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BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20200824T180000Z
DTEND:20200824T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/2
DESCRIPTION:Title: Parabolic Hilbert schemes on singular curves and representation theory\nby Eugene Gorsky (UC Davis) as part of UMass Amherst Representation the
ory seminar\n\n\nAbstract\nI will construct representations of various int
eresting algebras (such as rational Cherednik algebras and quantized Giese
ker varieties) using the geometry of parabolic Hilbert schemes of points o
n plane curve singularities. A connection to Coulomb branch algebras of Br
averman\, Finkelberg and Nakajima will be also outlined. The talk is based
on a joint work with Jose Simental and Monica Vazirani.\n
LOCATION:https://researchseminars.org/talk/UMassRep/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (UWisconsin-Madison)
DTSTART:20200914T200000Z
DTEND:20200914T210000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/3
DESCRIPTION:Title: Singular support of categories\nby Dima Arinkin (UWisconsin-Madison)
as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nIn m
any situations\, geometric objects on a space have some kind of singular s
upport\, which refines the usual support.\nFor instance\, for smooth X\, t
he singular support of a D-module (or a perverse sheaf) on X is as a conic
al subset\nof the cotangent bundle\; there is also a version of this notio
n for coherent sheaves on local complete intersections.\nI would like to d
escribe a higher categorical version of this notion.\n\nLet X be a smooth
variety\, and let Z be a closed conical isotropic subset of the cotangent
bundle of X. I will define a\n2-category associated with Z\; its objects m
ay be viewed as `categories over X with singular support in Z'. In particu
lar\, if Z is\nthe zero section\, this gives the notion of categories over
Z in the usual sense.\n\nThe project is motivated by the local geometric
Langlands correspondence\; time permitting\,\nI hope to sketch the relatio
n with the Langlands correspondence at the end of the talk.\n
LOCATION:https://researchseminars.org/talk/UMassRep/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nadler (UC Berkeley)
DTSTART:20200921T200000Z
DTEND:20200921T210000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/4
DESCRIPTION:Title: Verlinde formulas in Betti Geometric Langlands\nby David Nadler (UC B
erkeley) as part of UMass Amherst Representation theory seminar\n\n\nAbstr
act\nI will discuss recent progress in "gluing" automorphic categories of
sheaves found in arxiv:2003.11477 and joint work with Zhiwei Yun. Roughly
speaking\, the geometry involves the wonderful compactification/Vinberg de
generation of loop groups. I will focus on the case of curves of genus one
and its relation to the Drinfeld cocenter/topological Hochschild homolog
y category of the affine Hecke category.\n
LOCATION:https://researchseminars.org/talk/UMassRep/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University)
DTSTART:20201019T200000Z
DTEND:20201019T210000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/5
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot action repre
sentation\nby Martha Precup (Washington University) as part of UMass A
mherst Representation theory seminar\n\n\nAbstract\nIn 2015\, Brosnan and
Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs conjec
ture\, which links the combinatorics of chromatic symmetric functions to t
he geometry of Hessenberg varieties via a permutation group action on the
cohomology ring of regular semisimple Hessenberg varieties. This talk will
give a brief overview of that story and discuss how the dot action can be
computed in all Lie types using the Betti numbers of certain nilpotent He
ssenberg varieties. As an application\, we obtain new geometric insight in
to certain linear relations satisfied by chromatic symmetric functions\, k
nown as the modular law. This is joint work with Eric Sommers.\n
