BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Andrew Linshaw (Denver University)
DTSTART:20200910T190000Z
DTEND:20200910T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/1
DESCRIPTION:Title: Trialities of W-algebras\nby Andrew Linshaw (Denver Univ
ersity) as part of Rocky Mountain Rep Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinwei Yang (University of Alberta)
DTSTART:20200924T190000Z
DTEND:20200924T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/2
DESCRIPTION:Title: Recent progress on tensor categories of vertex operator alge
bras.\nby Jinwei Yang (University of Alberta) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nTensor categories of vertex operator a
lgebras play an important role in the study of vertex operator algebras an
d conformal field theories. A central problem of tensor category theory of
Huang-Lepowsky-Zhang is the existence of the vertex tensor category struc
ture. We develop a few general methods to establish the existence of tenso
r structure on module categories for vertex operator algebras\, especially
for non-rational and non-C_2 cofinite vertex operator algebras. As applic
ations\, we obtain the tensor structure of affine Lie algebras at various
levels\, affine Lie superalgebra gl(1|1)\, the Virasoro algebra at all cen
tral charges as well as the singlet algebras. We also study important pro
perties\, including constructions of projective covers\, fusion rules and
the rigidity of these tensor categories. This talk is based on joint work
with T. Creutzig\, Y.-Z. Huang\, F. Orosz Hunziker\, C. Jiang\, R. McRae a
nd D. Ridout.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20201001T210000Z
DTEND:20201001T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/3
DESCRIPTION:Title: The singular support of the Ising model\nby Reimundo Hel
uani (IMPA) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWe
prove a new Fermionic quasiparticle sum expression for the character of t
he Ising model vertex algebra\, related to the Jackson-Slater q-series ide
ntity of Rogers-Ramanujan type. We find\, as consequences\, an explicit mo
nomial basis for the Ising model\, and a description of its singular suppo
rt. We find that the ideal sheaf of the latter\, defining it as a subschem
e of the arc space of its associated scheme\, is finitely generated as a d
ifferential ideal. We prove three new q-series identities of the Rogers-Ra
manujan-Slater type associated with the three irreducible modules of the V
irasoro Lie algebra of central charge 1/2. This is joint work with G. E. A
ndrews and J. van Ekeren and is based on arxiv.org:2005.10769\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro Van Ekeren (UFF)
DTSTART:20201008T190000Z
DTEND:20201008T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/4
DESCRIPTION:Title: Schellekens list\, the Leech lattice and the very strange Fo
rmula.\nby Jethro Van Ekeren (UFF) as part of Rocky Mountain Rep Theor
y Seminar\n\n\nAbstract\n(joint work with Lam\, Moeller and Shimakura) If
V is a holomorphic vertex algebra of central charge 24 then its weight one
space V_1 is known to be a reductive Lie algebra which is either trivial\
, abelian of dimension 24 (in which case V is the Leech lattice vertex alg
ebra) or else one of 69 semisimple Lie algebras first determined by Schell
ekens in 1993. Until now the only known proof of Schelekens result was a h
eavily computational one involving case analysis and difficult integer pro
gramming problems. Recently Moeller and Scheithauer have established a bou
nd on the dimension of the weight one space of a holomorphic orbifold vert
ex algebra\, using the Deligne bound on the growth of coefficients of weig
ht 2 cusp forms. In this talk I will describe how the dimension bound toge
ther with Kac's very strange formula implies that all holomorphic vertex a
lgebras of central charge 24 and nontrivial weight one space are orbifolds
of the Leech lattice algebra. Since the automorphism group of the latter
algebra is known one can\, with a little more work\, recover Schellekens r
esult in this way.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Genra (University of Alberta)
DTSTART:20201015T190000Z
DTEND:20201015T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/5
DESCRIPTION:Title: Screenings and applications\nby Naoki Genra (University
of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nSc
reening operators are useful tools to characterize free field realizations
of vertex algebras\, and give new perspectives in the structures of them.
We explain screening operators of the beta-gamma system\, affine vertex (
super)algebras and W-(super)algebras. We also explain the applications to
the coset constructions\, representations and trialities of W-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Paris-Saclay university)
DTSTART:20201119T160000Z
DTEND:20201119T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/6
DESCRIPTION:Title: Singularities of nilpotent Slodowy slices and collapsing lev
els for W-algebras.\nby Anne Moreau (Paris-Saclay university) as part
of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nTo any vertex algebra
one can attach in a canonical way a certain Poisson variety\, called the a
ssociated variety. \nNilpotent Slodowy slices appear as associated varieti
es of admissible (simple) W-algebras. They also appear as Higgs branches o
f the Argyres-Douglas theories in 4d N=2 SCFT’s. These two facts are li
nked by the so-called Higgs branch conjecture. In this talk I will explai
n how to exploit the geometry of nilpotent Slodowy slices to study some pr
operties of W-algebras whose motivation stems from physics. In particular
I will be interested in collapsing levels for W-algebras. This is a joi
nt work (still in preparation) with Tomoyuki Arakawa and Jethro van Ekeren
.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Zhi Huang (Rutgers University)
DTSTART:20201105T200000Z
DTEND:20201105T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/7
DESCRIPTION:Title: Associative algebra and the representation theory of grading
-restricted vertex algebras.\nby Yi-Zhi Huang (Rutgers University) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will introduce
an associative algebra $A^{∞}(V)$ constructed using infinite matrices wi
th entries in a grading-restricted vertex algebra V. The Zhu algebra and i
ts generalizations by Dong-Li-Mason are very special subalgebras of $A^{
∞}(V)$. I will also introduce the new subalgebras $A^{N}(V)$ of $A^{∞}
$(V)\, which can be viewed as obtained from finite matrices with entries i
n V. I will then discuss the relations between lower-bounded generalized V
-modules and suitable modules for these associative algebras. This talk is
based on the paper arXiv:2009.00262.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Sato (Academia Sinica\, Taipei\, Taiwan)
DTSTART:20201029T190000Z
DTEND:20201029T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/8
DESCRIPTION:Title: Kazama-Suzuki coset vertex superalgebras at admissible level
s\nby Ryo Sato (Academia Sinica\, Taipei\, Taiwan) as part of Rocky Mo
untain Rep Theory Seminar\n\n\nAbstract\nThe Kazama-Suzuki coset vertex op
erator superalgebra associated with a simple Lie algebra g and its Cartan
subalgebra h is a ``super-analog'' of the parafermion vertex operator alge
bra associated with g. At positive integer levels\, the coset superalgebra
turns out to be C_2-cofinite and rational by the general theory of orbifo
lds (Miyamoto) and Heisenberg cosets (Creutzig-Kanade-Linshaw-Ridout)\, re
spectively. On the other hand\, at Kac-Wakimoto admissible levels\, the co
set superalgebra is not C_2-cofinite nor rational. In this talk we discuss
a relationship between the category of weight modules for the admissible
affine vertex algebra associated with g and that for the corresponding Kaz
ama-Suzuki coset vertex superalgebra. In our discussion the inverse Kazama
-Suzuki coset construction\, which is originally due to Feigin-Semikhatov-
Tipunin in the g=sl_2 case\, plays an important role. As an application\,
for g=sl_2 at level -1/2\, we determine all the fusion rules between simp
le weight modules of the Kazama-Suzuki coset vertex superalgebra and verif
y the conjectural Verlinde formula in this case (corresponding to Creutzig
-Ridout's result in the affine side). The last part is based on the joint
work with Shinji Koshida.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antun Milas (SUNY-Albany)
DTSTART:20201112T200000Z
DTEND:20201112T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/9
DESCRIPTION:Title: Some q-series identities related to characters of vertex alg
ebras\nby Antun Milas (SUNY-Albany) as part of Rocky Mountain Rep Theo
ry Seminar\n\n\nAbstract\nWe prove several families of q-series identities
that are motivated by the correspondence between 4d N = 2 superconformal
field theories (SCFTs) and vertex operator superalgebras. We also discuss
identities coming from certain non-commutative q-series and quivers\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darlayne Addabbo (University of Arizona)
DTSTART:20201022T190000Z
DTEND:20201022T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/10
DESCRIPTION:Title: Higher level Zhu algebras for vertex operator algebras\
nby Darlayne Addabbo (University of Arizona) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nI will discuss the level two Zhu algebra fo
r the Heisenberg vertex operator algebra and techniques used in determinin
g its structure. I will also discuss more general results helpful in deter
mining generators and relations for higher level Zhu algebras\, and in par
ticular\, will provide an example to clarify the necessity of an extra con
dition required in the definition of higher level Zhu algebras. (Joint wit
h Katrina Barron.)\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (Rutgers University)
DTSTART:20201203T200000Z
DTEND:20201203T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/11
DESCRIPTION:Title: Cohomological Field Theories from vertex operator algebras<
/a>\nby Chiara Damiolini (Rutgers University) as part of Rocky Mountain Re
p Theory Seminar\n\n\nAbstract\nIn this talk I will discuss certain proper
ties of sheaves of covacua and conformal blocks attached to modules over v
ertex operator algebras. After briefly recalling how these objects are con
structed from a geometric point of view\, I will focus on the conditions r
equired to construct Cohomological Field Theories from these sheaves. If t
ime permits I will also discuss open problems which naturally arise. This
is based on joint works with A. Gibney and N. Tarasca.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Tokyo)
DTSTART:20201210T200000Z
DTEND:20201210T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/12
DESCRIPTION:Title: Duality of subregular W-algebras and principal W-superalgeb
ras of type A and their representations in rational cases\nby Shigeno
ri Nakatsuka (University of Tokyo) as part of Rocky Mountain Rep Theory Se
minar\n\n\nAbstract\nRecently\, dualities among W-superalgebras and their
affine cosets conjectured by Gaiotto-Rapcak have been established in many
cases by Creutzig-Linshaw and Creutzig-Linshaw-Kanade by using universal o
bjects of such algebras. Independently\, Creutzig-Genra and I proved the d
uality in the case of subregular W-algebras and principal W-superalgebras
of type A by using free field realizations of those algebras. This point
of view upgrades the duality to a "reconstruction theorem" of one of the
algebra from the other one. The simplest example is the Kazama-Suzuki cose
t construction of N=2 superconformal algebra from the affine sl2 vertex al
gebra and its inverse by Feigin-Semikhatov-Tipunin. In this talk\, I will
explain this reconstruction theorem and then its application to the repres
entation theory of principal W-superalgebra side in the rational cases. Th
is talk is based on on-going project with Thomas Creutzig\, Naoki Genra an
d Ryo Sato\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drazen Adamovic (University of Zagreb)
DTSTART:20201217T200000Z
DTEND:20201217T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/13
DESCRIPTION:Title: Affine Vertex Algebras\, collapsing levels and representati
on theory\nby Drazen Adamovic (University of Zagreb) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nWe will review recent results a
ppearing in the last five years including the representation theory of
affine vertex algebras beyond the category O\, semi-simplicity of represe
ntations at collapsing levels and some applications to logarithmic verte
x algebras.\n\nPlease look in the seminar website for the link to join and
password\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto (Kyoto University)
DTSTART:20201126T000000Z
DTEND:20201126T010000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/14
DESCRIPTION:Title: On the log W-algebras\nby Shoma Sugimoto (Kyoto Univers
ity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFor a fin
ite dimensional simply-laced simple Lie algebra $g$ and an\ninteger $p\\ge
q 2$\, we can attach the logarithmic $W$-algebra $W(p)_Q$.\nWhen $g=sl_2$\
, $W(p)_Q$ is called the triplet $W$-algebra\, and studied by\nmany people
as one of the most famous examples of $C_2$-cofinite but\nirrational vert
ex operator algebra. However\, apart from the triplet\n$W$-algebra\, not m
uch is known about the log $W$-algebras $W(p)_Q$.\nIn this talk\, after we
construct $W(p)_Q$ and their modules\n$W(p\,\\lambda)_Q$ geometrically al
ong the preprint of Feigin-Tipunin\, first\nwe show the simplicity\, $W_k(
g)$-module structure\, and character formula\nof $W(p\,\\lambda)_Q$ when $
\\sqrt{p}\\bar\\lambda$ is in the closure of the\nfundamental alcove. In p
articular\, for $p\\geq h-1$\, $W(p)_Q$ is simple and\ndecomposed into sim
ple $W_k(g)$-modules.\nSecond we give a purely $W$-algebraic algorithm to
calculate nilpotent\nelements in the Zhu's $C_2$-algebra of $W(p)_Q$ much
easier than\nstraightforward way. Using this algorithm to the cases $g=sl_
3$ and\n$p=2\,3$\, we show that $W(p)_Q$ is $C_2$-cofinite in these cases.
