraic group admits a
natural stratification into "global spherical Schubert varieties". In the
case when the underlying curve is the affine line\, we determine algebrai
cally the global sections of the determinant line bundle over these global
Schubert varieties as modules over the corresponding Lie algebra of curre
nts. The resulting modules are the global Weyl modules (in the simply lace
d case) and generalizations thereof. This is a joint work with Ilya Dumans
ki and Evgeny Feigin.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia)
DTSTART:20200623T160000Z
DTEND:20200623T170000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/18
DESCRIPTION:Title: Centralizer of a regular unipotent element and perverse sheaves o
n the affine flag variety\nby Laura Rider (University of Georgia) as p
art of Geometric Representation Theory conference\n\n\nAbstract\nIn this t
alk\, I will give a geometric description of the category of representatio
ns of the centralizer of a regular unipotent element in a reductive algebr
aic group in terms of perverse sheaves on the Langlands dual affine flag v
ariety. This is joint work with R. Bezrukavnikov and S. Riche.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Vazirani (UC Davis)
DTSTART:20200624T180000Z
DTEND:20200624T190000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/19
DESCRIPTION:Title: The "Springer" representation of the DAHA\nby Monica Vaziran
i (UC Davis) as part of Geometric Representation Theory conference\n\n\nAb
stract\nThe Springer resolution and resulting Springer sheaf\nare key play
ers in geometric representation theory.\nWhile one can construct the Sprin
ger sheaf geometrically\,\nHotta and Kashiwara gave it a purely algebraic
reincarnation in\nthe language of equivariant $D(\\mathfrak{g})$-modules.\
n\nFor $G = GL_N$\, the endomorphism algebra of the Springer sheaf\,\nor e
quivalently of the associated $D$-module\,\nis isomorphic to $\\mathbb{C}[
\\mathcal{S}_n]$ the group algebra of\nthe symmetric group.\nIn this talk\
, I'll discuss a quantum analogue of this.\nIn joint work with Sam Gunning
ham and David Jordan\, we define\nquantum Hotta-Kashiwara $D$-modules $\\m
athrm{HK}_\\chi$\,\nand compute their endomorphism algebras.\nIn particula
r $\\mathrm{End}_{\\mathcal{D}_q(G)}(\\mathrm{HK}_0)\n\\simeq \\mathbb{C}[
\\mathcal{S}_n]$.\n\nThis is part of a larger program to understand the ca
tegory\nof strongly equivariant quantum $D$-modules.\nOur main tool to stu
dy this category is Jordan's elliptic Schur-Weyl\nduality functor to repr
esentations of the double affine Hecke algebra\n(DAHA).\nWhen we input $\\
mathrm{HK}_0$ into Jordan's functor\,\nthe endomorphism algebra over the D
AHA of the output is\n$\\mathbb{C}[\\mathcal{S}_n]$ from which we deduce
the result above.\n\nFrom studying the output of all the $\\mathrm{HK}_\\
chi$\, we are\nable to compute that for input a distinguished projective\
ngenerator of the category\nthe output is the DAHA module generated by th
e sign idempotent.\n\nThis is joint work with Sam Gunningham and David Jor
dan.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Campbell (Caltech)
DTSTART:20200624T191500Z
DTEND:20200624T194500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/20
DESCRIPTION:Title: Geometric class field theory and Cartier duality\nby Justin C
ampbell (Caltech) as part of Geometric Representation Theory conference\n\
n\nAbstract\nI will explain a generalized Albanese property for smooth cur
ves\, which implies Deligne's geometric class field theory with arbitrary
ramification. The proof essentially reduces to some well-known Cartier dua
lity statements. This is joint work with Andreas Hayash.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Zurich)
DTSTART:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/21
DESCRIPTION:Title: Parabolic restriction for Harish-Chandra bimodules and dynamical
R-matrices\nby Pavel Safronov (University of Zurich) as part of Geomet
ric Representation Theory conference\n\n\nAbstract\nThe category of Harish
-Chandra bimodules is ubiquitous in representation theory. In this talk I
will explain their relationship to the theory of dynamical $R$-matrices (g
oing back to the works of Donin and Mudrov) and quantum moment maps. I wil
l also relate the monoidal properties of the parabolic restriction functor
for Harish-Chandra bimodules to the so-called standard dynamical $R$-matr
ix. This is a report on work in progress\, joint with Artem Kalmykov.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20200625T180000Z
DTEND:20200625T190000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/22
DESCRIPTION:Title: Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra\nby
Eugene Gorsky (UC Davis) as part of Geometric Representation Theory confer
ence\n\n\nAbstract\nIn this note we give an alternative presentation of th
e rational\nCherednik algebra $H_c$ corresponding to the permutation repre
sentation of\n$S_n$. As an application\, we give an explicit combinatorial
basis for all\nstandard and simple modules if the denominator of $c$ is a
t least $n$\, and\ndescribe the action of $H_c$ in this basis. We also giv
e a basis for the\nirreducible quotient of the polynomial representation a
nd compare it to\nthe basis of fixed points in the homology of the parabol
ic Hilbert\nscheme of points on the plane curve singularity $\\{x^n=y^m\\}
$. This is a\njoint work with José Simental and Monica Vazirani.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Przezdziecki (University of Edinburgh)
DTSTART:20200625T191500Z
DTEND:20200625T194500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/23
DESCRIPTION:Title: An extension of Suzuki's functor to the critical level\nby To