LOCATION:https://researchseminars.org/talk/UMassRep/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Mazin (Kansas State University)
DTSTART:20200928T180000Z
DTEND:20200928T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/6
DESCRIPTION:Title: Equivariant K-theory of the partial flag varieties.\nby Mikhail Mazin
(Kansas State University) as part of UMass Amherst Representation theory
seminar\n\n\nAbstract\nBack in 1990 Beilinson\, Lusztig\, and MacPherson u
sed convolution algebras of diagonal orbits in the double partial flag var
ieties over finite fields to provide a geometric framework for the quantum
groups in type A. In 1998 Vasserot used equivariant K-theory of the Stein
berg subvarieties in the cotangent bundle of the double partial flag varie
ties to provide a geometric framework for the affine quantum group.\n\nIn
a joint project with Sergey Arkhipov\, we define an algebra $\\mathcal{A}_
n$ that plays the role of a $q=0$ degeneration of the affine quantum group
of type $A_n$\, and use the equivariant K-theory of the double partial fl
ag variety with $n$ steps to provide a geometric framework for it. Our alg
ebra is defined via generators and relations. Then for each dimension $d$
of the ambient space\, we show that there is a natural surjective map $\\m
athcal{A}_n\\to A(n\,d)$\, were $A(n\,d)$ is the equivariant K-theory of t
he double partial flag variety with n step in $\\mathbb{C}^d$ equipped wi
th the convolution product.\n
LOCATION:https://researchseminars.org/talk/UMassRep/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20201005T180000Z
DTEND:20201005T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/7
DESCRIPTION:Title: BFN Springer theory\nby Joel Kamnitzer (University of Toronto) as par
t of UMass Amherst Representation theory seminar\n\n\nAbstract\nGiven a re
presentation of a reductive group\,\nBraverman-Finkelberg-Nakajima have de
fined a remarkable Poisson\nvariety called the Coulomb branch. Their const
ruction of this space\nwas motivated by considerations from supersymmetric
gauge theories and\nsymplectic duality. The coordinate ring of this Coulo
mb branch is\ndefined as a kind of cohomological Hall algebra.\n\nWe devel
op a theory of Springer fibres related to\nBraverman-Finkelberg-Nakajima's
construction. We use these Springer\nfibres to construct modules for\n(q
uantized) Coulomb branch algebras. In doing so\, we partially prove a\nco
njecture of Baumann-Kamnitzer-Knutson and give evidence for\nconjectures o
f Hikita\, Nakajima\, and Kamnitzer-McBreen-Proudfoot. We\nalso prove a r
elation between BFN Springer fibres and quasimap spaces\n
LOCATION:https://researchseminars.org/talk/UMassRep/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (United States Naval Academy)
DTSTART:20200831T180000Z
DTEND:20200831T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/9
DESCRIPTION:Title: Nakajima quiver varieties and irreducible components of Springer fibers\nby Mee Seong Im (United States Naval Academy) as part of UMass Amherst
Representation theory seminar\n\n\nAbstract\nSpringer fibers and Nakajima
quiver varieties are amongst the most important objects in geometric repr
esentation theory. While Springer fibers can be used to geometrically cons
truct and classify irreducible representations of Weyl groups\, Nakajima q
uiver varieties play a key role in the geometric representation theory of
Kac--Moody Lie algebras.\nI will begin by first recalling some background
on the objects of interest mentioned above. I will then connect Springer f
ibers and quiver varieties by realizing the irreducible components of two-
row Springer fibers inside a suitable Nakajima quiver variety and describi
ng the resulting subvariety in terms of explicit quiver representations.\n
\nNext\, consider certain fixed-point subvarieties of these quiver varieti
es\, which were studied by Henderson--Licata and Li with the goal of devel
oping the geometric representation theory for certain coideal subalgebras.
