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BEGIN:VEVENT
SUMMARY:Andrew Linshaw (Denver University)
DTSTART:20200910T190000Z
DTEND:20200910T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/1
DESCRIPTION:Title: Trialities of W-algebras\nby Andrew Linshaw (Denver University)
as part of Rocky Mountain Rep Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinwei Yang (University of Alberta)
DTSTART:20200924T190000Z
DTEND:20200924T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/2
DESCRIPTION:Title: Recent progress on tensor categories of vertex operator algebras.\nby Jinwei Yang (University of Alberta) as part of Rocky Mountain Rep T
heory Seminar\n\n\nAbstract\nTensor categories of vertex operator algebras
play an important role in the study of vertex operator algebras and confo
rmal field theories. A central problem of tensor category theory of Huang-
Lepowsky-Zhang is the existence of the vertex tensor category structure. W
e develop a few general methods to establish the existence of tensor struc
ture on module categories for vertex operator algebras\, especially for no
n-rational and non-C_2 cofinite vertex operator algebras. As applications\
, we obtain the tensor structure of affine Lie algebras at various levels\
, affine Lie superalgebra gl(1|1)\, the Virasoro algebra at all central ch
arges as well as the singlet algebras. We also study important properties
\, including constructions of projective covers\, fusion rules and the rig
idity of these tensor categories. This talk is based on joint work with T.
Creutzig\, Y.-Z. Huang\, F. Orosz Hunziker\, C. Jiang\, R. McRae and D. R
idout.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20201001T210000Z
DTEND:20201001T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/3
DESCRIPTION:Title: The singular support of the Ising model\nby Reimundo Heluani (I
MPA) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWe prove
a new Fermionic quasiparticle sum expression for the character of the Isin
g model vertex algebra\, related to the Jackson-Slater q-series identity o
f Rogers-Ramanujan type. We find\, as consequences\, an explicit monomial
basis for the Ising model\, and a description of its singular support. We
find that the ideal sheaf of the latter\, defining it as a subscheme of th
e arc space of its associated scheme\, is finitely generated as a differen
tial ideal. We prove three new q-series identities of the Rogers-Ramanujan
-Slater type associated with the three irreducible modules of the Virasoro
Lie algebra of central charge 1/2. This is joint work with G. E. Andrews
and J. van Ekeren and is based on arxiv.org:2005.10769\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro Van Ekeren (UFF)
DTSTART:20201008T190000Z
DTEND:20201008T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/4
DESCRIPTION:Title: Schellekens list\, the Leech lattice and the very strange Formula.<
/a>\nby Jethro Van Ekeren (UFF) as part of Rocky Mountain Rep Theory Semin
ar\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\, abeli
an of dimension 24 (in which case V is the Leech lattice vertex algebra) o
r else one of 69 semisimple Lie algebras first determined by Schellekens i
n 1993. Until now the only known proof of Schelekens result was a heavily
computational one involving case analysis and difficult integer programmin
g problems. Recently Moeller and Scheithauer have established a bound on t
he dimension of the weight one space of a holomorphic orbifold vertex alge
bra\, using the Deligne bound on the growth of coefficients of weight 2 cu
sp forms. In this talk I will describe how the dimension bound together wi
th Kac's very strange formula implies that all holomorphic vertex algebras
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 result i
n this way.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Genra (University of Alberta)
DTSTART:20201015T190000Z
DTEND:20201015T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/5
DESCRIPTION:Title: Screenings and applications\nby Naoki Genra (University of Albe
rta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nScreening
operators are useful tools to characterize free field realizations of ver
tex algebras\, and give new perspectives in the structures of them. We exp
lain screening operators of the beta-gamma system\, affine vertex (super)a
lgebras and W-(super)algebras. We also explain the applications to the cos
et constructions\, representations and trialities of W-algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Paris-Saclay university)
DTSTART:20201119T160000Z
DTEND:20201119T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/6
DESCRIPTION:Title: Singularities of nilpotent Slodowy slices and collapsing levels for
W-algebras.\nby Anne Moreau (Paris-Saclay university) as part of Rock
y Mountain Rep Theory Seminar\n\n\nAbstract\nTo any vertex algebra one can
attach in a canonical way a certain Poisson variety\, called the associat
ed variety. \nNilpotent Slodowy slices appear as associated varieties of a
dmissible (simple) W-algebras. They also appear as Higgs branches of the
Argyres-Douglas theories in 4d N=2 SCFT’s. These two facts are linked by
the so-called Higgs branch conjecture. In this talk I will explain how t
o exploit the geometry of nilpotent Slodowy slices to study some propertie
s of W-algebras whose motivation stems from physics. In particular I will
be interested in collapsing levels for W-algebras. This is a joint work
(still in preparation) with Tomoyuki Arakawa and Jethro van Ekeren.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Zhi Huang (Rutgers University)
DTSTART:20201105T200000Z
DTEND:20201105T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/7
DESCRIPTION:Title: Associative algebra and the representation theory of grading-restri
cted vertex algebras.\nby Yi-Zhi Huang (Rutgers University) as part of
Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will introduce an asso
ciative algebra $A^{∞}(V)$ constructed using infinite matrices with entr
ies in a grading-restricted vertex algebra V. The Zhu algebra and its gene
ralizations by Dong-Li-Mason are very special subalgebras of $A^{∞}(V)$.