\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Kanade (University of Denver)
DTSTART:20210114T200000Z
DTEND:20210114T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/15
DESCRIPTION:Title: Principal characters of standard $A_2^{(2)}$-modules\nb
y Shashank Kanade (University of Denver) as part of Rocky Mountain Rep The
ory Seminar\n\n\nAbstract\nPrincipal characters of standard (i.e.\, highes
t weight\, integrable) modules for affine Lie algebras have been a rich s
ource of q-series and partition identities. The algebra $A_1^{(1)}$ (or\,
$\\hat{sl}_2$) was "understood" in this sense a few decades ago. On q-seri
es side\, this leads to identities of Gordon-Andrews and Andrews-Bressoud.
In this talk\, I'll present q-series identities related to the next "simp
lest" affine Lie algebra\, namely\, $A_2^{(2)}$. Here\, we get six familie
s of q-series identities confirming a conjecture of McLaughlin and Sills.
The main machinery used is that of Bailey pairs and Bailey lattices. This
is a joint work with Matthew C. Russell. (N.B.: These q-series include Vir
(3\,p) minimal model characters.)\n\nThe password is the universal central
extension of the Witt algebra: "V*******"\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cuibo Jiang (Shangai JiaoTong University)
DTSTART:20210122T000000Z
DTEND:20210122T010000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/16
DESCRIPTION:Title: Simplicity of vacuum modules and associated varieties.\
nby Cuibo Jiang (Shangai JiaoTong University) as part of Rocky Mountain Re
p Theory Seminar\n\n\nAbstract\nWe prove that the universal affine vertex
algebra associated with a simple Lie algebra $g$ is simple if and only if
the associated\nvariety of its unique simple quotient is equal to $g*$. W
e also derive an analogous result for the quantized Drinfeld-Sokolov reduc
tion applied to the universal affine vertex algebra. This is a joint work
with T. Arakawa and A. Moreau.\n\nhttps://cuboulder.zoom.us/j/98295022194\
nThe password is the universal central extension of the Witt algebra: "V**
*****"\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University)
DTSTART:20210128T160000Z
DTEND:20210128T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/17
DESCRIPTION:Title: Algebra objects in group-theoretical fusion categories.
\nby Ana Ros Camacho (Cardiff University) as part of Rocky Mountain Rep Th
eory Seminar\n\n\nAbstract\nAlgebras in tensor categories appear in severa
l interesting research areas\, like e.g. VOA extensions or spin topologica
l field theories\, but they are usually tricky to find. In this talk\, we
will explain how to generalize a result by Ostrik and Natale on algebra ob
jects in categories related to lattice VOAs to the case of so-called group
-theoretical fusion categories. The algebra objects we find for these also
have very good properties that we will describe in detail. We will assume
little knowledge of categories. Joint work with the WINART2 team Y. Moral
es\, M. Mueller\, J. Plavnik\, A. Tabiri and C. Walton\n\nThe password is
the universal central extension of the Witt algebra V*******\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Keller (University of Arizona)
DTSTART:20210204T200000Z
DTEND:20210204T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/18
DESCRIPTION:Title: Holographic Families of VOAs\nby Christoph Keller (Univ
ersity of Arizona) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstr
act\nPhysicists are interested in holographic families of VOAs. These are\
nfamilies of VOAs that on the one hand have dim $V_n$ `small' for `small'\
nn\, and on the other hand have some kind of large central charge limit.\n
I will discuss the motivation behind these requirements and the\nconnectio
n to extremal VOAs. I will then discuss some attempts at\nconstructing suc
h families\, namely permutation orbifold VOAs and\nlattice orbifold VOAs.
This talk is based on joint work with Thomas\nGemuenden.\n\nLink to join a
nd password can be found in the seminar's webpage.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Arakawa (Kyoto University)
DTSTART:20210211T230000Z
DTEND:20210212T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/19
DESCRIPTION:Title: 4D/2D duality and VOA theory\nby Tomoyuki Arakawa (Kyot
o University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\n
The 4D/2D duality discovered by Beem et at in physics gives a remarkable c
onnection between 4D N=2 SCFTs and VOAs. \nIt gives not only many new inte
resting examples of VOAs but also new perspectives to known VOAs\, such as
Frenkel-Styrkas’s modified regular representation of the Virasoro algeb
ra and Adamovic’s realization of N=4 small superconformal algebra.\nIn t
his talk I will discuss the 4D/2D duality from the VOA perspective\, start
ing from these examples.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20210218T200000Z
DTEND:20210218T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/20
DESCRIPTION:Title: Conjugation and positivity of conformal blocks\nby Bin
Gui (Rutgers University) as part of Rocky Mountain Rep Theory Seminar\n\n\
nAbstract\nGiven a strongly rational unitary VOA $V$\, a Hermitian form on
the space of its intertwining operators was introduced recently to unders
tand the unitarity of the representation modular tensor category $Rep(V)$.
It was actually shown that\, along with some natural assumptions\, if thi
s Hermitian form (which is necessarily non-degenerate) is positive\, namel
y\, if it is an inner product\, then $Rep(V)$ is unitary. The crucial step
of this story is to prove the positivity of the Hermitian form. In this t
alk\, I give a geometric interpretation of this positivity problem using t
he idea (self)conjugate Riemann surfaces and (self)conjugate conformal blo
cks.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McRae (Tsinghua University)
DTSTART:20210226T000000Z
DTEND:20210226T010000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/21
DESCRIPTION:Title: On semisimplicity of modules for C_2-cofinite vertex operat
or algebras\nby Robert McRae (Tsinghua University) as part of Rocky Mo
untain Rep Theory Seminar\n\n\nAbstract\nI will discuss work in progress r
elated to proving semisimplicity of the module category for a suitable pos
itive-energy\, self-contragredient\, C_2-cofinite vertex operator algebra
V. The goal is to show that the category of V-modules is semisimple if the
Zhu algebra of V is a semisimple algebra. The idea for proving this is to
show that the braided tensor category of V-modules is rigid with a non-de
generate braiding\, using tensor-categorical methods combined with the mod
ular invariance methods used by Huang to prove the Verlinde conjecture for
rational vertex operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Wood (Cardiff University)
DTSTART:20210304T160000Z
DTEND:20210304T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/22
DESCRIPTION:Title: There is always more that can be learnt from the free boson
\nby Simon Wood (Cardiff University) as part of Rocky Mountain Rep The
ory Seminar\n\n\nAbstract\nVertex operator algebras exhibit a feature much
like Lie\nalgebras in that they admit too many modules for the category o
f all\ntheir modules to exhibit nice structure. However\, good choices of
module\ncategory can lead to categories with very rich structure. For exam
ple\nthe categories of admissible modules over rational vertex operator\na
lgebras are modular tensor categories\, as proved by Huang. I will\npresen
t some recent work on making the study of vertex operator algebra\nmodule
categories more tractable by replacing them by Hopf algebras\, an\narguabl
y simpler algebraic structure. The guiding example will be the\nfree boson
.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mamoru Ueda (Kyoto University)
DTSTART:20210326T000000Z
DTEND:20210326T010000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/23
DESCRIPTION:Title: Affine super Yangians and rectangular W-superalgebras.\
nby Mamoru Ueda (Kyoto University) as part of Rocky Mountain Rep Theory Se
minar\n\n\nAbstract\nMotivated by the generalized AGT conjecture in this t
alk I will construct surjective homomorphisms from the affine super Yangia
ns to the universal enveloping algebras of rectangular $W$-superalgebras.
This result is a super affine analogue of a result of Ragoucy and Sorba\,
which gave surjective homomorphisms from finite Yangians of type $A$ to re
ctangular finite $W$-algebras of type $A$.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20210429T190000Z
DTEND:20210429T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/24
DESCRIPTION:Title: A remark on $\\mathbb{N}$-graded vertex algebras\nby Ga
ywalee Yamskulna (Illinois State University) as part of Rocky Mountain
Rep Theory Seminar\n\n\nAbstract\nIn this talk\, I will discuss an impact
of Leibniz algebras on the algebraic structure of $\\mathbb{N}$-graded ver
tex algebras. Along the way\, I will provide easy ways to characterize sev
eral types of $\\mathbb{N}$-graded vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Lu (University of Denver)
DTSTART:20210311T200000Z
DTEND:20210311T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/25
DESCRIPTION:Title: Skew representations of super Yangian.\nby Kang Lu (Uni
versity of Denver) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstr
act\nSkew representations (corresponding to skew Young diagrams) of Yangia
n and quantum affine algebra of type A were introduced by Cherednik and ex
tensively studied by Nazarov and Tarasov. In this talk\, we will discuss s
ome known results about skew representations of super Yangian of type A su
ch as Jacobi-Trudi identities\, Drinfeld functor\, irreducibility conditio
ns of tensor products\, and extended T-systems. We also discuss some open
problems related to tame modules of super Yangian. Some essential differen
ces comparing to the even case will be discussed as well.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Möller (Kyoto University)
DTSTART:20210401T230000Z
DTEND:20210402T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/26
DESCRIPTION:Title: Classification of Holomorphic VOAs in Central Charge 24
\nby Sven Möller (Kyoto University) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nI shall summarise recent results (and ongoing work)
regarding the classification of strongly rational\, holomorphic VOAs (or
CFTs) of central charge 24 (together with Jethro van Ekeren\, Gerald Höhn
\, Ching Hung Lam\, Nils Scheithauer and Hiroki Shimakura). First\, we sho
w that there is an abstract bijection (without classifying either side) be
tween these VOAs and the generalised deep holes of the Leech lattice VOA.