By applying this machinery\, I will give an explicit algebraic descriptio
n of the irreducible components of all two-row Springer fibers for classic
al types\, thereby generalizing results of Fung and Stroppel--Webster in t
ype A.\n\nThis is joint with C.-J. Lai and A. Wilbert.\n
LOCATION:https://researchseminars.org/talk/UMassRep/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Chen (Harvard)
DTSTART:20201123T190000Z
DTEND:20201123T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/10
DESCRIPTION:Title: Deligne-Lusztig duality on the category of automorphic sheaves and categ
orical 2nd adjointness\nby Lin Chen (Harvard) as part of UMass Amherst
Representation theory seminar\n\n\nAbstract\nThe Deligne-Lusztig duality
in the title\, which was conjectured by Drinfeld-Wang and Gaitsgory and pr
oved by the speaker\, relates the “miraculous duality” on the moduli s
tack G-torsors to certain parabolic induction/restriction functors. The (u
nramified) categorical 2nd adjointness\, which was a folklore among the ex
perts but proved and generalized by the speaker using nova methods\, is a
categorification of Bernstein’s famous 2nd adjointness. I will explain t
he relation between these two results\, as well as the common ideas in the
ir proofs: studying nearby cycles on certain geometric objects constructed
from the Vinberg semi-group.\n
LOCATION:https://researchseminars.org/talk/UMassRep/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Raskin (University of Texas at Austin)
DTSTART:20201102T210000Z
DTEND:20201102T220000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/11
DESCRIPTION:Title: Geometric Langlands for l-adic sheaves\nby Sam Raskin (University of
Texas at Austin) as part of UMass Amherst Representation theory seminar\n
\n\nAbstract\nIn celebrated work\, Beilinson-Drinfeld formulated a categor
ical analogue of the Langlands program for unramified automorphic forms. T
heir conjecture has appeared specialized to the setting of algebraic D-mod
ules: non-holonomic D-modules play a prominent role in known constructions
. \n\nIn this talk\, we will discuss a categorical conjecture suitable in
other geometric settings\, including l-adic sheaves. One of the main const
ructions is a suitable moduli space of local systems. We will also discuss
applications to unramified automorphic forms for function fields. This is
joint work with Arinkin\, Gaitsgory\, Kazhdan\, Rozenblyum\, and Varshavs
ky.\n
LOCATION:https://researchseminars.org/talk/UMassRep/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (UC Davis)
DTSTART:20201026T180000Z
DTEND:20201026T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/12
DESCRIPTION:Title: 3d mirror symmetry and HOMFLY-PT homology\nby Tudor Dimofte (UC Davi
s) as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nS
ince the original physical prediction of triply-graded HOMFLY-PT link homo
logy by Gukov-Schwarz-Vafa\, and its mathematical definition by Khovanov-R
ozansky\, many other (conjectural) constructions of HOMFLY-PT link homolog
y have appeared --- with different algebraic and geometric origins\, and m
anifesting different properties. One recent proposal of Oblomkov-Rozansky
(closely related to work of Gorsky-Neguț-Rasmussen) associated to a link
L a coherent sheaf E_L on a Hilbert scheme\, whose cohomology reproduces H
OMFLY-PT homology. Another proposal\, by Gorsky-Oblomkov-Rasmussen-Shende\
, computes HOMFLY-PT homology of algebraic knots via Borel-Moore homology
of affine Springer fibers. I will explain how the first (Hilbert scheme) c
onstruction is realized in the "B" twist of a 3d supersymmetric gauge theo
ry\, and then carefully apply 3d mirror symmetry to discover a variant of
the second (Springer fiber) construction. I will also indicate how both 3d
gauge theory setups are related to the original work of Gukov-Schwarz-Vaf
a based using M-theory on the resolved conifold. (Preprint soon to appear\
, with N. Garner\, J. Hilburn\, A. Oblomkov\, and L. Rozansky).\n
LOCATION:https://researchseminars.org/talk/UMassRep/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Rozenblyum (University of Chicago)
DTSTART:20201109T210000Z
DTEND:20201109T220000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/13
DESCRIPTION:Title: Integrable systems from Calabi-Yau categories\nby Nick Rozenblyum (U
niversity of Chicago) as part of UMass Amherst Representation theory semin
ar\n\n\nAbstract\nI will describe a general categorical approach to constr