I will also introduce the new subalgebras $A^{N}(V)$ of $A^{∞}$(V)\, wh
ich can be viewed as obtained from finite matrices with entries in V. I wi
ll 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://researchseminars.org/talk/RockyRepTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Sato (Academia Sinica\, Taipei\, Taiwan)
DTSTART:20201029T190000Z
DTEND:20201029T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/8
DESCRIPTION:Title: Kazama-Suzuki coset vertex superalgebras at admissible levels\n
by Ryo Sato (Academia Sinica\, Taipei\, Taiwan) as part of Rocky Mountain
Rep Theory Seminar\n\n\nAbstract\nThe Kazama-Suzuki coset vertex operator
superalgebra associated with a simple Lie algebra g and its Cartan subalge
bra h is a ``super-analog'' of the parafermion vertex operator algebra ass
ociated with g. At positive integer levels\, the coset superalgebra turns
out to be C_2-cofinite and rational by the general theory of orbifolds (Mi
yamoto) and Heisenberg cosets (Creutzig-Kanade-Linshaw-Ridout)\, respectiv
ely. On the other hand\, at Kac-Wakimoto admissible levels\, the coset sup
eralgebra is not C_2-cofinite nor rational. In this talk we discuss a rela
tionship between the category of weight modules for the admissible affine
vertex algebra associated with g and that for the corresponding Kazama-Suz
uki 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 simple weig
ht modules of the Kazama-Suzuki coset vertex superalgebra and verify the c
onjectural Verlinde formula in this case (corresponding to Creutzig-Ridout
's result in the affine side). The last part is based on the joint work wi
th Shinji Koshida.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antun Milas (SUNY-Albany)
DTSTART:20201112T200000Z
DTEND:20201112T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/9
DESCRIPTION:Title: Some q-series identities related to characters of vertex algebras\nby Antun Milas (SUNY-Albany) as part of Rocky Mountain Rep Theory Semi
nar\n\n\nAbstract\nWe prove several families of q-series identities that a
re motivated by the correspondence between 4d N = 2 superconformal field t
heories (SCFTs) and vertex operator superalgebras. We also discuss identit
ies coming from certain non-commutative q-series and quivers\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darlayne Addabbo (University of Arizona)
DTSTART:20201022T190000Z
DTEND:20201022T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/10
DESCRIPTION:Title: Higher level Zhu algebras for vertex operator algebras\nby Dar
layne Addabbo (University of Arizona) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nI will discuss the level two Zhu algebra for the H
eisenberg vertex operator algebra and techniques used in determining its s
tructure. I will also discuss more general results helpful in determining
generators and relations for higher level Zhu algebras\, and in particular
\, will provide an example to clarify the necessity of an extra condition
required in the definition of higher level Zhu algebras. (Joint with Katri
na Barron.)\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (Rutgers University)
DTSTART:20201203T200000Z
DTEND:20201203T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/11
DESCRIPTION:Title: Cohomological Field Theories from vertex operator algebras\nby
Chiara Damiolini (Rutgers University) as part of Rocky Mountain Rep Theor
y Seminar\n\n\nAbstract\nIn this talk I will discuss certain properties of
sheaves of covacua and conformal blocks attached to modules over vertex o
perator algebras. After briefly recalling how these objects are constructe
d from a geometric point of view\, I will focus on the conditions required
to construct Cohomological Field Theories from these sheaves. If time per
mits I will also discuss open problems which naturally arise. This is base
d on joint works with A. Gibney and N. Tarasca.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Tokyo)
DTSTART:20201210T200000Z
DTEND:20201210T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/12
DESCRIPTION:Title: Duality of subregular W-algebras and principal W-superalgebras of
type A and their representations in rational cases\nby Shigenori Naka
tsuka (University of Tokyo) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nRecently\, dualities among W-superalgebras and their affine
cosets conjectured by Gaiotto-Rapcak have been established in many cases b
y Creutzig-Linshaw and Creutzig-Linshaw-Kanade by using universal objects
of such algebras. Independently\, Creutzig-Genra and I proved the duality
