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BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20200824T180000Z
DTEND:20200824T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/2
DESCRIPTION:Title: Parabolic Hilbert schemes on singular curves and representation th
eory\nby Eugene Gorsky (UC Davis) as part of UMass Amherst Representat
ion theory seminar\n\n\nAbstract\nI will construct representations of vari
ous interesting algebras (such as rational Cherednik algebras and quantize
d Gieseker varieties) using the geometry of parabolic Hilbert schemes of p
oints on plane curve singularities. A connection to Coulomb branch algebra
s of Braverman\, Finkelberg and Nakajima will be also outlined. The talk i
s based on a joint work with Jose Simental and Monica Vazirani.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Arinkin (UWisconsin-Madison)
DTSTART:20200914T200000Z
DTEND:20200914T210000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/3
DESCRIPTION:Title: Singular support of categories\nby Dima Arinkin (UWisconsin-Ma
dison) as part of UMass Amherst Representation theory seminar\n\n\nAbstrac
t\nIn many situations\, geometric objects on a space have some kind of sin
gular support\, which refines the usual support.\nFor instance\, for smoot
h X\, the singular support of a D-module (or a perverse sheaf) on X is as
a conical subset\nof the cotangent bundle\; there is also a version of thi
s notion for coherent sheaves on local complete intersections.\nI would li
ke to describe 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 cot
angent bundle of X. I will define a\n2-category associated with Z\; its ob
jects may be viewed as `categories over X with singular support in Z'. In
particular\, if Z is\nthe zero section\, this gives the notion of categori
es over Z in the usual sense.\n\nThe project is motivated by the local geo
metric Langlands correspondence\; time permitting\,\nI hope to sketch the
relation with the Langlands correspondence at the end of the talk.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Nadler (UC Berkeley)
DTSTART:20200921T200000Z
DTEND:20200921T210000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/4
DESCRIPTION:Title: Verlinde formulas in Betti Geometric Langlands\nby David Nadle
r (UC Berkeley) as part of UMass Amherst Representation theory seminar\n\n
\nAbstract\nI will discuss recent progress in "gluing" automorphic categor
ies of sheaves found in arxiv:2003.11477 and joint work with Zhiwei Yun. R
oughly speaking\, the geometry involves the wonderful compactification/Vin
berg degeneration of loop groups. I will focus on the case of curves of ge
nus one and its relation to the Drinfeld cocenter/topological Hochschild
homology category of the affine Hecke category.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University)
DTSTART:20201019T200000Z
DTEND:20201019T210000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/5
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot actio
n representation\nby Martha Precup (Washington University) as part of
UMass Amherst Representation theory seminar\n\n\nAbstract\nIn 2015\, Brosn
an and Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs
conjecture\, which links the combinatorics of chromatic symmetric functio
ns to the geometry of Hessenberg varieties via a permutation group action
on the cohomology ring of regular semisimple Hessenberg varieties. This ta
lk 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 nilpo
tent Hessenberg varieties. As an application\, we obtain new geometric ins
ight into certain linear relations satisfied by chromatic symmetric functi
ons\, known as the modular law. This is joint work with Eric Sommers.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Mazin (Kansas State University)
DTSTART:20200928T180000Z
DTEND:20200928T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/6
DESCRIPTION:Title: Equivariant K-theory of the partial flag varieties.\nby Mikhai
l Mazin (Kansas State University) as part of UMass Amherst Representation
theory seminar\n\n\nAbstract\nBack in 1990 Beilinson\, Lusztig\, and MacPh
erson used convolution algebras of diagonal orbits in the double partial f
lag varieties over finite fields to provide a geometric framework for the
quantum groups in type A. In 1998 Vasserot used equivariant K-theory of th
e Steinberg subvarieties in the cotangent bundle of the double partial fla
g varieties to provide a geometric framework for the affine quantum group.
\n\nIn a joint project with Sergey Arkhipov\, we define an algebra $\\math
cal{A}_n$ that plays the role of a $q=0$ degeneration of the affine quantu
m group of type $A_n$\, and use the equivariant K-theory of the double par
tial flag variety with $n$ steps to provide a geometric framework for it.