ucting Hamiltonian actions on moduli spaces.\nIn particular cases\, this s
pecializes to give a "universal" Hitchin integrable system as well as\nthe
Calogero-Moser system. Moreover\, I will describe a generalization to hi
gher dimensions of a classical\nresult of Goldman which says that the Gold
man Lie algebra of free loops on a surface acts by Hamiltonian\nvector fie
lds on the character variety of the surface. A key input is a description
of deformations of\nCalabi-Yau structures\, which is of independent inter
est. This is joint work with Chris Brav.\n
LOCATION:https://researchseminars.org/talk/UMassRep/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto)
DTSTART:20201012T200000Z
DTEND:20201012T210000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/14
DESCRIPTION:Title: Category O via Zastava spaces\nby Alexander Braverman (University of
Toronto) as part of UMass Amherst Representation theory seminar\n\n\nAbst
ract\nIn my talk I will recall basic results about category O for\nfinite-
dimensional and affine Lie algebras - such as Kazhdan-Lusztig\nconjecture\
, Jantzen conjecture etc. I will then describe a new\ngeometric approach t
o proving these conjectures via so called Zastava\nspaces. developed in my
recent paper with Finkelberg and Nakajima. In\nthat paper we give a new p
roof of the Kazhdan-Lusztig conjecture for\nsemi-simple Lie algebras\, I w
ill describe how it should be possible to\nextend this to Jantzen conjectu
res and to the affine case.\n
LOCATION:https://researchseminars.org/talk/UMassRep/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shotaro Makisumi (Columbia)
DTSTART:20210201T190000Z
DTEND:20210201T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/15
DESCRIPTION:Title: Applications of curved Koszul duality to modular geometric representatio
n theory\nby Shotaro Makisumi (Columbia) as part of UMass Amherst Repr
esentation theory seminar\n\n\nAbstract\nRecall the Koszul duality between
symmetric and exterior algebras. When the exterior algebra is deformed to
a Koszul complex\, it turns out that one should equip the corresponding d
eformation of the symmetric algebra with a curvature. This is an example o
f the curved Koszul duality of Burke\, which builds on ideas of Keller\, L
efevre-Hasegawa\, and Positselski. I will give a slightly different (and s
ofter) take on these ideas\, then explain applications to modular geometri
c representation theory. Includes joint work with Matthew Hogancamp.\n
LOCATION:https://researchseminars.org/talk/UMassRep/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (Oxford)
DTSTART:20210208T190000Z
DTEND:20210208T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/16
DESCRIPTION:Title: What is a unipotent representation?\nby Lucas Mason-Brown (Oxford) a
s part of UMass Amherst Representation theory seminar\n\n\nAbstract\nThe c
oncept of a unipotent representation has its origins in the representation
theory of finite Chevalley groups. Let G(Fq) be the group of Fq-rational
points of a connected reductive algebraic group G. In 1984\, Lusztig compl
eted the classification of irreducible representations of G(Fq). He showed
:\n\n1) All irreducible representations of G(Fq) can be constructed from a
finite set of building blocks -- called `unipotent representations.'\n\n2
) Unipotent representations can be classified by certain geometric paramet
ers related to nilpotent orbits for a complex group associated to G(Fq).\n
\nNow\, replace Fq with C\, the field of complex numbers\, and replace G(F
q) with G(C). There is a striking analogy between the finite-dimensional r
epresentation theory of G(Fq) and the unitary representation theory of G(C
). This analogy suggests that all unitary representations of G(C) can be c
onstructed from a finite set of building blocks -- called `unipotent repre
sentations' -- and that these building blocks are classified by geometric
parameters related to nilpotent orbits. In this talk I will propose a de
finition of unipotent representations\, generalizing the Barbasch-Vogan no
tion of `special unipotent'. The definition I propose is geometric and cas
e-free. After giving some examples\, I will state a geometric classificati
on of unipotent representations\, generalizing the well-known result of Ba
rbasch-Vogan for special unipotents. \n\nThis talk is based on forthcoming
joint work with Ivan Loseu and Dmitryo Matvieievskyi.\n
