BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (Caltech)
DTSTART:20200623T140000Z
DTEND:20200623T143000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/2/"
 >Z-algebras from Coulomb branches</a>\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:20200624T140000Z
DTEND:20200624T143000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/3/"
 >Elliptic stable envelopes via loop spaces</a>\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:20200625T151500Z
DTEND:20200625T154500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/4/"
 >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:20200626T151500Z
DTEND:20200626T154500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/5/"
 >K-Motives and Koszul Duality</a>\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:20200622T144500Z
DTEND:20200622T154500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/6/"
 >Cotangent complexes of moduli spaces and Ginzburg dg algebras</a>\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:20200622T160000Z
DTEND:20200622T170000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/7/"
 >Yangians and cohomological Hall algebras of Higgs sheaves on curves</a>\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:20200622T180000Z
DTEND:20200622T190000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/11/
 ">Tate's thesis in the de Rham setting</a>\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:20200622T191500Z
DTEND:20200622T194500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/12/
 ">Fundamental local equivalences in quantum geometric Langlands</a>\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:20200623T144500Z
DTEND:20200623T154500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/13/
 ">Singularities of Schubert varieties within a right cell</a>\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:20200624T160000Z
DTEND:20200624T170000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/14/
 ">Modular representations and perverse sheaves on affine flag varieties</a
 >\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:20200623T180000Z
DTEND:20200623T190000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/15/
 ">Type D quiver representation varieties\, double Grassmannians\, and symm
 etric varieties</a>\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:20200623T191500Z
DTEND:20200623T194500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/16/
 ">K-theoretic Hall algebras</a>\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:20200624T144500Z
DTEND:20200624T154500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/17/
 ">Global Demazure modules</a>\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:20200623T160000Z
DTEND:20200623T170000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/18/
 ">Centralizer of a regular unipotent element and perverse sheaves on the a
 ffine flag variety</a>\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:20200624T180000Z
DTEND:20200624T190000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/19/
 ">The "Springer" representation of  the DAHA</a>\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:20200624T191500Z
DTEND:20200624T194500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/20/
 ">Geometric class field theory and Cartier duality</a>\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:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/21/
 ">Parabolic restriction for Harish-Chandra bimodules and dynamical R-matri
 ces</a>\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:20200625T180000Z
DTEND:20200625T190000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/22/
 ">Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra</a>\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:20200625T191500Z
DTEND:20200625T194500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/23/
 ">An extension of Suzuki's functor to the critical level</a>\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:20200625T200000Z
DTEND:20200625T210000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/24/
 ">A categorification of the Lusztig-Vogan module</a>\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:20200626T160000Z
DTEND:20200626T170000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/25/
 ">Conjectures on p-cells\, tilting modules\, and nilpotent orbits</a>\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:20200626T180000Z
DTEND:20200626T190000Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/26/
 ">Categorification of the Hecke algebra at roots of unity.</a>\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:20200626T191500Z
DTEND:20200626T194500Z
DTSTAMP:20260424T095106Z
UID:GRT-2020/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GRT-2020/27/
 ">Perverse sheaves and the cohomology of regular Hessenberg varieties</a>\
 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