Our algebra is defined via generators and relations. Then for each dimensi
on $d$ of the ambient space\, we show that there is a natural surjective m
ap $\\mathcal{A}_n\\to A(n\,d)$\, were $A(n\,d)$ is the equivariant K-theo
ry of the double partial flag variety with n step in $\\mathbb{C}^d$ equi
pped with the convolution product.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20201005T180000Z
DTEND:20201005T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/7
DESCRIPTION:Title: BFN Springer theory\nby Joel Kamnitzer (University of Toronto)
as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nGiv
en a representation of a reductive group\,\nBraverman-Finkelberg-Nakajima
have defined a remarkable Poisson\nvariety called the Coulomb branch. Thei
r construction of this space\nwas motivated by considerations from supersy
mmetric gauge theories and\nsymplectic duality. The coordinate ring of thi
s Coulomb branch is\ndefined as a kind of cohomological Hall algebra.\n\nW
e develop a theory of Springer fibres related to\nBraverman-Finkelberg-Nak
ajima's construction. We use these Springer\nfibres to construct modules
for\n(quantized) Coulomb branch algebras. In doing so\, we partially prov
e a\nconjecture of Baumann-Kamnitzer-Knutson and give evidence for\nconjec
tures of Hikita\, Nakajima\, and Kamnitzer-McBreen-Proudfoot. We\nalso pr
ove a relation between BFN Springer fibres and quasimap spaces\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (United States Naval Academy)
DTSTART:20200831T180000Z
DTEND:20200831T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/9
DESCRIPTION:Title: Nakajima quiver varieties and irreducible components of Springer f
ibers\nby Mee Seong Im (United States Naval Academy) as part of UMass
Amherst Representation theory seminar\n\n\nAbstract\nSpringer fibers and N
akajima quiver varieties are amongst the most important objects in geometr
ic representation theory. While Springer fibers can be used to geometrical
ly construct and classify irreducible representations of Weyl groups\, Nak
ajima quiver varieties play a key role in the geometric representation the
ory of Kac--Moody Lie algebras.\nI will begin by first recalling some back
ground on the objects of interest mentioned above. I will then connect Spr
inger fibers and quiver varieties by realizing the irreducible components
of two-row Springer fibers inside a suitable Nakajima quiver variety and d
escribing the resulting subvariety in terms of explicit quiver representat
ions.\n\nNext\, consider certain fixed-point subvarieties of these quiver
varieties\, which were studied by Henderson--Licata and Li with the goal o
f developing the geometric representation theory for certain coideal subal
gebras. By applying this machinery\, I will give an explicit algebraic des
cription of the irreducible components of all two-row Springer fibers for
classical types\, thereby generalizing results of Fung and Stroppel--Webst
er in type A.\n\nThis is joint with C.-J. Lai and A. Wilbert.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Chen (Harvard)
DTSTART:20201123T190000Z
DTEND:20201123T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/10
DESCRIPTION:Title: Deligne-Lusztig duality on the category of automorphic sheaves an
d categorical 2nd adjointness\nby Lin Chen (Harvard) as part of UMass
Amherst Representation theory seminar\n\n\nAbstract\nThe Deligne-Lusztig d
uality in the title\, which was conjectured by Drinfeld-Wang and Gaitsgory
and proved by the speaker\, relates the “miraculous duality” on the m
oduli stack G-torsors to certain parabolic induction/restriction functors.
