BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (Caltech)
DTSTART;VALUE=DATE-TIME:20200623T140000Z
DTEND;VALUE=DATE-TIME:20200623T143000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/2
DESCRIPTION:Title: Z-algebras from Coulomb branches\nby Oscar Kivinen (Caltech) as part
of Geometric Representation Theory conference\n\n\nAbstract\nI will explai
n how to obtain the Gordon-Stafford construction and some related construc
tions of $Z$-algebras in the literature\, using certain mathematical avata
rs of line defects in 3d $\\mathcal N$=$4$ theories. Time permitting\,
I will discuss the $K$-theoretic and elliptic cases as well.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (Harvard/Aarhus)
DTSTART;VALUE=DATE-TIME:20200624T140000Z
DTEND;VALUE=DATE-TIME:20200624T143000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/3
DESCRIPTION:Title: Elliptic stable envelopes via loop spaces\nby Michael McBreen (Harvar
d/Aarhus) as part of Geometric Representation Theory conference\n\n\nAbstr
act\nElliptic stable envelopes\, introduced by Aganagic and Okounkov\, are
a key ingredient in the study of quantum integrable systems attached to a
symplectic resolution. I will describe a relation between elliptic stable
envelopes on a hypertoric variety and a certain 'loop space' of that vari
ety. Joint with Artan Sheshmani and Shing-Tung Yau.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Bozec (Université de Montpeilier)
DTSTART;VALUE=DATE-TIME:20200625T151500Z
DTEND;VALUE=DATE-TIME:20200625T154500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/4
DESCRIPTION:Title: Relative critical loci\, quiver moduli\, and new lagrangian subvarieties<
/a>\nby Tristan Bozec (Université de Montpeilier) as part of Geometric Re
presentation Theory conference\n\n\nAbstract\nThe preprojective algebra of
a quiver naturally appears when computing\nthe cotangent to the quiver mo
duli\, via the moment map. When considering\nthe derived setting\, it is r
eplaced by its differential graded (dg)\nvariant\, introduced by Ginzburg.
This construction can be generalized\nusing potentials\, so that one retr
ieves critical loci when considering\nmoduli of perfect modules.\nOur idea
is to consider some relative\, or constrained critical loci\,\ndeformatio
ns of the above\, and study Calabi--Yau structures on the\nunderlying rela
tive versions of Ginzburg's dg-algebras. It yields for\ninstance some new
lagrangian subvarieties of the Hilbert schemes of\npoints on the plane.\n\
nThis reports a joint work with Damien Calaque and Sarah Scherotzke\narxiv
.org/abs/2006.01069\n
LOCATION:https://researchseminars.org/talk/GRT-2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20200626T151500Z
DTEND;VALUE=DATE-TIME:20200626T154500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/5
DESCRIPTION:Title: K-Motives and Koszul Duality\nby Jens Eberhardt (MPIM Bonn) as part o
f Geometric Representation Theory conference\n\n\nAbstract\nKoszul duality
\, as conceived by Beilinson-Ginzburg-Soergel\, describes a remarkable sym
metry in the representation theory of Langlands dual reductive groups. Geo
metrically\, Koszul duality can be stated as an equivalence of categories
of mixed (motivic) sheaves on flag varieties. In this talk\, I will argue
that there should be an an 'ungraded' version of Koszul duality between mo
nodromic constructible sheaves and equivariant $K$-motives on flag varieti
es. For this\, I will explain what $K$-motives are and present preliminary
results.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Scherotzke (Université du Luxembourg)
DTSTART;VALUE=DATE-TIME:20200622T144500Z
DTEND;VALUE=DATE-TIME:20200622T154500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/6
DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg algebras\nby Sar
ah Scherotzke (Université du Luxembourg) as part of Geometric Representat
ion Theory conference\n\n\nAbstract\nWe give an introduction to the notion
of moduli stack of a dg category. \nWe explain what shifted symplectic st
ructures are and how they are connected to Calabi-Yau structures on dg cat
egories. 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 work with
Damien Calaque and Tristan Bozec arxiv.org/abs/2006.01069\n
LOCATION:https://researchseminars.org/talk/GRT-2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (Université de Paris-Sud ORSAY)
DTSTART;VALUE=DATE-TIME:20200622T160000Z