The proof uses a dimension formula obtained by pairing the VOA character w
ith a vector-valued Eisenstein series and an averaged version of Kac's Lie
theoretic "very strange formula". This is a quantum analogue of the beaut
iful result by Conway\, Parker and Sloane (and Borcherds) that the deep ho
les of the Leech lattice are in natural bijection with the Niemeier lattic
es. Then\, we explain how this can be used to classify the (exactly 70) st
rongly rational\, holomorphic VOAs of central charge 24 with non-zero weig
ht-one space. (The case of zero weight-one space\, which includes the Moon
shine module\, is more difficult and still open.)\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Tsuchioka (Tokyo Institute of Technology)
DTSTART:20210408T230000Z
DTEND:20210409T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/27
DESCRIPTION:Title: A proof of conjectured partition identities of Nandi.\n
by Shunsuke Tsuchioka (Tokyo Institute of Technology) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nWe generalize the theory of linked
partition ideals due to Andrews using finite automata in formal language
theory and apply it to prove three Rogers-Ramanujan type identities of mod
ulo 14 that were posed by Nandi through vertex operator theoretic construc
tion of the level 4 standard modules of the affine Lie algebra $A^{(2)}_{2
}$. This is a joint work with Motoki Takigiku.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Kontrec (University of Zagreb)
DTSTART:20210415T160000Z
DTEND:20210415T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/28
DESCRIPTION:Title: Bershadsky-Polyakov vertex algebras at positive integer lev
els and duality\nby Ana Kontrec (University of Zagreb) as part of Rock
y Mountain Rep Theory Seminar\n\n\nAbstract\nOne of the simplest examples
of $\\mathcal{W}$-algebras is the Bershadsky-Polyakov vertex algebra $\\ma
thcal{W}^k(\\mathfrak{g}\, f_{min})$\, associated to $\\mathfrak{g} = sl(3
)$ and the minimal nilpotent element $f_{min}$.\nWe study the simple Ber
shadsky-Polyakov algebra $\\mathcal W_k$ at positive integer levels and o
btain a classification of their irreducible modules.\nIn the case $k=1$\,
we show that this vertex algebra has a Kazama-Suzuki-type dual isomorphic
to the simple affine vertex superalgebra $L_{k'} (osp(1 \\vert 2))$ for $
k'=-5/4$. This is joint work with D. Adamovic.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Qi (University of Manitoba)
DTSTART:20210422T190000Z
DTEND:20210422T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/29
DESCRIPTION:Title: Bosonic and fermionic constructions of meromorphic open-str
ing vertex algebras.\nby Fei Qi (University of Manitoba) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nMeromorphic open-string ver
tex algebras (abbre. MOSVAs) is a noncommutative generalization of the usu
al vertex algebra defined by Yi-Zhi Huang in 2012. Vertex operators still
satisfy the associativity but do not necessarily satisfy commutativity. In
this talk I will illustrate nontrivial examples of MOSVAs and modules we
know so far\, including the universal bosonic construction\, the universal
fermionic construction\, and the example from the geometry over constant
curvature manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ridout (University of Melbourne)
DTSTART:20210506T220000Z
DTEND:20210506T230000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/30
DESCRIPTION:Title: Weight modules for $\\mathfrak{sl}_3$ minimal models\nb
y David Ridout (University of Melbourne) as part of Rocky Mountain Rep The
ory Seminar\n\n\nAbstract\nMinimal models are simple vertex operator algeb
ras (VOAs) for\nwhich the structure of the associated universal VOA is som
ehow maximally\ndegenerate. Some minimal models are rational and $C_2$-co
finite\, eg\nthose for Virasoro or $N=1$\, and some are not. I will look
at some\nexamples which are not\, specifically the admissible-level affine
minimal\nmodels associated with $\\mathfrak{sl}_3$. The novelty here is
the fact\nthat the rank of the associated algebra is not $1$.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cris Negron (University of North Carolina)
DTSTART:20210513T190000Z
DTEND:20210513T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/31
DESCRIPTION:Title: Quantum SL(2) and logarithmic vertex operator algebras at (
p\,1)-central charge\nby Cris Negron (University of North Carolina) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will discuss j
oint work with Terry Gannon in which we provide a ribbon tensor equivalenc
e between the representation category of small quantum SL(2)\, at paramete
r q=exp(pi i/p)\, and the representation category of the triplet vertex op
erator algebra at integral parameter p>1. We provide similar quantum group
equivalences for representation categories associated to the Virasoro\, a
nd singlet vertex operator algebras at central charge c=1-6(p-1)^2/p.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ZacharyFehily (University of Melbourne)
DTSTART:20210520T220000Z
DTEND:20210520T230000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/32
DESCRIPTION:Title: Subregular W-algebras\nby ZacharyFehily (University of
Melbourne) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWhi
le regular W-algebras have enjoyed many years of study and attention\, rec
ent developments in physics have the less popular subregular W-algebras pl
aying an important role. Moreover\, these subregular W-algebras appear at
levels where the corresponding conformal field theory is likely non-ration
al. This necessitates a deeper understanding of the representation theory
of such vertex operator algebras at non-rational levels. In type $A_n$\, o
nly the n=1 ($sl_2$) and n=2 (Bershadsky-Polyakov algebra) cases are parti
cularly well-understood. In both cases an 'inverse reduction-by-stages' ap
proach\, first described for sl_2 in vertex operator algebra language by D
. Adamovic\, relates much of the representation theory to that of the corr
esponding regular W-algebra. In this talk\, I will describe how to general
ise this approach to all type A_n subregular W-algebras using screening op
erators developed by N. Genra.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20210930T190000Z
DTEND:20210930T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/33
DESCRIPTION:Title: The category O of affine osp(1|2n) at admissible level\
nby Thomas Creutzig (University of Alberta) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nosp(1|2n) behaves in many respects similar t
o finite dimensional simple Lie algebras. The same is expected to be true
for its affine vertex algebra and we will see that this is indeed true for
the category O at admissible level.\nI will explain how to construct the
universal affine vertex superalgebra of osp(1|2n) by translating the equiv
ariant CDO of sp(2n). This construction gives valuable information about t
he simple affine vertex superalgebra at admissible level\, in particular w
e will be able to understand that the category O at admissible level is a
braided fusion supercategory.\n\nPlease check our seminar website for the
link and password to join the talk.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Yale University)
DTSTART:20211007T190000Z
DTEND:20211007T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/34
DESCRIPTION:Title: The Drinfeld--Sokolov reduction of admissible representatio
ns of affine Lie algebras\nby Gurbir Dhillon (Yale University) as part
of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFix an affine Lie alg
ebra ̂gκ with associated principal affine W-algebra Wκ. A basic conject
ure of Frenkel–Kac–Wakimoto asserts that Drinfeld–Sokolov reduction
sends admissible ̂gκ-modules to zero or cohomological shifts of minimal
series Wκ-modules. In recent work\, we proved this conjecture and a natur
al generalization to the spectrally flowed Drinfeld–Sokolov reduction fu
nctors and to a larger family of ̂gκ-modules. This extends the previous
results of Arakawa and Arakawa--Creutzig--Feigin. In the talk\, we review
the history and statement of the conjecture\, discuss the form the answer
takes\, and highlight a few ingredients of its proof which may be of use e
lsewhere.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rupert (Utah State University)
DTSTART:20211014T150000Z
DTEND:20211014T160000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/35
DESCRIPTION:Title: Uprolling Unrolled Quantum Groups\nby Matthew Rupert (U
tah State University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAb
stract\nI will discuss joint work with Thomas Creutzig where we construct
families of commutative (super) algebra objects in the category of weight
modules for unrolled restricted quantum groups of a simple Lie algebra at
roots of unity. We study their categories of local modules and derive cond
itions for these categories being finite\, non-degenerate\, and ribbon. Ba
sed on motivation from the rank one examples\, we expect that these catego
ries should be equivalent to module categories for vertex operator algebra
s\, and we present conjectures for the structure of module categories for
the higher rank Triplet and Bp vertex operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronika Pedić (University of Zagreb)
DTSTART:20211021T150000Z
DTEND:20211021T160000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/36
DESCRIPTION:Title: Representation theory and fusion rules for Weyl vertex alge
bras and beyond\nby Veronika Pedić (University of Zagreb) as part of
Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWeyl vertex algebra is an
interesting example of a non-rational and non C2-cofinite vertex algebra.
We describe fusion rules in the category of Weyl vertex algebra weight mo
dules and explicitly construct the intertwining operators appearing in the
se equations. We describe applications of our methods to other VOAs\, in p
articular the M(p) singlet. We present a result which relates irreducible
weight modules for the Weyl vertex algebra to the irreducible modules of t
he affine Lie superalgebra gl(1|1). This part of the talk is based on join
t work with D. Adamović.\n\nIn the second part we present results of a jo
int project with D. Addabbo\, K. Barron\, K. Batistelli\, F. Orosz Hunzike
r and G. Yamskulna. Among other things we calculate the first Zhu algebra
of the Weyl vertex algebra.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal (North Carolina State)
DTSTART:20211028T150000Z
DTEND:20211028T160000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/37
DESCRIPTION:Title: Logarithmic vertex algebras.\nby Juan Villareal (North
Carolina State) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract
\nIn this talk\, I want to explain a generalization of vertex algebras cal
led logarithmic vertex algebras\, which is a vertex algebra with logarithm
ic singularities in the operator product expansion of quantum fields. In t
his work\, we develop a framework that allows many results about vertex al
gebras to be extended to logarithmic vertex algebras. Finally\, I will men
tion one example which is motivated by physics\, this example exhibits so
me unexpected new features that are peculiar to the logarithmic case. This
is joint work with Bojko Bakalov.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathrin Bringmann (University of Cologne)
DTSTART:20211111T160000Z
DTEND:20211111T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/39
DESCRIPTION:Title: Modularity of class number generating function\nby Kath
rin Bringmann (University of Cologne) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nI my talk I will speak about various results relat
ed to the modularity of the class number generating function and some appl
ications.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20211123T200000Z
DTEND:20211123T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/40
DESCRIPTION:Title: Borcherds identity in logarithmic coordinates.\nby Reim
undo Heluani (IMPA) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbst
ract\nThe exponential change of coordinates z = exp(t) induces an automorp
hism on every conformal vertex algebra. Vertex operators in these new coor
dinates play an essential role in Zhu's proof of modularity of conformal b
locks. In this talk we'll take a look at a version of Borcherds formula fo
r these operators. Unlike the usual formula involving Laurent expansions o
f rational functions\, this formula uses Fourier expansion and explicit do
mains of convergence.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Wang (Xiamen University)
DTSTART:20211202T230000Z
DTEND:20211203T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/41
DESCRIPTION:Title: Trigonometric Lie algebras\, affine Lie algebras\, and vert
ex algebras\nby Qing Wang (Xiamen University) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nWe present natural connections among t
rigonometric Lie algebras\, affine Lie algebras\, and vertex algebras. Mor
e specifically\, we prove that restricted modules for trigonometric Lie al
gebras naturally correspond to equivariant quasi modules for the affine ve
rtex algebra. Furthermore\, we prove that every quasi-finite unitary highe
st weight irreducible module of type A trigonometric Lie algebra gives ris
e to an irreducible equivariant quasi module for the simple affine vertex
algebra. This is a joint work with Haisheng Li and Shaobin Tan.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20211209T200000Z
DTEND:20211209T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/42
DESCRIPTION:Title: Non-semisimple 3d TQFTs for the Feigen-Tipunin algebras and
quantum groups\nby Niklas Garner (University of Washington) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will describe a class
of physical 3d QFTs that conjecturally serve as non-semisimple\, derived
generalizations of Chern-Simons theory with compact gauge group SU(n). The
se 3d QFTs admit two different boundary conditions furnishing VOAs\, one o
f which being a Feigen-Tipunin algebra\, and we conjecture a novel logarit
hmic level-rank-like duality that relates them. Modules for the Feigen-Tip
unin algebra are expected to be related to modules for the quantum group v
ia a logarithmic Kazhdan-Lusztig-like correspondence\, thereby connecting
our physical QFT to mathematical TQFTs built from modules of the quantum g
roup. Our proposed physical QFT offers a new perspective on these VOAs and
mathematical TQFTs and allows for the use of techniques in supersymmetric
QFT to analyze their properties. This is based on joint work with T. Creu
tzig\, T. Dimofte\, and N. Geer.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haisheng Li (Rutgers University)
DTSTART:20211216T200000Z
DTEND:20211216T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/43
DESCRIPTION:Title: Deforming vertex algebras by module and comodule actions of
vertex bialgebras.\nby Haisheng Li (Rutgers University) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nPreviously\, we studied a n
otion of vertex bialgebra and a notion of module vertex algebra for a vert
ex bialgebra\, and gave a smash product construction of nonlocal vertex a
lgebras. Here\, we introduce a notion of right comodule vertex algebra fo
r a vertex bialgebra. Among the main results\, we give a construction of
quantum vertex algebras from vertex algebras with a right comodule vertex
algebra structure and a compatible (left) module vertex algebra structure
for a vertex bialgebra. As an application\, we obtain a family of deform
ations of the lattice vertex algebras. This is based on a joint work with
Naihuan Jing\, Fei Kong\, and Shaobin Tan.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Linshaw (University of Denver)
DTSTART:20220127T200000Z
DTEND:20220127T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/44
DESCRIPTION:Title: Vertex algebras and arc spaces\nby Andrew Linshaw (Univ
ersity of Denver) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nVertex algebras are certain noncommutative\, nonassociative algebraic
structures that arose out of physics in the 1980s. They were axiomatized b
y Borcherds in his proof of the Moonshine Conjecture\, and in the last 35
years they have become important in a diverse range of subjects. A fruitfu
l perspective is that many vertex algebras can be viewed as quantizations
of coordinate rings of arc spaces. In this talk\, I will give an introduct
ion to vertex algebras\, arc spaces\, and their interconnections. This is
based on joint work with Bailin Song.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Primc (University of Zagreb)
DTSTART:20220203T200000Z
DTEND:20220203T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/45
DESCRIPTION:Title: New partition identities from $C_l^{(1)}$-modules\nby M
irko Primc (University of Zagreb) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nIn joint work with S. Capparelli\, A. Meurman\, and A.