The (unramified) categorical 2nd adjointness\, which was a folklore among
the experts but proved and generalized by the speaker using nova methods\
, is a categorification of Bernstein’s famous 2nd adjointness. I will ex
plain the relation between these two results\, as well as the common ideas
in their proofs: studying nearby cycles on certain geometric objects cons
tructed from the Vinberg semi-group.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Raskin (University of Texas at Austin)
DTSTART:20201102T210000Z
DTEND:20201102T220000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/11
DESCRIPTION:Title: Geometric Langlands for l-adic sheaves\nby Sam Raskin (Univer
sity of Texas at Austin) as part of UMass Amherst Representation theory se
minar\n\n\nAbstract\nIn celebrated work\, Beilinson-Drinfeld formulated a
categorical analogue of the Langlands program for unramified automorphic f
orms. Their conjecture has appeared specialized to the setting of algebrai
c D-modules: non-holonomic D-modules play a prominent role in known constr
uctions. \n\nIn this talk\, we will discuss a categorical conjecture suita
ble in other geometric settings\, including l-adic sheaves. One of the mai
n constructions 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 V
arshavsky.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (UC Davis)
DTSTART:20201026T180000Z
DTEND:20201026T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/12
DESCRIPTION:Title: 3d mirror symmetry and HOMFLY-PT homology\nby Tudor Dimofte (
UC Davis) as part of UMass Amherst Representation theory seminar\n\n\nAbst
ract\nSince the original physical prediction of triply-graded HOMFLY-PT li
nk homology by Gukov-Schwarz-Vafa\, and its mathematical definition by Kho
vanov-Rozansky\, many other (conjectural) constructions of HOMFLY-PT link
homology have appeared --- with different algebraic and geometric origins\
, and manifesting different properties. One recent proposal of Oblomkov-Ro
zansky (closely related to work of Gorsky-Neguț-Rasmussen) associated to
a link L a coherent sheaf E_L on a Hilbert scheme\, whose cohomology repro
duces HOMFLY-PT homology. Another proposal\, by Gorsky-Oblomkov-Rasmussen-
Shende\, computes HOMFLY-PT homology of algebraic knots via Borel-Moore ho
mology of affine Springer fibers. I will explain how the first (Hilbert sc
heme) construction is realized in the "B" twist of a 3d supersymmetric gau
ge theory\, and then carefully apply 3d mirror symmetry to discover a vari
ant of the second (Springer fiber) construction. I will also indicate how
both 3d gauge theory setups are related to the original work of Gukov-Schw
arz-Vafa 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://stable.researchseminars.org/talk/UMassRep/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Rozenblyum (University of Chicago)
DTSTART:20201109T210000Z
DTEND:20201109T220000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/13
DESCRIPTION:Title: Integrable systems from Calabi-Yau categories\nby Nick Rozenb
lyum (University of Chicago) as part of UMass Amherst Representation theor
y seminar\n\n\nAbstract\nI will describe a general categorical approach to
constructing Hamiltonian actions on moduli spaces.\nIn particular cases\,
this specializes to give a "universal" Hitchin integrable system as well
as\nthe Calogero-Moser system. Moreover\, I will describe a generalizatio
n to higher dimensions of a classical\nresult of Goldman which says that t
he Goldman Lie algebra of free loops on a surface acts by Hamiltonian\nvec
tor fields on the character variety of the surface. A key input is a desc
ription of deformations of\nCalabi-Yau structures\, which is of independen
t interest. This is joint work with Chris Brav.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Braverman (University of Toronto)
DTSTART:20201012T200000Z
DTEND:20201012T210000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/14
DESCRIPTION:Title: Category O via Zastava spaces\nby Alexander Braverman (Univer
sity of Toronto) as part of UMass Amherst Representation theory seminar\n\
n\nAbstract\nIn my talk I will recall basic results about category O for\n
finite-dimensional and affine Lie algebras - such as Kazhdan-Lusztig\nconj
ecture\, Jantzen conjecture etc. I will then describe a new\ngeometric app
roach to proving these conjectures via so called Zastava\nspaces. develope
d in my recent paper with Finkelberg and Nakajima. In\nthat paper we give
a new proof of the Kazhdan-Lusztig conjecture for\nsemi-simple Lie algebra
s\, I will describe how it should be possible to\nextend this to Jantzen c
onjectures and to the affine case.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shotaro Makisumi (Columbia)
DTSTART:20210201T190000Z
DTEND:20210201T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/15
DESCRIPTION:Title: Applications of curved Koszul duality to modular geometric repres
entation theory\nby Shotaro Makisumi (Columbia) as part of UMass Amher
st Representation theory seminar\n\n\nAbstract\nRecall the Koszul duality
between symmetric and exterior algebras. When the exterior algebra is defo
rmed to a Koszul complex\, it turns out that one should equip the correspo
nding deformation of the symmetric algebra with a curvature. This is an ex