DTEND;VALUE=DATE-TIME:20200622T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/7
DESCRIPTION:Title: Yangians and cohomological Hall algebras of Higgs sheaves on curves\n
by Olivier Schiffmann (Université de Paris-Sud ORSAY) as part of Geometri
c 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 case of $\
\mathbb P^1$\, and relate its COHA to the affine Yangian of $\\mathfrak{sl
}_2$\n
LOCATION:https://researchseminars.org/talk/GRT-2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Raskin (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20200622T180000Z
DTEND;VALUE=DATE-TIME:20200622T190000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/11
DESCRIPTION:Title: Tate's thesis in the de Rham setting\nby Sam Raskin (University of T
exas at Austin) as part of Geometric Representation Theory conference\n\n\
nAbstract\nThis is joint work with Justin Hilburn. We will explain a theor
em showing that $D$-modules on the Tate vector space of Laurent series are
equivalent to ind-coherent sheaves on the space of rank 1 de Rham local s
ystems on the punctured disc equipped with a flat section. Time permitting
\, we will also describe an application of this result in the global setti
ng. Our results may be understood as a geometric refinement of Tate's idea
s in the setting of harmonic analysis. They also may be understood as a pr
oof of a strong form of the 3d mirror symmetry conjectures: our results am
ount to an equivalence of A/B-twists of the free hypermultiplet and a $U(1
)$-gauged hypermultiplet.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Stanford University)
DTSTART;VALUE=DATE-TIME:20200622T191500Z
DTEND;VALUE=DATE-TIME:20200622T194500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/12
DESCRIPTION:Title: Fundamental local equivalences in quantum geometric Langlands\nby Gu
rbir Dhillon (Stanford University) as part of Geometric Representation The
ory conference\n\n\nAbstract\nIn quantum geometric Langlands\, the Satake
equivalence plays a less prominent role than in the classical theory. Gait
sgory-Lurie proposed a conjectural substitute\, later termed the fundament
al local equivalence\, relating categories of arc-integrable Kac-Moody rep
resentations 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 joint work
with Justin Campbell and Sam Raskin.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Lanini (Università di Roma Tor Vergata)
DTSTART;VALUE=DATE-TIME:20200623T144500Z
DTEND;VALUE=DATE-TIME:20200623T154500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/13
DESCRIPTION:Title: Singularities of Schubert varieties within a right cell\nby Martina
Lanini (Università di Roma Tor Vergata) as part of Geometric Representati
on Theory conference\n\n\nAbstract\nWe describe an algorithm which takes a
s input any pair of\npermutations and gives as output two permutations lyi
ng in the same\nKazhdan-Lusztig right cell. There is an isomorphism betwee
n the\nRichardson varieties corresponding to the two pairs of permutations
\nwhich preserves the singularity type. This fact has applications in the\
nstudy of $W$-graphs for symmetric groups\, as well as in finding examples
\nof reducible associated varieties of sln-highest weight modules\, and\nc
omparing various bases of irreducible representations of the symmetric\ngr
oup or its Hecke algebra. This is joint work with Peter McNamara.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART;VALUE=DATE-TIME:20200624T160000Z
DTEND;VALUE=DATE-TIME:20200624T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/14
DESCRIPTION:Title: Modular representations and perverse sheaves on affine flag varieties\nby Roman Bezrukavnikov (MIT) as part of Geometric Representation Theory
conference\n\n\nAbstract\nI will give an overview of a joint project with
Simon Riche and Laura Rider and another one\nwith Dima Arinkin aimed at a
modular version of the equivalence between two geometric realization of t
he affine Hecke algebra and derived Satake equivalence respectively. As a
byproduct we obtain a proof of the Finkelberg-Mirkovic conjecture and a po
ssible approach to understanding cohomology of higher Frobenius kernels wi
th coefficients in a $G$-module.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenna Rajchgot (University of Saskatchewan)
DTSTART;VALUE=DATE-TIME:20200623T180000Z
DTEND;VALUE=DATE-TIME:20200623T190000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/15