Primc (arXiv:2106.06262) we conjecture combinatorial Rogers-Ramanujan typ
e identities for colored partitions\, related to standard representations
of symplectic affine Lie algebras. The conjecture is stated in purely comb
inatorial terms\, and it is supported by numerical evidence. In my talk\,
I will state the conjecture and then explain the representation theory bac
kground.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schweigert (University of Hamburg)
DTSTART:20220210T200000Z
DTEND:20220210T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/46
DESCRIPTION:Title: Rigidity in conformal field theory and vertex algebras beyo
nd rigidity\nby Christoph Schweigert (University of Hamburg) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nRigidity of tensor cate
gories plays an important role\, in quantum topology\nand in the represent
ation theory of many algebraic objects\, in particular of\nHopf algebras a
nd vertex algebras. In this talk\, we discuss inherent restrictions of the
notion of rigidity. We then explain why rigidity is so useful in the stud
y of bulk fields of conformal field theories.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uhi Rinn Suh (Seoul National University)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/47
DESCRIPTION:Title: N=1 Supersymmetric (SUSY) W-algebras\nby Uhi Rinn Suh (
Seoul National University) as part of Rocky Mountain Rep Theory Seminar\n\
n\nAbstract\nAs a SUSY analogue of vertex algebras\, Heluani and Kac intro
duced SUSY vertex algebras. On the other hand\, in physics literature\, SU
SY counterpart of Toda theory has been studied. In particular\, Madsen and
Ragoucy described an N=1 SUSY analogue of the quantum Drinfeld-Sokolov re
duction. In this talk\, I will explain the SUSY Hamiltonian reduction proc
ess in terms of supersymmetric vertex algebras. This is based on the joint
work with Molev and Ragoucy.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Yu (Xiamen University)
DTSTART:20220303T230000Z
DTEND:20220304T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/48
DESCRIPTION:Title: Fusion products of twisted modules in permutation orbifolds
\nby Nina Yu (Xiamen University) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nThe orbifold theory studies a vertex operator algeb
ra under the action of a finite group. The goal is to understand the repre
sentation theory for the fixed point vertex operator subalgebra. The main
feature in orbifold theory is the appearance of the twisted modules. The p
ermutation orbifolds study the action of the symmetric group of degree k o
n the k-tensor product of a vertex operator algebra. In [Dong-Li-Xu-Yu\; 2
019]\, we determined the fusion product of any untwisted module with any t
wisted module for permutation orbifolds. In this talk I will talk about fu
sion products of twisted modules for permutation orbifolds. This is a join
t work with C. Dong and F. Xu.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Williams (University of Edinburgh)
DTSTART:20220310T200000Z
DTEND:20220310T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/49
DESCRIPTION:Title: Exceptional super Lie algebras and their representations fr
om M-theory\nby Brian Williams (University of Edinburgh) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nRecently\, a program for ma
thematically realizing a ubiquitous relationship in physics called hologra
phy in terms of Koszul duality has been proposed. In this talk I will expl
ain how three exceptional super Lie algebras appear in a (twisted) version
of this correspondence in the context of M-theory. One of these Lie algeb
ras\, which Kac calls E(3|6)\, plays a particular important role related t
o the AGT correspondence and we will argue how its representation theory s
heds light on the holographic story and beyond.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20220818T190000Z
DTEND:20220818T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/50
DESCRIPTION:Title: Factorization resolutions\nby Angela Gibney (University
of Pennsylvania) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nIn recent work with Damiolini and Tarasca\, extending previous results
\, we have shown that simple modules over a vertex operator algebra V of C
FT-type determine sheaves of coinvariants\, and dual sheaves of conformal
blocks on certain moduli spaces of stable pointed curves. If V is strongly
rational\, these are vector bundles\, with Chern classes in the tautologi
cal ring. The factorization formula\, which relies on rationality of V\, p
layed a crucial role in proving these results. In this talk I will discuss
recent work with Damiolini and Krashen\, where we introduce factorization
presentations\, applicable to C_1-cofinite V. As I'll explain\, this new
perspective simplifies the original proof of factorization and gives evide
nce that modules over strongly finite VOAs may determine vector bundles.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20220331T190000Z
DTEND:20220331T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/51
DESCRIPTION:Title: On the cohomology of vertex algebras and Poisson vertex alg
ebras.\nby Bojko Bakalov (North Carolina State University) as part of
Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFollowing Beilinson and D
rinfeld\, we describe vertex algebras as Lie\nalgebras for a certain opera
d of $n$-ary chiral operations. This\nallows us to introduce the cohomolog
y of a vertex algebra $V$ as a Lie\nalgebra cohomology. When $V$ is equipp
ed with a good filtration\, its\nassociated graded is a Poisson vertex alg
ebra. We relate the\ncohomology of $V$ to the variational Poisson cohomolo
gy studied\npreviously by De Sole and Kac. This talk is based on joint wor
k with\nAlberto De Sole\, Reimundo Heluani\, Victor Kac\, and Veronica Vig
noli.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (University of California\, Davis)
DTSTART:20220407T190000Z
DTEND:20220407T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/52
DESCRIPTION:Title: Beta-gamma VOA and 3d mirror symmetry\nby Wenjun Niu (U
niversity of California\, Davis) as part of Rocky Mountain Rep Theory Semi
nar\n\n\nAbstract\nIn this talk\, I will explain our study of the category
of modules of the beta-gamma VOA from the point of view of 3d mirror symm
etry. I will introduce a category of modules of the beta-gamma VOA\, conta
ining the category studied by Ridout-Wood and Allen-Wood. We propose that
this category is the category of line operators for a twisted 3d N=4 theor
y. I will explain that using a relation of beta-gamma and affine Lie super
algebra of \\mathfrak{gl}(1|1)\, we can show that this category has the st
ructure of a braided tensor category. This relation is an example of 3d ab
elian mirror symmetry. If time permits\, I will talk about a relation to m
atrix factorizations. This is based on joint work with Andrew Ballin.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Rozhkovskaya (Kansas State University)
DTSTART:20220414T190000Z
DTEND:20220414T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/53
DESCRIPTION:Title: Transformations of Vertex operators of Hall-Littlewood Poly
nomials\nby Natalia Rozhkovskaya (Kansas State University) as part of
Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWe study the effect of li
near transformations on quantum fields\, with the main example of applicat
ion to vertex operator presentations of Hall-Littlewood polynomials. The c
onstruction is illustrated with examples that include certain version
s of multiparameter symmetric functions\, dual Grothendieck polynomials\
, deformations by cyclotomic polynomials\, and some other variations of Sc
hur symmetric functions that exist in the literature. Linear transformatio
ns of quantum fields effectively describe preservation of commutation rel
ations of operators\, stability of symmetric polynomials\, polynomial tau
functions of the KP and the BKP hierarchy.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chongying Dong (University of California Santa Cruz)
DTSTART:20220428T220000Z
DTEND:20220428T230000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/54
DESCRIPTION:Title: Pointed modular tensor category\nby Chongying Dong (Uni
versity of California Santa Cruz) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nA modular tensor category is pointed if every simple o
bject is a simple current. We show that any pointed modular tensor catego
ry is equivalent to the module category of a lattice vertex operator algeb
ra. Moreover\, if the pointed modular tensor category C is the module cate
gory of a twisted Drinfeld double associated to a finite abelian group G a
nd a 3-cocycle with coefficients in U(1)\, then there exists a self dual
positive definite even lattice L such that G can be realized an automorph
ism group of lattice vertex operator algebra $V_L\,$ $V_L^G$ is also a la
ttice vertex operator algebra and C is equivalent to the module category
of $V_L^G.$ This is a joint work with S. Ng and L. Ren.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Linshaw (University of Denver)
DTSTART:20220505T190000Z
DTEND:20220505T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/55
DESCRIPTION:Title: Global sections of the chiral de Rham complex for Calabi-Ya
u and hyperkahler manifolds.\nby Andrew Linshaw (University of Denver)
as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFor any compl
ex manifold M\, the chiral de Rham complex is a sheaf of vertex algebras o
n M that was introduced in 1998 by Malikov\, Schechtman\, and Vaintrob. It
is N-graded by conformal weight\, and the weight zero piece coincides wit
h the ordinary de Rham sheaf. When M is a Calabi-Yau manifold with holonom
y group SU(d)\, it was shown by Ekstrand\, Heluani\, Kallen and Zabzine th
at the algebra of global sections $\\Omega^{ch}(M)$ contains a certain ver
tex algebra defined by Odake which is an extension of the N=2 superconform
al algebra. When M is a hyperkahler manifold\, it was shown by Ben-Zvi\, H
eluani\, and Szczesny that $\\Omega^{ch}(M)$ contains the small N=4 superc
onformal algebra. In this talk\, we will show that in both cases\, these s
ubalgebras are actually the full algebras of global sections. In an earlie
r work\, Bailin Song has shown that the global section algebra can be iden
tified with a certain subalgebra of a free field algebra which is invarian
t under the action of an infinite-dimensional Lie algebra of Cartan type.