ample of the curved Koszul duality of Burke\, which builds on ideas of Kel
ler\, Lefevre-Hasegawa\, and Positselski. I will give a slightly different
(and softer) take on these ideas\, then explain applications to modular g
eometric representation theory. Includes joint work with Matthew Hogancamp
.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (Oxford)
DTSTART:20210208T190000Z
DTEND:20210208T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/16
DESCRIPTION:Title: What is a unipotent representation?\nby Lucas Mason-Brown (Ox
ford) as part of UMass Amherst Representation theory seminar\n\n\nAbstract
\nThe concept of a unipotent representation has its origins in the represe
ntation theory of finite Chevalley groups. Let G(Fq) be the group of Fq-ra
tional points of a connected reductive algebraic group G. In 1984\, Luszti
g completed 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
parameters related to nilpotent orbits for a complex group associated to G
(Fq).\n\nNow\, replace Fq with C\, the field of complex numbers\, and repl
ace G(Fq) with G(C). There is a striking analogy between the finite-dimens
ional representation theory of G(Fq) and the unitary representation theory
of G(C). This analogy suggests that all unitary representations of G(C) c
an be constructed from a finite set of building blocks -- called `unipoten
t representations' -- and that these building blocks are classified by ge
ometric parameters related to nilpotent orbits. In this talk I will propo
se a definition of unipotent representations\, generalizing the Barbasch-V
ogan notion of `special unipotent'. The definition I propose is geometric
and case-free. After giving some examples\, I will state a geometric class
ification of unipotent representations\, generalizing the well-known resul
t of Barbasch-Vogan for special unipotents. \n\nThis talk is based on fort
hcoming joint work with Ivan Loseu and Dmitryo Matvieievskyi.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Dranowski (UToronto)
DTSTART:20210222T190000Z
DTEND:20210222T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/17
DESCRIPTION:Title: A Mirkovic-Vybornov isomorphism for the Beilinson-Drinfeld Grassm
annian\, in action\nby Anne Dranowski (UToronto) as part of UMass Amhe
rst Representation 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
geometric Satake correspondence on rigorous footing) yield a perfect basis
in the coordinate ring of the unipotent subgroup\, C[N]. In particular\,
they showed that the product of two MV basis vectors in C[N] is given by i
ntersection multiplicities appearing in the intersection of the BD degener
ation of the product of the corresponding MV cycles with the central fibre
. In this talk we describe how the Mirkovic-Vybornov isomorphism can be ge
neralized to give a concrete way to compute such products when G=GL_m. Tim
e permitting we discuss connections to cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Lusztig (MIT)
DTSTART:20210308T190000Z
DTEND:20210308T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/18
DESCRIPTION:Title: Fourier Transform and Finite Analogues\nby George Lusztig (MI
T) as part of UMass Amherst Representation theory seminar\n\n\nAbstract\nW
e are now about 200 years since the introduction of Fourier transform (for
functions on the real line). This has become one of the most important to
ols not only in pure mathematics but also in applied math and engineering.
In this talk we will discuss some of its analogues when the real line is
replaced by something finite. The two main topics of the talk are:\n1) How
to write Fourier transform over a symplectic vector space over the field
with two elements as a triangular matrix?\n2) A nonabelian analogue of Fou
rier transform (related to representation theory).\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iordan Ganev (Weizmann)
DTSTART:20210315T180000Z
DTEND:20210315T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/19
DESCRIPTION:Title: The QR decomposition for radial neural networks.\nby Iordan G
anev (Weizmann) as part of UMass Amherst Representation theory seminar\n\n
\nAbstract\nWe present a perspective on neural networks stemming from quiv
er representation theory. This point of view emphasizes the symmetries inh
erent in neural networks\, interacts nicely with gradient descent\, and ha
s the potential to improve training algorithms. As an application\, we est
ablish an analog of the QR decomposition for radial neural networks\, whic
h leads to a dimensional reduction result. This talk is intended for an au
dience with a background in representation theory\; we explain all concept
s relating to neural networks and machine learning from first principles.
It is based on joint work with Robin Walters.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART:20210322T180000Z
DTEND:20210322T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/20
DESCRIPTION:Title: BV-BFV formalism and asymptotic quantization\nby Kasia Rejzne
r (University of York) as part of UMass Amherst Representation theory semi
nar\n\n\nAbstract\nIn this talk I will present the recent results obtained
in collaboration with Michele Schiavina concerning a generalization of th
e BV-BFV formalism to theories with non-trivial asymptotics "at infinity".