DESCRIPTION:Title: Type D quiver representation varieties\, double Grassmannians\, and symm
etric varieties\nby Jenna Rajchgot (University of Saskatchewan) as par
t of Geometric Representation Theory conference\n\n\nAbstract\nSince the 1
980s\, mathematicians have found connections between orbit closures in typ
e $A$ quiver representation varieties and Schubert varieties in type $A$ f
lag varieties. For example\, singularity types appearing in type $A$ quive
r orbit closures coincide with those appearing in Schubert varieties in ty
pe $A$ flag varieties (Bobinski-Zwara)\; combinatorics of type $A$ quiver
orbit closure containment is governed by Bruhat order on the symmetric gro
up (follows from work of Zelevinsky\, Kinser-R.)\; and multiple researcher
s have produced formulas for classes of type $A$ quiver orbit closures in
equivariant cohomology and $K$-theory in terms of Schubert polynomials\, G
rothendieck polynomials\, and related objects.\n \nAfter recalling some of
this type $A$ story\, I will discuss joint work with Ryan Kinser on type
$D$ quiver representation varieties. I will describe explicit embeddings w
hich completes a circle of links between orbit closures in type $D$ quiver
representation varieties\, $B$-orbit closures (for a Borel subgroup $B$ o
f $GL_n$) in certain symmetric varieties $GL_n/K$\, and $B$-orbit closures
in double Grassmannians $Gr(a\, n) \\times Gr(b\, n)$. I will end with so
me geometric and combinatorial consequences\, as well as a brief discussio
n of joint work in progress with Zachary Hamaker and Ryan Kinser on formul
as for classes of type $D$ quiver orbit closures in equivariant cohomology
.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Padurariu (MIT)
DTSTART;VALUE=DATE-TIME:20200623T191500Z
DTEND;VALUE=DATE-TIME:20200623T194500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/16
DESCRIPTION:Title: K-theoretic Hall algebras\nby Tudor Padurariu (MIT) as part of Geome
tric Representation Theory conference\n\n\nAbstract\nGiven a quiver with p
otential\, Kontsevich-Soibelman constructed a Hall algebra on the cohomolo
gy of the stack of representations of $(Q\,W)$. In particular cases\, one
recovers positive parts of Yangians as defined by Maulik-Okounkov. For gen
eral $(Q\,W)$\, the Hall algebra has nice structure properties\, for examp
le Davison-Meinhardt proved a PBW theorem for it using the decomposition t
heorem.\n\nOne can define a $K$-theoretic version of this algebra using ce
rtain categories of singularities that depend on the stack of representati
ons of $(Q\,W)$. In particular cases\, these Hall algebras are positive pa
rts of quantum affine algebras. We show that some of the structure propert
ies in cohomology\, such as the PBW theorem\, can be lifted to $K$-theory\
, replacing the use of the decomposition theorem with semi-orthogonal deco
mpositions.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (HSE Moscow)
DTSTART;VALUE=DATE-TIME:20200624T144500Z
DTEND;VALUE=DATE-TIME:20200624T154500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/17
DESCRIPTION:Title: Global Demazure modules\nby Michael Finkelberg (HSE Moscow) as part
of Geometric Representation Theory conference\n\n\nAbstract\nThe Beilinson
-Drinfeld Grassmannian of a simple complex algebraic group admits a natura
l stratification into "global spherical Schubert varieties". In the case w
hen the underlying curve is the affine line\, we determine algebraically t
he global sections of the determinant line bundle over these global Schube
rt varieties as modules over the corresponding Lie algebra of currents. Th
e resulting modules are the global Weyl modules (in the simply laced case)
and generalizations thereof. This is a joint work with Ilya Dumanski and
Evgeny Feigin.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia)
DTSTART;VALUE=DATE-TIME:20200623T160000Z
DTEND;VALUE=DATE-TIME:20200623T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/18
DESCRIPTION:Title: Centralizer of a regular unipotent element and perverse sheaves on the a
ffine flag variety\nby Laura Rider (University of Georgia) as part of
Geometric Representation Theory conference\n\n\nAbstract\nIn this talk\, I
will give a geometric description of the category of representations of t
he centralizer of a regular unipotent element in a reductive algebraic gro
up in terms of perverse sheaves on the Langlands dual affine flag variety.