They key observation is that this algebra can be described using the arc s
pace analogue of Weyl's first and second fundamental theorems of invariant
theory for the special linear and symplectic groups. This is a joint work
with Bailin Song.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20220901T190000Z
DTEND:20220901T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/56
DESCRIPTION:Title: Vertex tensor categories and C_1 cofiniteness\nby Thoma
s Creutzig (University of Alberta) as part of Rocky Mountain Rep Theory Se
minar\n\n\nAbstract\nA major challenge in VOA theory is to show that a giv
en category of modules admits a vertex tensor category structure. It turns
out that C_1-cofiniteness plus a few additional conditions is sufficient
to ensure the existence of vertex tensor category. I will illustrate this
in examples and explain its use beyond C_1-cofinite modules.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20220908T190000Z
DTEND:20220908T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/57
DESCRIPTION:Title: Frobenius exact symmetric tensor categories.\nby Victor
Ostrik (University of Oregon) as part of Rocky Mountain Rep Theory Semina
r\n\n\nAbstract\nI will report on a joint work with K.Coulembier and P.Eti
ngof. We give a characterization of symmetric tensor categories over field
s of positive characteristic which admit an exact tensor functor to the Ve
rlinde category\; in particular we give a characterization of Tannakian ca
tegories. A crucial ingredient of this characterization is exactness of th
e Frobenius twist functor which mimics the Frobenius twist for representat
ions of algebraic groups. We will also discuss some applications to modula
r representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (Indiana University-Purdue University Indianapolis)
DTSTART:20221013T190000Z
DTEND:20221013T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/58
DESCRIPTION:Title: Extensions of deformed W-algebras.\nby Evgeny Mukhin (I
ndiana University-Purdue University Indianapolis) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nI will discuss the combinatorics of qq
-characters as a tool for constructing deformed W-algebras and their exten
sions. \nThis is a report on a joint work in progress with B. Feigin and
M. Jimbo.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Sadowski (Ursinus College)
DTSTART:20221020T190000Z
DTEND:20221020T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/59
DESCRIPTION:Title: Weight-one elements of vertex operator algebras and automor
phisms of categories of generalized twisted modules\nby Chris Sadowski
(Ursinus College) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstr
act\nGiven a weight-one element u of a vertex operator algebra V \, we con
struct an automorphism of the category of generalized g-twisted modules fo
r automorphisms of g fixing u. We apply these results to the case that V i
s an affine vertex algebra to obtain explicit results on these automorphis
ms of categories. In particular\, we give explicit constructions of certai
n generalized twisted modules from generalized twisted modules associated
to diagram automorphisms of finite-dimensional simple Lie algebras and gen
eralized (untwisted) modules. This talk is based on a joint work with Yi-Z
hi Huang.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Genra (Kavli IMPU)
DTSTART:20220922T230000Z
DTEND:20220923T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/60
DESCRIPTION:Title: Coset constructions of W-superalgebras of type B\nby Na
oki Genra (Kavli IMPU) as part of Rocky Mountain Rep Theory Seminar\n\n\nA
bstract\nWe talk about coset constructions of principal W-superalgebras of
osp(1|2n)\, which are analogs of coset constructions of principal W-algeb
ras of type ADE by Arakawa-Creutzig-Linshaw. The cosets are useful not onl
y to study the category of modules at non-degenerate admissible levels\, b
ut also to prove the existence of embeddings of the affine vertex superalg
ebras of osp(1|2n) into the equivariant W-algebras of sp(2n) times 2n+1 fr
ee fermions. This leads to the rigidity of the category O of affine sp(2n)
at admissible levels as a corollary. This is joint work with Thomas Creut
zig and Andrew Linshaw.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University)
DTSTART:20220825T190000Z
DTEND:20220825T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/61
DESCRIPTION:Title: Zesting link invariants\nby Julia Plavnik (Indiana Univ
ersity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIt was
conjectured that modular categories were determined by its modular data (
S- and T-matrices). In 2017\, Mignard and Schauenburg presented a family o
f counterexamples to this conjecture\, which led to the study of link inva
riants beyond modular data to distinguish these categories. In this talk w
e will discuss ribbon zesting\, which is a construction of modular categor
ies\, and how it is related to the family of Mignard-Schauenburg counterex
amples. To better understand this relation\, we look into how zesting affe
cts link invariants such as the W-matrix and the B-tensor. This talk is ba
sed on joint work with Colleen Delaney and Sung Kim (https://arxiv.org/abs
/2107.11374).\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20220915T190000Z
DTEND:20220915T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/62
DESCRIPTION:Title: Duality of hook-type W-superalgebras via convolution operat
ions\nby Shigenori Nakatsuka (University of Alberta) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nHook type W-superalgebras are W
-superalgebras whose affine cosets appear at junctions of supersymmetric i
nterfaces in N = 4 Super Yang Mills gauge theory. Their affine cosets enjo
y a Feigin-Frenkel type duality as proven by Creutzig and Linshaw by the u
niqueness property of these algebras. I will explain how this duality is e
nhanced to a reconstruction theorem for the W-superalgebra themselves via
convolution operation with ``shifted" chiral differential operators. If ti
me permits\, I will talk about its representation theoretic applications a
nd module characters. The talk is based on my joint work with Thomas Creut
zig\, Andrew Linshaw and Ryo Sato.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinwei Yang (Shanghai Jiao Tong University)
DTSTART:20220929T230000Z
DTEND:20220930T000000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/63
DESCRIPTION:Title: Ribbon categories for the singlet algebras and their extens
ions.\nby Jinwei Yang (Shanghai Jiao Tong University) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nIn this talk\, we summarize ou
r recent work on the tensor categories for the singlet algebras\, includin
g the tensor structure on the category of the atypical modules\, as well a
s on the full category of C_1-cofinite modules. We will also apply these r
esults to study representation theory of vertex algebras that are extensio
ns of the singlet algebras\, especially the B_p-algebra. This talk is base
d on a series of joint work with T. Creutzig and R. McRae.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McRae (YMSC\, Tsinghua University)
DTSTART:20221111T000000Z
DTEND:20221111T010000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/64
DESCRIPTION:Title: Non-rigid Kazhdan-Lusztig tensor categories for affine sl_2
at admissible levels and quantum groups.\nby Robert McRae (YMSC\, Tsi
nghua University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nI will present upcoming joint work with Jinwei Yang on the non-semisim
ple Kazhdan-Lusztig categories KL^k(sl_2) of affine sl_2 at admissible lev
els k = −2 + p/q\, where p > 1 and q > 0 are relatively prime integers.
KL^k(sl_2) is the category of finite-length modules for affine sl_2 at lev
el k whose composition factors are irreducible highest-weight modules whos
e highest weights are dominant integral for the finite-dimensional subalge
bra sl_2. We show that KL^k(sl_2) admits the\nvertex algebraic braided ten
sor category structure of Huang-Lepowsky-Zhang\, but that it is not rigid.
Instead\, an object of KL^k(sl_2) is rigid if and only if it is projectiv
e and\, moreover\, KL^k(sl_2) has enough projectives\; most of the indecom
posable projective objects are logarithmic modules\, which means that the
Virasoro L(0) operator acts non-semisimply. We show also that the monoidal
subcategory of rigid and projective objects is tensor equivalent to tilti
ng modules for quantum sl_2 at the root of unity e^{pi i/(k+2)}. This lead
s to a universal property for KL^k(sl_2)\, which allows us to construct an
essentially surjective (but not fully faithful) exact tensor functor from
KL^k(sl2) to the category of finite-dimensional weight modules for quantu
m sl_2 at e^{pi i/(k+2)}.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20221208T200000Z
DTEND:20221208T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/65
DESCRIPTION:Title: From N-graded vertex algebras to Leibniz algebras and back.
\nby Gaywalee Yamskulna (Illinois State University) as part of Rocky M
ountain Rep Theory Seminar\n\n\nAbstract\nA large portion of the literatur
e in both mathematics and physics is concerned with vertex algebras V that
are of CFT-type and rational. It is natural to ask whether there are othe
r significant classes of vertex algebras that well-behaved from the repres
entation theoretic point of view such as \n\nNon CFT-type\, and rational
for some category of modules or \n\nNon CFT-type and irrational but the m
odule category has other nice properties such as C_2-condition. \n\nFor t
his talk\, I will focus on a study of representation theory of N-graded ve
rtex algebras. To be precise\, I will describe an algebraic structure of r
ational N-graded vertex algebras\, provide some tools to determine when N-
graded vertex algebras are irrational and describe roles of Leibniz algebr
as on the study of N-graded vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (Weizmann Institute of Science)
DTSTART:20221117T180000Z
DTEND:20221117T190000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/66
DESCRIPTION:Title: Linkage classes for Kac-Moody superalgebras and the Duflo-S
erganova functors\nby Maria Gorelik (Weizmann Institute of Science) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIn this talk\, I
will present a uniform description of the linkage classes for finite dime
nsional and affine Kac-Moody superalgebras. These linkage classes are then
used to parametrize the blocks in the category O. I will describe the in
teraction between these linkage classes and the Duflo-Serganova functors.
The latter are homological functors from the category of representations o
f a Lie superalgebra to the category of representations of a Lie superalge
bra of the same type\, but smaller rank.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (University of Melbourne)
DTSTART:20221103T190000Z
DTEND:20221103T200000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/67
DESCRIPTION:Title: Rationality of subregular W-algebras of type B.\nby Jus
tine Fasquel (University of Melbourne) as part of Rocky Mountain Rep Theor
y Seminar\n\n\nAbstract\nIn this talk\, we present several results on the
rationality of W-algebras associated with subregular nilpotent elements of
the Lie algebra so(2n+1) as well as applications to W-superalgebras of ty
pe osp(2|2n). The case n=2 was studied in my thesis\; the generalization f
or higher ranks and the « super » cases is an on going work with Shigeno
ri Nakatsuka (Alberta).\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20230309T210000Z
DTEND:20230309T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/68
DESCRIPTION:Title: Quantum groups and VOAs\nby Thomas Creutzig (University
of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nT
here are two natural sources of braided tensor categories: categories of m
odules of VOAs and quantum groups. Jointly with Matt Rupert and Simon Lent
ner\, we are developing a theory on relating the two and in this talk I wi
ll explain that under suitable conditions a VOA category is a relative Dri
nfeld center\, while this is always true for quantum groups. This implies
nice correspondences as e.g. the one between singlet algebra and unrolled
small quantum group of sl(2) at root of unity.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryam Khaqan (Stockholm University)
DTSTART:20230316T170000Z
DTEND:20230316T180000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/69
DESCRIPTION:Title: Vertex operators for imaginary gl2-subalgebras in the Monst
er Lie algebra.\nby Maryam Khaqan (Stockholm University) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nThe Monster Lie algebra is
a quotient of the physical space of the vertex algebra tensor product of a
specific rank-2 lattice vertex algebra with the Moonshine module of Frenk
el\, Lepowsky\, and Meurman. \n\nIn this talk\, I will describe elements i
n the tensor product vertex algebra that project onto generators of gl2-su
balgebras corresponding to each imaginary simple root of the Monster Lie a
lgebra. Furthermore\, for a fixed imaginary simple root\, I will illustrat
e how the action of the Monster simple group on the Moonshine module induc
es an orbit of each gl2-subalgebra of the Monster Lie algebra constructed
in this way. We conjecture that this Monster action is non-trivial. \n\nTh
is talk is based on joint work with Darlayne Addabbo\, Lisa Carbone\, Eliz
abeth Jurisich\, and Scott H. Murray.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ole Warnaar (The University of Queensland)
DTSTART:20230413T210000Z
DTEND:20230413T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/71
DESCRIPTION:Title: Cylindric partitions and character formulas for W algebras<
/a>\nby Ole Warnaar (The University of Queensland) as part of Rocky Mounta
in Rep Theory Seminar\n\n\nAbstract\nCylindric partitions are an affine an
alogue of plane partitions. In this talk I will explain the role cylindric
partitions have played in recent years in the computation of characters o
f the vertex operator algebra W_r(p\,p').\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Hekmati (University of Auckland)
DTSTART:20230420T200000Z
DTEND:20230420T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/72
DESCRIPTION:Title: Distributional characters on toric contact manifolds.\n
by Pedram Hekmati (University of Auckland) as part of Rocky Mountain Rep T
heory Seminar\n\n\nAbstract\nToric contact manifolds have a nice combinato
rial description in terms of their moment cones. This paves the way for an
explicit computation of their various invariants\, such as the fundamenta
l group\, cohomology ring and contact homology. In this talk\, I will disc
uss the transverse Dirac operator on these manifolds. It features notably
in certain supersymmetric gauge theories and its T-equivariant index chara
cter determines a distribution on the torus T\, for which we derive a simp
le and explicit formula.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Valeri (Sapienza University of Rome)
DTSTART:20230427T170000Z
DTEND:20230427T180000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/73
DESCRIPTION:Title: Deformations of W-algebras and differential-difference equa
tions\nby Daniele Valeri (Sapienza University of Rome) as part of Rock
y Mountain Rep Theory Seminar\n\n\nAbstract\nIn this talk I will review so
me results about q-deformations of W-algebras and their relations with dif
ferential-difference equations.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lachowska (EPFL Lausanne)
DTSTART:20230504T170000Z
DTEND:20230504T180000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/74
DESCRIPTION:Title: The small quantum group and related geometry\nby Anna L
achowska (EPFL Lausanne) as part of Rocky Mountain Rep Theory Seminar\n\n\
nAbstract\nLet $u_q(g)$ denote the small quantum group associated to a sem
isimple complex Lie algebra g and a root of unity q. \n\nI will describe s
ome recent results on the structure of the center of u_q(g) and discuss it
s relation to the geometry of the Springer resolution and the affine Sprin
ger fibers. \n\nA lower bound on the dimension of the center of $u_q(g)$ s
uggests a connection with the representation theory \n\nof the rational Ch
erednik algebra.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Lentner (University of Hamburg)
DTSTART:20230511T200000Z
DTEND:20230511T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/75
DESCRIPTION:Title: A theory of logarithmic Kazhdan-Lusztig correspondences.\nby Simon Lentner (University of Hamburg) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nWe want to understand braided tensor categor
ies U that have a\ncommutative algebra and a known braided tensor category
C of local\nmodules. Our first result is that U is a relative Drinfeld ce
nter of the\ncategory B of twisted modules\, our second result is that in
good cases\nwe can understand B in terms of a Hopf algebra in C and we dev
elop\nmethods to determine this Hopf algebra. Hence we can determine U\nex
plicitly.\n\nIn particular we can prove that if U is equivalent as an abel
ian\ncategory to representations of a quantum group\, or certain\ngenerali
zations\, and if it has a commutative algebra as above\, then it\nis equiv
alent already as braided tensor category.\n\nThe main application we have
in mind are the categories of\nrepresentations of certain vertex alebras\,
which are defined as kernel\nof screenings in a free field realization. I
n this case the latter gives\nby construction a commutative algebra with k
nown C and conjecturally the\nHopf algebra above should be the Nichols alg
ebra of screenings. With our\nresults above we can prove in some cases bra
ided category equivalences\nto certain quantum groups\, which are instance
s of logarithmic Kazhdan\nLusztig conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivana Vukorepa (University of Zagreb)
DTSTART:20230525T180000Z
DTEND:20230525T190000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/76
DESCRIPTION:Title: Tensor category $KL_k(sl_{2n})$ via minimal affine $W$--alg
ebras at the non-admissible level $k=-\\frac{2n+1}{2}$\nby Ivana Vukor
epa (University of Zagreb) as part of Rocky Mountain Rep Theory Seminar\n\
n\nAbstract\nRepresentation theory of simple affine vertex algebra $L_k(\\
mathfrak{g})$\, for arbitrary simple Lie algebra $\\mathfrak{g}$ and gener
al level $k \\in \\mathbb{C}$\, is a very important direction in the theor
y of vertex algebras. Some of the best understood cases are non-negative i
nteger levels $k \\in \\mathbb{Z}_{\\geq 0}$ and so-called admissible leve
ls. \n\nIn the present talk we consider special non-admissible levels for
$\\mathfrak{g} = \\mathfrak{sl}_m$. We prove that $KL_k(\\mathfrak{sl}_m)$
is a semi-simple\, rigid braided tensor category for all even $m \\geq 4$
\, and $k=-\\frac{m+1}{2}$. Moreover\, all modules in $KL_k(\\mathfrak{sl}
_m)$ are simple-currents and they appear in the decomposition of conformal
embeddings $\\mathfrak{gl}_m \\hookrightarrow \\mathfrak{sl}_{m+1}$ at le
vel $k=-\\frac{m+1}{2}$. For this we inductively identify minimal affine $
W$--algebra $W_{k-1}(\\mathfrak{sl}_{m+2}\,\\theta)$ as simple current ext
ension of $L_k(\\mathfrak{sl}_m) \\otimes \\mathcal{H} \\otimes \\mathcal{
M}$\, where $\\mathcal{H}$ is the rank one Heisenberg vertex algebra\, and
$\\mathcal{M}$ the singlet vertex algebra for $c=-2$. This is joint work
with D. Adamovi\\'{c}\, T. Creutzig and O. Per\\v{s}e.\n\\end{document}\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumah Al-Ali (Saudi Electronic University)
DTSTART:20230601T160000Z
DTEND:20230601T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/77
DESCRIPTION:Title: Orbifolds of Gaiotto-Rapčák Y-algebras\nby Masoumah A
l-Ali (Saudi Electronic University) as part of Rocky Mountain Rep Theory S
eminar\n\n\nAbstract\nGaiotto and Rapčák introduced an important family
of vertex algebras called $Y_ {N_1\,N_2\, N_3}[\\psi]$-algebras where $N_1
\, N_2\, N_3$ are nonnegative integers and $\\psi$ is a complex parameter.