LOCATION:https://researchseminars.org/talk/UMassRep/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Dranowski (UToronto)
DTSTART:20210222T190000Z
DTEND:20210222T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/17
DESCRIPTION:Title: A Mirkovic-Vybornov isomorphism for the Beilinson-Drinfeld Grassmannian\
, in action\nby Anne Dranowski (UToronto) as part of UMass Amherst Rep
resentation theory seminar\n\n\nAbstract\nIn their recent paper on the MV
basis and DH measures\, Baumann\, Kamnitzer and Knutson showed that the MV
cycles (named after Mirkovic and Vilonen who used them to put the geometr
ic Satake correspondence on rigorous footing) yield a perfect basis in the
coordinate ring of the unipotent subgroup\, C[N]. In particular\, they sh
owed that the product of two MV basis vectors in C[N] is given by intersec
tion multiplicities appearing in the intersection of the BD degeneration o
f the product of the corresponding MV cycles with the central fibre. In th
is talk we describe how the Mirkovic-Vybornov isomorphism can be generaliz
ed to give a concrete way to compute such products when G=GL_m. Time permi
tting we discuss connections to cluster algebras.\n
LOCATION:https://researchseminars.org/talk/UMassRep/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Lusztig (MIT)
DTSTART:20210308T190000Z
DTEND:20210308T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/18
DESCRIPTION:Title: Fourier Transform and Finite Analogues\nby George Lusztig (MIT) as p
art of UMass Amherst Representation theory seminar\n\n\nAbstract\nWe are n
ow about 200 years since the introduction of Fourier transform (for functi
ons on the real line). This has become one of the most important tools not
only in pure mathematics but also in applied math and engineering. In thi
s talk we will discuss some of its analogues when the real line is replace
d by something finite. The two main topics of the talk are:\n1) How to wri
te Fourier transform over a symplectic vector space over the field with tw
o elements as a triangular matrix?\n2) A nonabelian analogue of Fourier tr
ansform (related to representation theory).\n
LOCATION:https://researchseminars.org/talk/UMassRep/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iordan Ganev (Weizmann)
DTSTART:20210315T180000Z
DTEND:20210315T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/19
DESCRIPTION:Title: The QR decomposition for radial neural networks.\nby Iordan Ganev (W
eizmann) as part of UMass Amherst Representation theory seminar\n\n\nAbstr
act\nWe present a perspective on neural networks stemming from quiver repr
esentation theory. This point of view emphasizes the symmetries inherent i
n neural networks\, interacts nicely with gradient descent\, and has the p
otential to improve training algorithms. As an application\, we establish
an analog of the QR decomposition for radial neural networks\, which leads
to a dimensional reduction result. This talk is intended for an audience
with a background in representation theory\; we explain all concepts relat
ing to neural networks and machine learning from first principles. It is b
ased on joint work with Robin Walters.\n
LOCATION:https://researchseminars.org/talk/UMassRep/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART:20210322T180000Z
DTEND:20210322T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/20
DESCRIPTION:Title: BV-BFV formalism and asymptotic quantization\nby Kasia Rejzner (Univ
ersity of York) as part of UMass Amherst Representation theory seminar\n\n
\nAbstract\nIn this talk I will present the recent results obtained in col
laboration with Michele Schiavina concerning a generalization of the BV-BF
V formalism to theories with non-trivial asymptotics "at infinity". The or
iginal BV-BFV framework is a tool for quantizing gauge theories on manifol
ds with boundary. The new idea is to extend this to situations where inste
ad of boundary conditions one imposes falloff conditions for fields in the
theory. The main example I will discuss is quantum electrodynamics on Min
kowski spacetime\n
LOCATION:https://researchseminars.org/talk/UMassRep/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnav Tripathy (Harvard)
DTSTART:20210412T180000Z
DTEND:20210412T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/21
DESCRIPTION:Title: K3s as hyperkahler quotients\nby Arnav Tripathy (Harvard) as part of
UMass Amherst Representation theory seminar\n\n\nAbstract\nI'll explain i
n some detail a construction\, joint with M. Zimet\, of K3 surfaces as hyp