This is joint work with R. Bezrukavnikov and S. Riche.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Vazirani (UC Davis)
DTSTART;VALUE=DATE-TIME:20200624T180000Z
DTEND;VALUE=DATE-TIME:20200624T190000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/19
DESCRIPTION:Title: The "Springer" representation of the DAHA\nby Monica Vazirani (UC D
avis) as part of Geometric Representation Theory conference\n\n\nAbstract\
nThe Springer resolution and resulting Springer sheaf\nare key players in
geometric representation theory.\nWhile one can construct the Springer she
af geometrically\,\nHotta and Kashiwara gave it a purely algebraic reincar
nation in\nthe language of equivariant $D(\\mathfrak{g})$-modules.\n\nFor
$G = GL_N$\, the endomorphism algebra of the Springer sheaf\,\nor equivale
ntly of the associated $D$-module\,\nis isomorphic to $\\mathbb{C}[\\mathc
al{S}_n]$ the group algebra of\nthe symmetric group.\nIn this talk\, I'll
discuss a quantum analogue of this.\nIn joint work with Sam Gunningham and
David Jordan\, we define\nquantum Hotta-Kashiwara $D$-modules $\\mathrm{H
K}_\\chi$\,\nand compute their endomorphism algebras.\nIn particular $\\ma
thrm{End}_{\\mathcal{D}_q(G)}(\\mathrm{HK}_0)\n\\simeq \\mathbb{C}[\\mathc
al{S}_n]$.\n\nThis is part of a larger program to understand the category\
nof strongly equivariant quantum $D$-modules.\nOur main tool to study this
category is Jordan's elliptic Schur-Weyl\nduality functor to representat
ions of the double affine Hecke algebra\n(DAHA).\nWhen we input $\\mathrm{
HK}_0$ into Jordan's functor\,\nthe endomorphism algebra over the DAHA of
the output is\n$\\mathbb{C}[\\mathcal{S}_n]$ from which we deduce the res
ult above.\n\nFrom studying the output of all the $\\mathrm{HK}_\\chi$\,
we are\nable to compute that for input a distinguished projective\ngenera
tor of the category\nthe output is the DAHA module generated by the sign
idempotent.\n\nThis is joint work with Sam Gunningham and David Jordan.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Campbell (Caltech)
DTSTART;VALUE=DATE-TIME:20200624T191500Z
DTEND;VALUE=DATE-TIME:20200624T194500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/20
DESCRIPTION:Title: Geometric class field theory and Cartier duality\nby Justin Campbell
(Caltech) as part of Geometric Representation Theory conference\n\n\nAbst
ract\nI will explain a generalized Albanese property for smooth curves\, w
hich implies Deligne's geometric class field theory with arbitrary ramific
ation. The proof essentially reduces to some well-known Cartier duality st
atements. This is joint work with Andreas Hayash.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Zurich)
DTSTART;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/21
DESCRIPTION:Title: Parabolic restriction for Harish-Chandra bimodules and dynamical R-matri
ces\nby Pavel Safronov (University of Zurich) as part of Geometric Rep
resentation Theory conference\n\n\nAbstract\nThe category of Harish-Chandr
a bimodules is ubiquitous in representation theory. In this talk I will ex
plain their relationship to the theory of dynamical $R$-matrices (going ba
ck to the works of Donin and Mudrov) and quantum moment maps. I will also
relate the monoidal properties of the parabolic restriction functor for Ha
rish-Chandra bimodules to the so-called standard dynamical $R$-matrix. Thi
s is a report on work in progress\, joint with Artem Kalmykov.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART;VALUE=DATE-TIME:20200625T180000Z
DTEND;VALUE=DATE-TIME:20200625T190000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
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 conference\n\
n\nAbstract\nIn this note we give an alternative presentation of the ratio
nal\nCherednik algebra $H_c$ corresponding to the permutation representati
on 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 at least
$n$\, and\ndescribe the action of $H_c$ in this basis. We also give a bas
is for the\nirreducible quotient of the polynomial representation and comp
are it to\nthe basis of fixed points in the homology of the parabolic Hilb
ert\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://researchseminars.org/talk/GRT-2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Przezdziecki (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20200625T191500Z
DTEND;VALUE=DATE-TIME:20200625T194500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/23
DESCRIPTION:Title: An extension of Suzuki's functor to the critical level\nby Tomasz Pr
zezdziecki (University of Edinburgh) as part of Geometric Representation T
heory conference\n\n\nAbstract\nSuzuki's functor relates the representatio
n theory of the affine Lie algebra to the representation theory of the rat
ional Cherednik algebra in type A. In this talk\, we discuss an extension
of this functor to the critical level\, $t=0$ case. This case is special b