These vertex algebras arise as a simple one-parameter quotients of the un
iversal two-parameters $W_\\infty$-algebra and serve as building blocks fo
r many interesting vertex algebras. The universal two parameters $W_\\inft
y$-algebra has a full automorphism group $Z_2$ and these algebras inherit
this action. We shall study the structure of their orbifolds. Regardless o
f the extremal cases\, we show that these orbifolds are generated by a sin
gle field of weight four\, and we give strong finite generating set.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jehanne Dousse (University of Geneva)
DTSTART:20230608T200000Z
DTEND:20230608T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/78
DESCRIPTION:Title: Characters of level 1 $C_n^{(1)}$-modules\, integer partiti
ons\, and the Capparelli-Meurman-Primc-Primc conjecture\nby Jehanne Do
usse (University of Geneva) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nA partition of a positive integer n is a non-increasing sequ
ence of positive integers whose sum is n.\nSince Lepowsky\, Milne\, and Wi
lson's seminal work in the 1980's\, several connections have been establis
hed between integer partitions and characters of standard modules of affin
e Lie algebras. Among these\, an approach initiated by Primc in the 1990
’s and developed by the speaker and Konan in the past few years consists
in studying crystal bases of the modules to obtain character formulas whi
ch can be expressed in terms of generalised partitions.\nIn this talk\, we
show how our method applies to level 1 standard modules of $C_n^{(1)}$ to
give several expressions for their characters as generating functions for
generalised partitions. Doing this\, we prove a recent conjecture of Capp
arelli-Meurman-Primc-Primc on characters of level k standard modules of $C
_n^{(1)}$ in the particular case of level 1.\nThis is joint work with Isaa
c Konan.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20230406T200000Z
DTEND:20230406T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/79
DESCRIPTION:Title: On Feigin-Tipunin type extension of W-algebras\nby Shig
enori Nakatsuka (University of Alberta) as part of Rocky Mountain Rep Theo
ry Seminar\n\n\nAbstract\nThe triplet algebra is an extension of the (p\,1
)-model of Virasoro algebra\, which is a famous example of C2-cofinite but
irrational VOA. Feigin and Tipunin gave a construction and generalization
of this algebra to simply-laced principal W-algebras by using VOA bundles
over flag varieties. In this talk\, we'll generalize their construction f
or all the W-algebras and then explain their properties for $sl(2)$. The t
alk is based on my on-going joint work with Thomas Creutzig and Shoma Sugi
moto.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Kanade (University of Denver)
DTSTART:20230914T200000Z
DTEND:20230914T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/80
DESCRIPTION:Title: Invariants of torus links and characters of VOAs.\nby S
hashank Kanade (University of Denver) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nI will explain how the characters of various ratio
nal and non-rational VOAs of type A are obtained from sl_r invariants of t
orus \nlinks. Specifically\, we will consider principal W algebras\, (1\,p
) singlet and\n(1\,p) triplet VOAs.\n\nThe password is the central extensi
on of the Witt algebra V*******\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marijana Butorac (University of Rijeka)
DTSTART:20230921T200000Z
DTEND:20230921T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/81
DESCRIPTION:Title: Combinatorial construction of standard modules for affine L
ie algebras.\nby Marijana Butorac (University of Rijeka) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nIn this talk I will present
the construction of combinatorial bases of standard modules with rectangu
lar highest weights for affine Lie algebras\, which relies on the construc
tion of quasi--particle bases of the Feigin--Stoyanovsky principal subspac
es. This talk is based on a joint project with S. Kožić and M. Primc.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Qi (University of Denver)
DTSTART:20230928T200000Z
DTEND:20230928T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/82
DESCRIPTION:Title: On extensions of left modules for a meromorphic open-string
vertex algebra.\nby Fei Qi (University of Denver) as part of Rocky Mo
untain Rep Theory Seminar\n\n\nAbstract\nGiven two left modules $W_1\, W_2
$ for a meromorphic open-string vertex algebra $V$\, we will first use Hua
ng's cohomology to describe the equivalence classes of modules $U$ fitting
in the exact sequence $0 \\to W_2 \\to U \\to W_1 \\to 0$ while satisfyin
g a technical convergence condition. Then\, we will explain that the techn
ical convergence condition automatically holds if $V$ contains a nice suba
lgebra $V_0$\, such that $W_1$ and $W_2$ are semisimple $V_0$-modules\, an
d the products of intertwining operators converge. Here $V_0$ is not requi
red to be conformally embedded into $V$. Nor will we need $V$-modules to f
orm a tensor category. The result leads to a new method for computing $\\t
ext{Ext}^1(W_1\, W_2)$.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni de Arriba de la Hera (Instituto de Ciencias Matemáticas)
DTSTART:20231005T160000Z
DTEND:20231005T170000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/83
DESCRIPTION:Title: Supersymmetric Vertex Algebras and Killing Spinors\nby
Andoni de Arriba de la Hera (Instituto de Ciencias Matemáticas) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe goal of the talk is
to construct embeddings of the N=2 superconformal vertex algebra\, motiva
ted by mirror symmetry\, into the chiral de Rham complex\, provided that w
e have solutions to the Killing spinor equations. Our approach to the chir
al de Rham complex is based on the universal construction by Bressler and
Heluani\, which applies to any Courant algebroid over a smooth manifold. T
he Killing spinor equations that are considered come from the approach to
special holonomy based on Courant algebroids in generalized geometry and a
re inspired by the physics of heterotic supergravity and string theory. Th
e embeddings are given in two different set-ups. Firstly\, for equivariant
Courant algebroids over homogeneous manifolds\, where the construction re
duces to embeddings into the superaffinization of a quadratic Lie algebra\
, and the Killing spinor equations become purely algebraic conditions that
can be checked on explicit examples. As an application\, we present the f
irst examples of (0\,2) mirror symmetry on compact non-Kähler complex man
ifolds. These results are included in axiv:2012.01851\, recently published
in International Mathematical Research Notices. Secondly\, for transitive
Courant algebroids over complex manifolds\, where these equations are equ
ivalent to the Hull-Strominger system\, with origins in the heterotic sigm
a-model studied by physicists. Several examples have been studied where th
e obtained results are applied. These results are included in arxiv:2305.0
6836. This talk is based on my PhD thesis\, and is a joint work with Luis
Álvarez-Cónsul and Mario Garcia-Fernandez.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Caradot (Henan University)
DTSTART:20231012T200000Z
DTEND:20231012T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/84
DESCRIPTION:Title: The cohomological variety of a vertex operator algebra.