The original BV-BFV framework is a tool for quantizing gauge theories on
manifolds with boundary. The new idea is to extend this to situations wher
e instead of boundary conditions one imposes falloff conditions for fields
in the theory. The main example I will discuss is quantum electrodynamics
on Minkowski spacetime\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnav Tripathy (Harvard)
DTSTART:20210412T180000Z
DTEND:20210412T190000Z
DTSTAMP:20260404T094338Z
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 ex
plain in some detail a construction\, joint with M. Zimet\, of K3 surfaces
as hyperkahler quotients as a ("quadruply affine'') generalization of the
classical Kronheimer construction using the McKay equivalence. As time pe
rmits\, I may explain some aspects of our original motivation to use a var
iant of 3d mirror symmetry to solve for the exact K3 metric and enumerativ
e geometry via open disc counts.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Beraldo (Oxford)
DTSTART:20210503T180000Z
DTEND:20210503T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/22
DESCRIPTION:Title: On the geometric Ramanujan conjecture\nby Dario Beraldo (Oxfo
rd) as part of UMass Amherst Representation theory seminar\n\n\nAbstract\n
After discussing the notion of temperedness arising in the geometric Langl
ands program\, I’ll sketch a proof of a version of the Ramanujan conject
ure in that setting. Essential ingredients for the definition and the proo
f are the derived Satake equivalence and the Deligne-Lusztig (or Alvis-Cur
tis) duality functors.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia\, Athens)
DTSTART:20210405T180000Z
DTEND:20210405T190000Z
DTSTAMP:20260404T094338Z
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 Represent
ation theory seminar\n\n\nAbstract\nThere are two categorical realizations
of the affine Hecke algebra: constructible sheaves on the affine flag var
iety and coherent sheaves on the Langlands dual Steinberg variety. A funda
mental problem in geometric representation theory is to relate these two c
ategories by a category equivalence. This was achieved by Bezrukavnikov in
characteristic 0 about a decade ago. In this talk\, I will discuss a firs
t step toward solving this problem in the modular case joint with R. Bezru
kavnikov and S. Riche.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Loseu (Yale)
DTSTART:20210215T190000Z
DTEND:20210215T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/24
DESCRIPTION:Title: Modular representations of semisimple Lie algebras\nby Ivan L
oseu (Yale) as part of UMass Amherst Representation theory seminar\n\n\nAb
stract\nLet G be a semisimple algebraic group over an algebraically closed
field F of very large positive characteristic. We give a combinatorial cl
assification and find Kazhdan-Lusztig type character formulas for modules
over the Lie algebra $\\mathfrak{g}$ that are equivariantly irreducible wi
th respect to an action of a certain subgroup of G whose connected compone
nt is a torus. This is a joint work with Roman Bezrukavnikov.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter)
DTSTART:20210301T190000Z
DTEND:20210301T200000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/25
DESCRIPTION:Title: Strongly-fusion 2-categories are grouplike\nby Theo Johnson-F
reyd (Perimeter) as part of UMass Amherst Representation theory seminar\n\
n\nAbstract\nA *fusion category* is a finite semisimple monoidal category
in which the unit object is indecomposable\, equivalently has trivial endo
morphism algebra. There are two natural categorifications of this notion:
a *fusion 2-category* is a finite semisimple monoidal 2-category in which
the unit object is indecomposable\, and a *strongly fusion 2-category* is
one in which the unit object has trivial endomorphism algebra. As I will e
xplain in this talk\, fusion 2-categories are extremely rich\, with a seem
ingly-wild classification\, whereas strongly-fusion 2-category are very si
mple: they are essentially just finite groups. Based on joint work with Ma
tthew Yu.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT)
DTSTART:20210419T180000Z
DTEND:20210419T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/26
DESCRIPTION:Title: Microlocal sheaves and representations\nby Roman Bezrukavniko
v (MIT) as part of UMass Amherst Representation theory seminar\n\n\nAbstra
ct\nI will give an overview of a joint project (in progress) with Pablo Bo
ixeda Alvarez\, Michael McBreen and Zhiwei Yun relating representations of
quantum groups and finite W-algebras to microlocal sheaves.\nTime permitt
ing\, I will touch upon a related joint work with Pablo\, Peng Shan and Er
ic Vasserot on the center of the small quantum group.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Elias (UOregon Eugene)
DTSTART:20210426T180000Z
DTEND:20210426T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/27
DESCRIPTION:Title: Introduction to the Hecke category and the diagonalization of the
full twist\nby Ben Elias (UOregon Eugene) as part of UMass Amherst Re
presentation theory seminar\n\n\nAbstract\nThe group algebra of the symmet
ric group has a large commutative subalgebra generated by Young-Jucys-Murp
hy elements\, which acts diagonalizably on any irreducible representation.