erkahler quotients as a ("quadruply affine'') generalization of the classi
cal Kronheimer construction using the McKay equivalence. As time permits\,
I may explain some aspects of our original motivation to use a variant of
3d mirror symmetry to solve for the exact K3 metric and enumerative geome
try via open disc counts.\n
LOCATION:https://researchseminars.org/talk/UMassRep/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Beraldo (Oxford)
DTSTART:20210503T180000Z
DTEND:20210503T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/22
DESCRIPTION:Title: On the geometric Ramanujan conjecture\nby Dario Beraldo (Oxford) as
part of UMass Amherst Representation theory seminar\n\n\nAbstract\nAfter d
iscussing the notion of temperedness arising in the geometric Langlands pr
ogram\, I’ll sketch a proof of a version of the Ramanujan conjecture in
that setting. Essential ingredients for the definition and the proof are t
he derived Satake equivalence and the Deligne-Lusztig (or Alvis-Curtis) du
ality functors.\n
LOCATION:https://researchseminars.org/talk/UMassRep/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia\, Athens)
DTSTART:20210405T180000Z
DTEND:20210405T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/23
DESCRIPTION:Title: Modular Perverse Sheaves on the Affine Flag Variety\nby Laura Rider
(University of Georgia\, Athens) as part of UMass Amherst Representation t
heory seminar\n\n\nAbstract\nThere are two categorical realizations of the
affine Hecke algebra: constructible sheaves on the affine flag variety an
d coherent sheaves on the Langlands dual Steinberg variety. A fundamental
problem in geometric representation theory is to relate these two categori
es by a category equivalence. This was achieved by Bezrukavnikov in charac
teristic 0 about a decade ago. In this talk\, I will discuss a first step
toward solving this problem in the modular case joint with R. Bezrukavniko
v and S. Riche.\n
LOCATION:https://researchseminars.org/talk/UMassRep/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Loseu (Yale)
DTSTART:20210215T190000Z
DTEND:20210215T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/24
DESCRIPTION:Title: Modular representations of semisimple Lie algebras\nby Ivan Loseu (Y
ale) as part of UMass Amherst Representation theory seminar\n\n\nAbstract\
nLet G be a semisimple algebraic group over an algebraically closed field
F of very large positive characteristic. We give a combinatorial classific
ation and find Kazhdan-Lusztig type character formulas for modules over th
e Lie algebra $\\mathfrak{g}$ that are equivariantly irreducible with resp
ect to an action of a certain subgroup of G whose connected component is a
torus. This is a joint work with Roman Bezrukavnikov.\n
LOCATION:https://researchseminars.org/talk/UMassRep/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter)
DTSTART:20210301T190000Z
DTEND:20210301T200000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/25
DESCRIPTION:Title: Strongly-fusion 2-categories are grouplike\nby Theo Johnson-Freyd (P
erimeter) as part of UMass Amherst Representation theory seminar\n\n\nAbst
ract\nA *fusion category* is a finite semisimple monoidal category in whic
h the unit object is indecomposable\, equivalently has trivial endomorphis
m algebra. There are two natural categorifications of this notion: a *fusi
on 2-category* is a finite semisimple monoidal 2-category in which the uni
t object is indecomposable\, and a *strongly fusion 2-category* is one in
which the unit object has trivial endomorphism algebra. As I will explain
in this talk\, fusion 2-categories are extremely rich\, with a seemingly-w
ild classification\, whereas strongly-fusion 2-category are very simple: t
hey are essentially just finite groups. Based on joint work with Matthew Y
u.\n
LOCATION:https://researchseminars.org/talk/UMassRep/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20210419T180000Z
DTEND:20210419T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/26
DESCRIPTION:Title: Microlocal sheaves and representations\nby Roman Bezrukavnikov (MIT)
as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nI w
ill give an overview of a joint project (in progress) with Pablo Boixeda A
lvarez\, Michael McBreen and Zhiwei Yun relating representations of quantu
m groups and finite W-algebras to microlocal sheaves.\nTime permitting\, I
will touch upon a related joint work with Pablo\, Peng Shan and Eric Vass