ecause the respective categories of representations have large centres. Ou
r main result describes the relationship between these centres\, and provi
des a partial geometric interpretation in terms of Calogero-Moser spaces a
nd opers.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Romanov (Sydney)
DTSTART;VALUE=DATE-TIME:20200625T200000Z
DTEND;VALUE=DATE-TIME:20200625T210000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/24
DESCRIPTION:Title: A categorification of the Lusztig-Vogan module\nby Anna Romanov (Syd
ney) as part of Geometric Representation Theory conference\n\n\nAbstract\n
Admissible representations of real reductive Lie groups are a key player i
n the world of unitary representation theory. The characters of irreducibl
e admissible representations were described by Lustig-Vogan in the 80’s
in terms of a geometrically-defined module over the associated Hecke algeb
ra. In this talk\, I’ll describe a categorification of this module using
Soergel bimodules\, with a focus on examples. This is work in progress.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramod Achar (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20200626T160000Z
DTEND;VALUE=DATE-TIME:20200626T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
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 Representat
ion Theory conference\n\n\nAbstract\nFor quantum groups at a root of unity
\, there is a web of theorems (due to Bezrukavnikov and Ostrik\, and relyi
ng on work of Lusztig) connecting the following topics: (i) tilting module
s\; (ii) vector bundles on nilpotent orbits\; and (iii) Kazhdan–Lusztig
cells in the affine Weyl group. In this talk\, I will review these results
\, and I will explain a (partly conjectural) analogous picture for reducti
ve algebraic groups over fields of positive characteristic\, inspired by a
conjecture of Humphreys. This is joint work with W. Hardesty and S. Riche
.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Elias (University of Oregon)
DTSTART;VALUE=DATE-TIME:20200626T180000Z
DTEND;VALUE=DATE-TIME:20200626T190000Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/26
DESCRIPTION:Title: Categorification of the Hecke algebra at roots of unity.\nby Ben Eli
as (University of Oregon) as part of Geometric Representation Theory confe
rence\n\n\nAbstract\nCategorical representation theory is filled with grad
ed additive categories (defined by generators and relations) whose Grothen
dieck groups are algebras over $\\mathbb{Z}[q\,q^{-1}]$. For example\, Kho
vanov-Lauda-Rouquier (KLR) algebras categorify the quantum group\, and the
diagrammatic Hecke categories categorify Hecke algebras. Khovanov introdu
ced Hopfological algebra in 2006 as a method to potentially categorify 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 specializatio
n into a $p$-dg algebra. The $p$-dg Grothendieck group of a $p$-dg algebr
a is automatically a module over $\\mathbb{Z}[\\zeta_{2p}]$... but it is N
OT automatically the specialization of the ordinary Grothendieck group at
a root of unity!\n\nUpgrading the categorification to a $p$-dg algebra 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 is: what
IS the $p$-dg Grothendieck group? Do you get the quantum group/hecke alge
bra at a root of unity\, or not?\nThis is a really hard question\, and cur
rently the only techniques for establishing such a result involve explicit
knowledge of all the important idempotents in the category. These techniq
ues sufficed for quantum $\\mathfrak{sl}_n$ with $n \\le 3$\, but new tech
niques are required to make further progress.\n\nAfter reviewing the theor
y of $p$-dg algebras and their Grothendieck groups\, we will present some
new techniques and conjectures\, which we hope will blow your mind.\nEvery
thing is joint with You Qi.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Balibanu (Harvard)
DTSTART;VALUE=DATE-TIME:20200626T191500Z
DTEND;VALUE=DATE-TIME:20200626T194500Z
DTSTAMP;VALUE=DATE-TIME:20240328T104108Z
UID:GRT-2020/27
DESCRIPTION:Title: Perverse sheaves and the cohomology of regular Hessenberg varieties\
nby Ana Balibanu (Harvard) as part of Geometric Representation Theory conf
erence\n\n\nAbstract\nHessenberg varieties are a distinguished family of p
rojective varieties associated to a semisimple complex algebraic group. We
use the formalism of perverse sheaves to study their cohomology rings. We
give a partial characterization\, in terms of the Springer correspondence
\, of the irreducible representations which appear in the action of the We
yl group on the cohomology ring of a regular semisimple Hessenberg variety
. We also prove a support theorem for the universal family of regular Hess
enberg varieties\, and we deduce that its fibers\, though not necessarily
smooth\, always have the "Kähler package". This is joint work with Peter
Crooks.\n
LOCATION:https://researchseminars.org/talk/GRT-2020/27/
END:VEVENT
END:VCALENDAR