The goal of this talk is to give an accessible introduction to the catego
rification of this story. The main players are: Soergel bimodules\, which
categorify the Hecke algebra of the symmetric group\; Rouquier complexes\,
which categorify the braid group where Young-Jucys-Murphy elements live\;
and the Elias-Hogancamp theory of categorical diagonalization\, which all
ows one to construct projections to "eigencategories."\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Vazirani (UC Davis)
DTSTART:20210329T180000Z
DTEND:20210329T190000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/28
DESCRIPTION:Title: Elliptic Schur-Weyl duality and representations of the DAHA\n
by Monica Vazirani (UC Davis) as part of UMass Amherst Representation theo
ry seminar\n\n\nAbstract\nBuilding on the work of Calaque-Enriquez-Etingof
\, Lyubashenko-Majid\,\nand Arakawa-Suzuki\, Jordan constructed a functor
from quantum D-modules\non special linear groups to representations of the
double affine Hecke\nalgebra (DAHA) in type A. When we input quantum fun
ctions on GL(N) the\noutput is L(k^N)\, the irreducible DAHA representatio
n indexed by an N\nby k rectangle. For the specified parameters\, L(k^N)
is Y-semisimple\,\ni.e. one can diagonalize the Dunkl operators. We give
an explicit\ncombinatorial description of this module via its Y-weight bas
is in\nterms of skew tableaux\, or equivalently\, periodic tableaux of\nr
ectangular shape. \nThis is joint work with David Jordan.\nIf time allows\
, I will talk about work in progress with \nSam Gunningham and David Jord
an on the \nquantum Hotta-Kashiwara D-modules\, their endomorphim algebras
\,\nand which DAHA representations they become after applying Jordan's\nel
liptic Schur-Weyl functor.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Campbell (UChicago)
DTSTART:20220215T193000Z
DTEND:20220215T203000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/29
DESCRIPTION:Title: Affine Harish-Chandra bimodules and Steinberg-Whittaker localizat
ion\nby Justin Campbell (UChicago) as part of UMass Amherst Representa
tion theory seminar\n\n\nAbstract\nThis talk will be about my paper of the
same title with Gurbir Dhillon. It is well-known that the center of the e
nveloping algebra of an affine Kac-Moody algebra at noncritical level is t
rivial. Nonetheless\, its representation theory shares many features with
that of a finite-dimensional semisimple Lie algebra\, including a block de
composition of category O. We propose an analogue\, for any affine Weyl gr
oup orbit at noncritical level\, of the category of Kac-Moody representati
ons with the corresponding "generalized central character." We also constr
uct equivalences relating various categories of affine Harish-Chandra bimo
dules\, Whittaker modules\, and Whittaker D-modules on the loop group\, ge
neralizing known equivalences in the finite-dimensional case proved by Ber
nstein-Gelfand\, Beilinson-Bernstein\, Milicic-Soergel\, and others.\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Eduardo Simental (MPIM)
DTSTART:20220301T193000Z
DTEND:20220301T203000Z
DTSTAMP:20260404T094338Z
UID:UMassRep/30
DESCRIPTION:by Jose Eduardo Simental (MPIM) as part of UMass Amherst Repre
sentation theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UMassRep/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh)
DTSTART:20220322T183000Z
DTEND:20220322T193000Z
DTSTAMP:20260404T094338Z
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://stable.researchseminars.org/talk/UMassRep/32/
END:VEVENT
END:VCALENDAR