\nby Antoine Caradot (Henan University) as part of Rocky Mountain Rep Theo
ry Seminar\n\n\nAbstract\nGiven a vertex operator algebra V\, one can atta
ch a graded Poisson algebra called the C2-algebra. The associated Poisson
variety is an important invariant for V and is known as the associated var
iety of V. In this talk\, we will introduce the cohomological variety of a
vertex operator algebra\, a notion cohomologically dual to that of the as
sociated variety. First\, we will motivate and define this variety\, as we
ll as give some of its structural properties. Then we will explain how to
extract information on the Yoneda algebra defining this variety. Lastly\,
we will apply those results to the simple vertex operator algebras constru
cted from the Virasoro Lie algebra and finite dimensional simple Lie algeb
ras. This is a joint work with Cuipo Jiang (Shanghai Jiao Tong University)
and Zongzhu Lin (Kansas State University).\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdi Huang
DTSTART:20231026T200000Z
DTEND:20231026T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/85
DESCRIPTION:Title: Weighted Poisson polynomial rings and their Poisson valuati
ons\nby Hongdi Huang as part of Rocky Mountain Rep Theory Seminar\n\n\
nAbstract\nA commutative algebra $A$ together with a Lie bracket satisfyin
g the Leibniz rule is called a Poisson algebra\, which is named in honor o
f Siméon Denis Poisson. Poisson structures appear in many contexts\, incl
uding string theory\, classical (quantum) mechanics\, and differential geo
metry. In this talk\, we will talk about Poisson structure on weighted pol
ynomial rings and introduce Poisson valuations. Furthermore\, we will see
that the Poisson valuations play an important role in characterizing the
Poisson automorphism groups of certain Poisson algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART:20231102T200000Z
DTEND:20231102T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/86
DESCRIPTION:Title: Going to the other side\nby Sergei Gukov (California In
stitute of Technology) as part of Rocky Mountain Rep Theory Seminar\n\n\nA
bstract\nAt its core\, this talk will be about a relation between characte
rs of modules of logarithmic vertex algebras in the positive and negative
Kazhdan-Lusztig (KL) zones. The main concrete result will be an easy-to-us
e step-by-step computational algorithm that produces a character of a log-
VOA\, say\, in the positive KL zone from the expression in the negative KL
zone\, and vice versa. An equally (if not more!) valuable conceptual mess
age of this talk will be an explanation that the same bijective relation p
lays an important role in very different areas of mathematics (and even ph
ysics) under other guises.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agustina Czenky (University of Oregon)
DTSTART:20231116T210000Z
DTEND:20231116T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/87
DESCRIPTION:Title: Low rank symmetric fusion categories in positive characteri
stic.\nby Agustina Czenky (University of Oregon) as part of Rocky Moun
tain Rep Theory Seminar\n\n\nAbstract\nIn this talk\, we look at the class
ification problem for symmetric fusion categories in positive characterist
ic. We recall the second Adams operation on the Grothendieck ring and use
its properties to obtain some classification results. In particular\, we s
how that the Adams operation is not the identity for any non-trivial symme
tric fusion category. We also give lower bounds for the rank of a (non-sup
er-Tannakian) symmetric fusion category in terms of the characteristic of
the field. As an application of these results\, we classify all symmetric
fusion categories of rank 3 and those of rank 4 with exactly two self-dual
simple objects.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Kovalchuk (University of Denver)
DTSTART:20231130T210000Z
DTEND:20231130T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/88
DESCRIPTION:Title: On the universal 2-parameter VOA of type $W(1^3\,2\,3^3\,4\
,\\dots)$.\nby Vladimir Kovalchuk (University of Denver) as part of Ro
cky Mountain Rep Theory Seminar\n\n\nAbstract\nW-(super)algebras have gene
rated great interest in recent years due to their numerous applications in
mathematics and physics. The process of Hamiltonian reduction in stages s
uggests that W-(super)algebras often arise as extensions of tensor product
s basic building blocks. In type A\, we expect that the building blocks ar
e the Gaiotto-Rapcak Y-algebras which arise as 1-parameter quotients of th
e universal 2-parameter VOA of type W(2\,3\,…). For types B\, C\, and D\
, the quotients of the universal 2-parameter VOA of type W(2\,4\,…) prov
ide some\, but not all\, of the necessary building blocks. In this talk we
discuss a new universal 2-parameter VOA of type W(1^3\,2\,3^3\,4\,…)\,
whose 1-parameter quotients are expected to account for the missing buildi
ng blocks for W-(super)algebras of types B\, C\, and D. There are 8 infini
te families of such quotients\, which are analogues of the Gaiotto-Rapcak
Y-algebras. We will explain the process behind the construction of this un
iversal two-parameter VOA and discuss several applications. This is a join
work with Thomas Creutzig and Andrew Linshaw.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (University of Alberta)
DTSTART:20231019T200000Z
DTEND:20231019T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/89
DESCRIPTION:Title: On unimodularity in the theory of tensor categories\nby
Harshit Yadav (University of Alberta) as part of Rocky Mountain Rep Theor
y Seminar\n\n\nAbstract\nUnimodularity a classical notion shows up in vari
ous areas like linear algebra\, lattices\, Poisson algebras\, etc. In this
talk\, we focus on unimodular Hopf algebras and unimodular tensor categor
ies. We will introduce unimodular module categories and use them to constr
uct Frobenius algebras and unimodular tensor categories. These ideas will
be illustrated with examples drawn from Hopf algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20240125T210000Z
DTEND:20240125T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/90
DESCRIPTION:Title: Reflective centers of module categories and quantum K-matri
ces\nby Chelsea Walton (Rice University) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nThis talk will be on joint work with Robert
Laugwitz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtain
ing solutions to the quantum reflection equation (qRE). To start\, given a
braided monoidal category C and C-module category M\, we introduce a vers
ion of the Drinfeld center Z(C) of C adapted for M. We refer to this categ
ory as the "reflective center" E_C(M) of M. Just like Z(C) is a canonical
braided monoidal category attached to C\, we show that E_C(M) is a canonic
al braided module category attached to M. We will also discuss the case wh
en C is the category of modules over a quasitriangular Hopf algebra H\, an
d show how quantum K-matrices arise in this setting (thus yielding solutio
ns to the qRE).\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20240201T210000Z
DTEND:20240201T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/91
DESCRIPTION:Title: A family of rational VOAs as type C cosets\nby Thomas C
reutzig (University of Alberta) as part of Rocky Mountain Rep Theory Semin
ar\n\n\nAbstract\nVladimir Kovalchuk constructed a two parameter family of
VOA that have an affine sp(2) as subalgebra and in each even positive con
formal weight a singlet and at each odd one an sp(2)-triplet. This structu
re is the third universal family of W-algebras after the W-infinity algeb
ra and its even spin analogue and quotients of one-parameter subfamilies o
f Vladimir algebras are often realized by cosets of certain W-algebras of
orthosymplectic type. Very much like in the W-infinity case and in the eve
n spin case it is expected that there are quotients that are rational and
lisse. I will explain that this expectation is indeed true and it is given
by a novel family of rational and lisse cosets. This is joint work with V
lad Kovalchuk and Andy Linshaw.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto (Tsinghua University)
DTSTART:20240208T210000Z
DTEND:20240208T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/92
DESCRIPTION:Title: Feigin-Tipunin algorithm\nby Shoma Sugimoto (Tsinghua U
niversity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe
Feigin-Tipunin algorithm is a combinatorial and iterative algorithm intro
duced by the speaker recently to construct and study log VA(-module)s that
have the q-series valued quantum invariant of 3-mfds called homological b
lock introduced by S. Gukov et al. as their characters.\nThe key point is
that at each step of the iteration\, a geometric representation theory can
be used as in the usual Feigin-Tipunin construction\, so that the represe
ntation theory of the log-VA can be studied without having to examine its
complicated algebraic structure.\nIn this talk\, after describing the spea
ker's previous work\, it will be explained that if the FT algorithm can be
applied to a certain lattice VOA-module\, we can construct a log VA-modul
e with the homological block of the (N+2)-Seifert 3-mfd as its character.\
n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20240215T210000Z
DTEND:20240215T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/93
DESCRIPTION:Title: On the structure of W-algebras in type A\nby Shigenori
Nakatsuka (University of Alberta) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nIn physics\, the webs of W-algebras are introduced as
the vertex algebras associated with the (p\, q)-webs of interfaces in the
topologically twisted N = 4 super Yang-Mills theory. This class of vertex
algebras are generalizations and extensions of the so-called vertex algebr
as at the corner\, or equivalently the affine cosets of hook-type W-algebr
as in type A. Although not proven yet in general\, it has recently been no
ticed that the webs of W-algebras actually recover the general W-algebras
in type A through the ``reduction by stages". In this talk\, I will presen
t the first non-trivial examples and some interesting phenomena found in t
he course both in rational and irrational cases. The talk is based on a jo
int work with T. Creutzig\, J. Fasquel\, and A. Linshaw.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Angiono (Universidad Nacional de Córdoba)
DTSTART:20240229T210000Z
DTEND:20240229T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/95
DESCRIPTION:Title: Contragredient Lie algebras in symmetric tensor categories<
/a>\nby Iván Angiono (Universidad Nacional de Córdoba) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nDue to a celebrated result by D
eligne\, symmetric tensor categories of moderate growth over (algebraicall
y closed) fields of characteristic zero correspond to categories of repres
entations of affine algebraic supergroups. Once we move to positive charac
teristic\, we need to take into account the Verlinde category Ver_p: Coule
mbier-Etingof-Ostrik proved recently that every such symmetric tensor cate
gory is the one of representations of an algebraic group in Ver_p\, under
some restrictions. Thus\, we wonder how to describe algebraic groups in Ve
r_p\, which in turn correspond to pairs of usual algebraic groups and Lie
algebras in Ver_p\, as described by Venkatesh.\nThis leads to the question
of how to obtain Lie algebras in Ver_p. This talk is based on joint works
with J. Plavnik and G. Sanmarco where we look for examples of these Lie a
lgebras. We prove the existence of contragredient Lie algebras in symmetri
c tensor algebras generalizing Kac-Moody construction of Lie (super) algeb
ras\, which at the same time give a description of some examples obtained
previously by 'semi simplifying' usual Lie algebras and provide new Lie al
gebras in Ver_p.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Argyres (University of Cincinnati)
DTSTART:20240307T210000Z
DTEND:20240307T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/96
DESCRIPTION:Title: The extended vertex algebra of 4-dimensional N=2 superconfo
rmal field theories\nby Philip Argyres (University of Cincinnati) as p
art of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe local operator
s of a unitary 4d N=2 SCFT in twisted Schur cohomology form a vertex opera
tor algebra (VOA). By "local operator" we mean one associated with a poin
t in space-time. We show that to every 4d N=2 SCFT there is associated a
vertex algebra containing the VOA of local twisted Schur operators as a pr
oper subalgebra. The new vertex operators of this larger vertex algebra a
re associated with certain extended operators (line\, surface\, etc.) in t
wisted Schur cohomology. Though we can compute some partial results in si
mple SCFTs\, the structure of these extended vertex algebras is still larg
ely mysterious.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Université Paris-Saclay)
DTSTART:20240314T150000Z
DTEND:20240314T160000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/97
DESCRIPTION:Title: On a series of simple affine VOAs at non-admissible level a
rising from rank one 4D SCFTs.\nby Anne Moreau (Université Paris-Sacl
ay) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIt is know
n by the works of Adamović and Perše that the affine simple vertex algeb
ras associated with G2 and B3 at level -2 can be conformally embedded into
L−2(D4). \nIn this talk\, I will present a join work with Tomoyuki Arak
awa\, Xuanzhong Dai\, Justine Fasquel\, Bohan Li on the classification to
the irreducible highest weight modules of these vertex algebras. \nI will
also describe their associated varieties: it turns out that the associated
variety of that corresponding to G2 is the orbifold of the associated var
iety of that corresponding to D4 by the symmetric group of degree 3 which
is the Dynkin diagram automorphism group of D4. This provides a new intere
sting example of associated variety satisfying a number of conjectures in
the context of orbifold vertex algebras. It is interesting to notice that
these vertex algebra also appear as the vertex operator algebras correspon
ding to rank one Argyres–Douglas theories in four dimension with flavour
symmetry G2 and B3.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rupert (University of Saskatchewan)
DTSTART:20240321T200000Z
DTEND:20240321T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/98
DESCRIPTION:Title: Constructing Quantum Vertex (Co)-Algebras associated to Yan
gians\nby Matthew Rupert (University of Saskatchewan) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nQuantum vertex algebras are de
formations of vertex algebras introduced by Etingof and Kazhdan in 1998. T
hey are families of vertex operators with relations deformed by a solution
of the quantum Yang-Baxter equation. There is also a dual notion of quant
um vertex coalgebras which deform vertex coalgebras. In this talk I will e
xplain how to construct two distinct structures of a quantum vertex coalge
bra on the Yangian associated to any simple finite-dimensional complex Lie
algebra\, and how to induce quantum vertex algebra structures on the dual
Yangian. This talk is based on ongoing work with Alex Weekes and Curtis W
endlandt.\n\nQuantum vertex algebras are deformations of vertex algebras i
ntroduced by Etingof and Kazhdan in 1998. They are families of vertex oper
ators with relations deformed by a solution of the quantum Yang-Baxter equ
ation. There is also a dual notion of quantum vertex coalgebras which defo
rm vertex coalgebras. In this talk I will explain how to construct two dis
tinct structures of a quantum vertex coalgebra on the Yangian associated t