erot on the center of the small quantum group.\n
LOCATION:https://researchseminars.org/talk/UMassRep/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Elias (UOregon Eugene)
DTSTART:20210426T180000Z
DTEND:20210426T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/27
DESCRIPTION:Title: Introduction to the Hecke category and the diagonalization of the full t
wist\nby Ben Elias (UOregon Eugene) as part of UMass Amherst Represent
ation theory seminar\n\n\nAbstract\nThe group algebra of the symmetric gro
up has a large commutative subalgebra generated by Young-Jucys-Murphy elem
ents\, which acts diagonalizably on any irreducible representation. The go
al of this talk is to give an accessible introduction to the categorificat
ion of this story. The main players are: Soergel bimodules\, which categor
ify the Hecke algebra of the symmetric group\; Rouquier complexes\, which
categorify the braid group where Young-Jucys-Murphy elements live\; and th
e Elias-Hogancamp theory of categorical diagonalization\, which allows one
to construct projections to "eigencategories."\n
LOCATION:https://researchseminars.org/talk/UMassRep/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Vazirani (UC Davis)
DTSTART:20210329T180000Z
DTEND:20210329T190000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/28
DESCRIPTION:Title: Elliptic Schur-Weyl duality and representations of the DAHA\nby Moni
ca Vazirani (UC Davis) as part of UMass Amherst Representation theory semi
nar\n\n\nAbstract\nBuilding on the work of Calaque-Enriquez-Etingof\, Lyub
ashenko-Majid\,\nand Arakawa-Suzuki\, Jordan constructed a functor from qu
antum D-modules\non special linear groups to representations of the double
affine Hecke\nalgebra (DAHA) in type A. When we input quantum functions
on GL(N) the\noutput is L(k^N)\, the irreducible DAHA representation index
ed by an N\nby k rectangle. For the specified parameters\, L(k^N) is Y-se
misimple\,\ni.e. one can diagonalize the Dunkl operators. We give an expl
icit\ncombinatorial description of this module via its Y-weight basis in\n
terms of skew tableaux\, or equivalently\, periodic tableaux of\nrectangu
lar shape. \nThis is joint work with David Jordan.\nIf time allows\, I wil
l talk about work in progress with \nSam Gunningham and David Jordan on t
he \nquantum Hotta-Kashiwara D-modules\, their endomorphim algebras\,\nand
which DAHA representations they become after applying Jordan's\nelliptic
Schur-Weyl functor.\n
LOCATION:https://researchseminars.org/talk/UMassRep/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Campbell (UChicago)
DTSTART:20220215T193000Z
DTEND:20220215T203000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/29
DESCRIPTION:Title: Affine Harish-Chandra bimodules and Steinberg-Whittaker localization
\nby Justin Campbell (UChicago) as part of UMass Amherst Representation th
eory seminar\n\n\nAbstract\nThis talk will be about my paper of the same t
itle with Gurbir Dhillon. It is well-known that the center of the envelopi
ng algebra of an affine Kac-Moody algebra at noncritical level is trivial.
Nonetheless\, its representation theory shares many features with that of
a finite-dimensional semisimple Lie algebra\, including a block decomposi
tion of category O. We propose an analogue\, for any affine Weyl group orb
it at noncritical level\, of the category of Kac-Moody representations wit
h the corresponding "generalized central character." We also construct equ
ivalences relating various categories of affine Harish-Chandra bimodules\,
Whittaker modules\, and Whittaker D-modules on the loop group\, generaliz
ing known equivalences in the finite-dimensional case proved by Bernstein-
Gelfand\, Beilinson-Bernstein\, Milicic-Soergel\, and others.\n
LOCATION:https://researchseminars.org/talk/UMassRep/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Eduardo Simental (MPIM)
DTSTART:20220301T193000Z
DTEND:20220301T203000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/30
DESCRIPTION:by Jose Eduardo Simental (MPIM) as part of UMass Amherst Repre
sentation theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UMassRep/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART:20220322T183000Z
DTEND:20220322T193000Z
DTSTAMP:20260422T212610Z
UID:UMassRep/32
DESCRIPTION:by Pavel Safronov (University of Edinburgh) as part of UMass A
mherst Representation theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UMassRep/32/
END:VEVENT
END:VCALENDAR