masz Przezdziecki (University of Edinburgh) as part of Geometric Represent
ation Theory conference\n\n\nAbstract\nSuzuki's functor relates the repres
entation theory of the affine Lie algebra to the representation theory of
the rational Cherednik algebra in type A. In this talk\, we discuss an ext
ension of this functor to the critical level\, $t=0$ case. This case is sp
ecial because the respective categories of representations have large cent
res. Our main result describes the relationship between these centres\, an
d provides a partial geometric interpretation in terms of Calogero-Moser s
paces and opers.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Romanov (Sydney)
DTSTART:20200625T200000Z
DTEND:20200625T210000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/24
DESCRIPTION:Title: A categorification of the Lusztig-Vogan module\nby Anna Roman
ov (Sydney) as part of Geometric Representation Theory conference\n\n\nAbs
tract\nAdmissible representations of real reductive Lie groups are a key p
layer in the world of unitary representation theory. The characters of irr
educible admissible representations were described by Lustig-Vogan in the
80’s in terms of a geometrically-defined module over the associated Heck
e algebra. In this talk\, I’ll describe a categorification of this modul
e using Soergel bimodules\, with a focus on examples. This is work in prog
ress.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramod Achar (Louisiana State University)
DTSTART:20200626T160000Z
DTEND:20200626T170000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/25
DESCRIPTION:Title: Conjectures on p-cells\, tilting modules\, and nilpotent orbits\nby Pramod Achar (Louisiana State University) as part of Geometric Repr
esentation Theory conference\n\n\nAbstract\nFor quantum groups at a root o
f unity\, there is a web of theorems (due to Bezrukavnikov and Ostrik\, an
d relying on work of Lusztig) connecting the following topics: (i) tilting
modules\; (ii) vector bundles on nilpotent orbits\; and (iii) Kazhdan–L
usztig cells in the affine Weyl group. In this talk\, I will review these
results\, and I will explain a (partly conjectural) analogous picture for
reductive algebraic groups over fields of positive characteristic\, inspir
ed by a conjecture of Humphreys. This is joint work with W. Hardesty and S
. Riche.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Elias (University of Oregon)
DTSTART:20200626T180000Z
DTEND:20200626T190000Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/26
DESCRIPTION:Title: Categorification of the Hecke algebra at roots of unity.\nby
Ben Elias (University of Oregon) as part of Geometric Representation Theor
y conference\n\n\nAbstract\nCategorical representation theory is filled wi
th graded additive categories (defined by generators and relations) whose
Grothendieck groups are algebras over $\\mathbb{Z}[q\,q^{-1}]$. For exampl
e\, Khovanov-Lauda-Rouquier (KLR) algebras categorify the quantum group\,
and the diagrammatic Hecke categories categorify Hecke algebras. Khovanov
introduced Hopfological algebra in 2006 as a method to potentially categor
ify the specialization of these $\\mathbb{Z}[q\,q^{-1}]$-algebras at $q =
\\zeta_n$ a root of unity. The schtick is this: one equips the category (e
.g. the KLR algebra) with a derivation $d$ of degree $2$\, which satisfies
$d^p = 0$ after specialization to characteristic $p$\, making this specia
lization into a $p$-dg algebra. The $p$-dg Grothendieck group of a $p$-dg
algebra is automatically a module over $\\mathbb{Z}[\\zeta_{2p}]$... but
it is NOT automatically the specialization of the ordinary Grothendieck gr
oup at a root of unity!\n\nUpgrading the categorification to a $p$-dg alge
bra was done for quantum groups by Qi-Khovanov and Qi-Elias. Recently\, Qi
-Elias accomplished the task for the diagrammatic Hecke algebra in type $A
$\, and ruled out the possibility for most other types. Now the question i
s: what IS the $p$-dg Grothendieck group? Do you get the quantum group/hec
ke algebra at a root of unity\, or not?\nThis is a really hard question\,
and currently the only techniques for establishing such a result involve e
xplicit knowledge of all the important idempotents in the category. These
techniques sufficed for quantum $\\mathfrak{sl}_n$ with $n \\le 3$\, but n
ew techniques are required to make further progress.\n\nAfter reviewing th
e theory of $p$-dg algebras and their Grothendieck groups\, we will presen
t some new techniques and conjectures\, which we hope will blow your mind.
\nEverything is joint with You Qi.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Balibanu (Harvard)
DTSTART:20200626T191500Z
DTEND:20200626T194500Z
DTSTAMP:20260404T094804Z
UID:GRT-2020/27
DESCRIPTION:Title: Perverse sheaves and the cohomology of regular Hessenberg varieti
es\nby Ana Balibanu (Harvard) as part of Geometric Representation Theo
ry conference\n\n\nAbstract\nHessenberg varieties are a distinguished fami
ly of projective varieties associated to a semisimple complex algebraic gr
oup. We use the formalism of perverse sheaves to study their cohomology ri
ngs. We give a partial characterization\, in terms of the Springer corresp
ondence\, of the irreducible representations which appear in the action of
the Weyl group on the cohomology ring of a regular semisimple Hessenberg
variety. We also prove a support theorem for the universal family of regul
ar Hessenberg varieties\, and we deduce that its fibers\, though not neces
sarily smooth\, always have the "Kähler package". This is joint work with
Peter Crooks.\n
LOCATION:https://stable.researchseminars.org/talk/GRT-2020/27/
END:VEVENT
END:VCALENDAR