o any simple finite-dimensional complex Lie algebra\, and how to induce qu
antum vertex algebra structures on the dual Yangian. This talk is based on
ongoing work with Alex Weekes and Curtis Wendlandt.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Raymond (Université Laval)
DTSTART:20240404T200000Z
DTEND:20240404T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/99
DESCRIPTION:Title: Zhu's algebras and related structures.\nby Christopher
Raymond (Université Laval) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nIn this talk\, I want to give a pedagogical overview of Zhu'
s algebras and then describe an alternative approach to understanding thei
r algebraic structure that has resurfaced in 3D-2D correspondences. First\
, I will introduce the approach to Zhu's algebras in physics and the resul
ting calculational framework. Following that\, I'll describe the link betw
een Zhu's algebras and Yangians and briefly discuss how these links are re
alised in physics if time permits.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Castellan (University of Glasgow)
DTSTART:20240411T200000Z
DTEND:20240411T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/100
DESCRIPTION:Title: Chiralization of star products\nby Simone Castellan (U
niversity of Glasgow) as part of Rocky Mountain Rep Theory Seminar\n\n\nAb
stract\nA star-product on a Poisson algebra $\\mathcal{A}$ is an associati
ve product * such that ${\\bf A}:= (\\mathcal{A}\, *)$ is a (formal) quant
ization of$\\mathcal{A}$. Famous examples are the Moyal-Weyl and Gutt star
product\, which quantize the symmetric algebra of a symplectic vector spa
ce and of a Lie algebra\, respectively. Suppose that we can realize $\\ma
thcal{A}$ and ${\\bf A}$ as the Zhu algebras of a Poisson vertex algebra $
\\mathcal{V}$ and of a vertex algebra ${\\bf V}$\, respectively. A chiral
ization of * is a deformation of the Poisson vertex algebra structure on $
\\mathcal{V}$\, that becomes the star-product * after applying the Zhu-fun
ctor. In this talk\, I will explain the general framework and some general
results on the problem\, and then I’ll show how to compute some explici
t formulae for the chiralization of some classical star-products\, like th
e Moyal-Weyl and Gutt star products. This talk is based on arXiv:2308.1341
2\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ridout (University of Melbourne)
DTSTART:20240328T200000Z
DTEND:20240328T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/101
DESCRIPTION:Title: Inverse quantum hamiltonian reduction for beginners.\n
by David Ridout (University of Melbourne) as part of Rocky Mountain Rep Th
eory Seminar\n\n\nAbstract\nQuantum hamiltonian reduction refers to a coll
ection of\nfunctors that map the module category of a given affine vertex
algebra\nto those of its associated W-algebras.\nSome of these functors ar
e reasonably well understood and then the\nrepresentation theory of the W-
algebra is accessible.\nBut some are not.\nInverse quantum hamiltonian red
uction is a recent discovery that there\n(sometimes) exist functors in the
opposite direction: from a given\nW-algebra module category to that of an
other W-algebra\, which may be the\naffine vertex algebra itself.\nI will
give an overview of the simplest example\, which connects the\nmodule cate
gories of the Virasoro and sl2 minimal model vertex operator\nalgebras.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mamoru Ueda (University of Alberta)
DTSTART:20240418T200000Z
DTEND:20240418T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/102
DESCRIPTION:Title: Affine Yangians and W-algebras\nby Mamoru Ueda (Univer
sity of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstrac
t\nCreutzig-Diaconescu-Ma conjectured that there exists a homomorphism fro
m the shifted affine Yangian to the universal enveloping algebra of an ite
rated W-algebra. They also conjectured that this homomorphism will induce
a resolution of the generalized AGT conjecture. In this talk\, I will expl
ain how to construct a homomorphism from the affine Yangian of type A to t
he universal enveloping algebra of a W-algebra including the non-rectangul
ar W-algebra. I expect that this homomorphism can be extended to the shift
ed affine Yangian.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University)
DTSTART:20240222T210000Z
DTEND:20240222T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/103
DESCRIPTION:Title: On the classification of rigid Frobenius algebras in Dijkg
raaf-Witten categories.\nby Ana Ros Camacho (Cardiff University) as pa
rt of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe study and class
ification of algebra objects in modular tensor categories has a strong mot
ivation from the conformal field theoretical point of view\, these objects
being related to e.g. full theories [Fuchs-Runkel-Schweigert] and extensi
ons of vertex operator algebras [Huang-Kirillov-Lepowsky\, Creutzig-Kanade
-McRae for superalgebras]. In this talk\, I will present a classification
of rigid\, Frobenius algebras in the so-called Dijkgraaf-Witten categories
\, which we achieved using Frobenius monoidal functors. Joint work with Ro
bert Laugwitz and Sam Hannah\, based on SIGMA 19 (2023)\, 075\, 42 pages.\
n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20241003T200000Z
DTEND:20241003T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/104
DESCRIPTION:Title: On the algebraic structure of $N$-Graded Vertex Algebras $
V=\\oplus_{n=0}^{\\infty}V_n$ when $V_0$ is a Gorenstein ring and Their Re
lation to vertex algebras of CFT-Type\nby Gaywalee Yamskulna (Illinois
State University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstr
act\nIn this talk\, I will explore the algebraic properties of an $\\mathb
b{N}$-graded vertex algebra associated with Gorenstein rings. Through this
framework\, I will demonstrate how these vertex algebras offer a natural
bridge to the shifted theory of vertex algebras of the CFT type.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (Virginia Commonwealth University)
DTSTART:20241205T210000Z
DTEND:20241205T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/106
DESCRIPTION:Title: Coinvariants of metaplectic representations and abelian va
rieties\nby Nicola Tarasca (Virginia Commonwealth University) as part
of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nSpaces of coinvariant
s have classically been constructed by assigning representations of affine
Lie algebras\, and more generally\, vertex operator algebras\, to pointed
algebraic curves. Removing curves out of the picture\, I will construct s
paces of coinvariants at abelian varieties with respect to the action of a
n infinite-dimensional Lie algebra. I will show how these spaces globalize
to twisted D-modules on moduli of abelian varieties\, extending the class
ical picture from moduli of curves. This is based on the preprint arXiv:23
01.13227.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (University of Alberta)
DTSTART:20241010T200000Z
DTEND:20241010T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/107
DESCRIPTION:Title: Rigidity of vertex tensor categories.\nby Harshit Yada
v (University of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n
\nAbstract\nThanks to the advances over the last decade\, we now have a re
asonable understanding of when a vertex operator algebra (VOA) admits a ve
rtex tensor category that is braided monoidal. However\, rigidity of such
categories is often quite difficult to establish and is proven by ad hoc m
ethods.\nI will present recent joint work (https://arxiv.org/abs/2409.1461
8) with Thomas Creutzig\, Robert McRae and Kenichi Shimizu where we develo
p techniques for proving rigidity of vertex tensor categories. Namely\, gi
ven an extension of VOAs V ⊂ W\, we establish results that allow us to p
rove rigidity to Rep(V) given rigidity of Rep(W) and vice versa.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Beneish (University of North Texas)
DTSTART:20241024T200000Z
DTEND:20241024T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/108
DESCRIPTION:Title: Replicable functions arising from code-lattice VOAs fixed
by automorphisms\nby Lea Beneish (University of North Texas) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWe ascertain properties
of the algebraic structures in towers of codes\, lattices\, and vertex op
erator algebras (VOAs) by studying the associated subobjects fixed by lift
s of code automorphisms. In the case of sublattices fixed by subgroups of
code automorphisms\, we identify replicable functions that occur as quotie
nts of the associated theta functions by suitable eta products. We show th
at these lattice theta quotients can produce replicable functions not asso
ciated to any individual automorphisms. Moreover\, we show that the struct
ure of the fixed subcode can induce certain replicable lattice theta quoti
ents and we provide a general code theoretic characterization of order dou
bling for lifts of code automorphisms to the lattice-VOA. Finally\, we pro
ve results on the decompositions of characters of fixed subVOAs. This talk
is based on joint work with Jennifer Berg\, Eva Goedhart\, Hussain M. Kad
hem\, Allechar Serrano López\, and Stephanie Treneer.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (University of Melbourne)
DTSTART:20241031T200000Z
DTEND:20241031T210000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/109
DESCRIPTION:Title: Partial and inverse Hamiltonian reductions for W-algebras<
/a>\nby Justine Fasquel (University of Melbourne) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nW-algebras are vertex algebras obtaine
d form quantum Hamiltonian reductions of an affine vertex algebra. These r
eductions are naturally upgraded to functors from the category of modules
over the affine vertex algebras to the category of the modules over the co
rresponding W-algebras. However\, they are difficult to control in general
. Recently\, two approaches have been developed to improve our understandi
ng of the functors. One consists in spitting the functor into small pieces
that are easier to deal with (partial reductions)\, the other aims to rev
erse the quantum Hamiltonian reduction procedure (inverse Hamiltonian redu
ctions). In this talk\, I will discuss about recent advances in these comp
lementary approaches. The talk is based on recent papers with T. Creutzig\
, A. Linshaw and S. Nakatsuka and with Z. Fehily\, E. Fursman and S. Nakat
suka.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lau (Université Laval)
DTSTART:20241212T210000Z
DTEND:20241212T220000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/110
DESCRIPTION:Title: Good filtrations\, Lie algebras representations\, and free
Jordan algebras\nby Michael Lau (Université Laval) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nAffine Lie algebras are univers
al central extensions of algebras of matrices over Laurent polynomials.
In the case of sl_2\, the ring of Laurent polynomials can be replaced with
any unital Jordan algebra. This gives a very large family of Lie algebr
as. Motivated by this connection between Lie and Jordan theory\, we desc
ribe a category of Lie algebra weight modules\, whose homological properti
es are related to the long-standing open problem of computing graded dimen
sions of free Jordan algebras. No prior knowledge of Jordan algebras wil
l be assumed. This talk is based on joint work with Olivier Mathieu.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (FAU Erlangen-Nürnberg)
DTSTART:20250327T183000Z
DTEND:20250327T193000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/111
DESCRIPTION:Title: Verlinde's formula in logarithmic CFT\nby Thomas Creut
zig (FAU Erlangen-Nürnberg) as part of Rocky Mountain Rep Theory Seminar\
n\n\nAbstract\nA while ago and with David Ridout a Verlinde formula for th
e affine VOAs of sl(2) at admissible level was conjectured. This is a VOA
whose representation category is neither finite nor semisimple. Our idea w
as to replace the Verlinde S-matrix by an S-kernel and atypical modules by
their resolutions of typical modules to get a natural Verlinde formula co
njecture. I will explain why this formalism is true.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arim Song (University of Denver)
DTSTART:20250403T183000Z
DTEND:20250403T193000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/112
DESCRIPTION:Title: Supersymmetric W-algebras vs. W-algebras\nby Arim Song
(University of Denver) as part of Rocky Mountain Rep Theory Seminar\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Caradot (Jean Monnet University)
DTSTART:20250417T183000Z
DTEND:20250417T193000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/113
DESCRIPTION:Title: $C_2$-(co)algebras and vertex (co)algebra duality\nby
Antoine Caradot (Jean Monnet University) as part of Rocky Mountain Rep The
ory Seminar\n\n\nAbstract\nIn order to investigate the representation theo
ry of a vertex algebra $V$\, a fruitful strategy is to look at the propert
ies of its $C_2$-algebra $R(V)$. This Poisson algebra reflects interesting
properties of the vertex algebra and is often easier to handle than the v
ertex algebra itself. In this talk\, we are interested in studying vertex
algebras in a closed monoidal category\, and in providing a description of
the dual versions of $V$ and $R(V)$ when those exist. We introduce vertex
algebras graded by an abelian group and explain how to "dualize" the defi
nition to obtain a graded vertex coalgebra. This leads to the notion of th
e $C_2$-coalgebra of a vertex coalgebra. We will describe its properties a
nd show that the duality vertex algebra / vertex coalgebra passes down to
a duality $C_2$-algebra / $C_2$-coalgebra. We will also explain how this d
ualities carry on to the respective modules / comodules.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villarreal (University of Colorado Boulder)
DTSTART:20250501T183000Z
DTEND:20250501T193000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/115
DESCRIPTION:Title: Intertwiners and filtrations\nby Juan Villarreal (Univ
ersity of Colorado Boulder) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nIn this talk we introduce a canonical decreasing filtration
on intertwiners of a vertex algebra. We study the associated graded spaces
. Then\, we define Poisson vertex intertwiners and Poisson intertwiners. W
e obtain relations between the associated varieties of modules of a vertex
algebra.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronika Pedić Tomić (University of Zagreb)
DTSTART:20250515T183000Z
DTEND:20250515T193000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/116
DESCRIPTION:by Veronika Pedić Tomić (University of Zagreb) as part of Ro
cky Mountain Rep Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Zhang (Tsinghua University)
DTSTART:20250522T150000Z
DTEND:20250522T160000Z
DTSTAMP:20260404T094534Z
UID:RockyRepTheory/117
DESCRIPTION:Title: The sewing-factorization theorem for $C_2$-cofinite VOAs\nby Hao Zhang (Tsinghua University) as part of Rocky Mountain Rep Theor
y Seminar\n\n\nAbstract\nIn this talk\, I will present a sewing-factorizat
ion theorem for conformal blocks in arbitrary genus associated to a (possi
bly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus
analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover\, I will
explain the relation between our result and pseudotraces\, and confirm som
e of the conjectures by Gainuditnov-Runkel. The relationship between our r
esult and coends will also be discussed. The talk is based on an ongoing p
roject (arXiv: 2305.10180\, 2411.07707\, 2503.23995) joint with Bin Gui.\n
LOCATION:https://stable.researchseminars.org/talk/RockyRepTheory/117/
END:VEVENT
END:VCALENDAR