in the case of subregular W-algebras and principal W-superalgebras of typ
e 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 coset const
ruction of N=2 superconformal algebra from the affine sl2 vertex algebra a
nd its inverse by Feigin-Semikhatov-Tipunin. In this talk\, I will explain
this reconstruction theorem and then its application to the representatio
n theory of principal W-superalgebra side in the rational cases. This talk
is based on on-going project with Thomas Creutzig\, Naoki Genra and Ryo S
ato\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drazen Adamovic (University of Zagreb)
DTSTART:20201217T200000Z
DTEND:20201217T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/13
DESCRIPTION:Title: Affine Vertex Algebras\, collapsing levels and representation theo
ry\nby Drazen Adamovic (University of Zagreb) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nWe will review recent results appearin
g in the last five years including the representation theory of affine
vertex algebras beyond the category O\, semi-simplicity of representation
s at collapsing levels and some applications to logarithmic vertex algeb
ras.\n\nPlease look in the seminar website for the link to join and passwo
rd\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto (Kyoto University)
DTSTART:20201126T000000Z
DTEND:20201126T010000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/14
DESCRIPTION:Title: On the log W-algebras\nby Shoma Sugimoto (Kyoto University) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFor a finite dim
ensional simply-laced simple Lie algebra $g$ and an\ninteger $p\\geq 2$\,
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 vertex oper
ator algebra. However\, apart from the triplet\n$W$-algebra\, not much is
known about the log $W$-algebras $W(p)_Q$.\nIn this talk\, after we constr
uct $W(p)_Q$ and their modules\n$W(p\,\\lambda)_Q$ geometrically along the
preprint of Feigin-Tipunin\, first\nwe show the simplicity\, $W_k(g)$-mod
ule structure\, and character formula\nof $W(p\,\\lambda)_Q$ when $\\sqrt{
p}\\bar\\lambda$ is in the closure of the\nfundamental alcove. In particul
ar\, for $p\\geq h-1$\, $W(p)_Q$ is simple and\ndecomposed into simple $W_
k(g)$-modules.\nSecond we give a purely $W$-algebraic algorithm to calcula
te 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://researchseminars.org/talk/RockyRepTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Kanade (University of Denver)
DTSTART:20210114T200000Z
DTEND:20210114T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/15
DESCRIPTION:Title: Principal characters of standard $A_2^{(2)}$-modules\nby Shash
ank Kanade (University of Denver) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nPrincipal characters of standard (i.e.\, highest weigh
t\, integrable) modules for affine Lie algebras have been a rich source o
f 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-series side
\, this leads to identities of Gordon-Andrews and Andrews-Bressoud. In thi
s talk\, I'll present q-series identities related to the next "simplest" a
ffine Lie algebra\, namely\, $A_2^{(2)}$. Here\, we get six families of q-
series identities confirming a conjecture of McLaughlin and Sills. The mai
n machinery used is that of Bailey pairs and Bailey lattices. This is a jo
int work with Matthew C. Russell. (N.B.: These q-series include Vir(3\,p)
minimal model characters.)\n\nThe password is the universal central extens
ion of the Witt algebra: "V*******"\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cuibo Jiang (Shangai JiaoTong University)
DTSTART:20210122T000000Z
DTEND:20210122T010000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/16
DESCRIPTION:Title: Simplicity of vacuum modules and associated varieties.\nby Cui
bo Jiang (Shangai JiaoTong University) as part of Rocky Mountain Rep Theor
y 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 as
sociated\nvariety of its unique simple quotient is equal to $g*$. We also
derive an analogous result for the quantized Drinfeld-Sokolov reduction ap
plied 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 pa
ssword is the universal central extension of the Witt algebra: "V*******"\
n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University)
DTSTART:20210128T160000Z
DTEND:20210128T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/17
DESCRIPTION:Title: Algebra objects in group-theoretical fusion categories.\nby An
a Ros Camacho (Cardiff University) as part of Rocky Mountain Rep Theory Se
minar\n\n\nAbstract\nAlgebras in tensor categories appear in several inter
esting research areas\, like e.g. VOA extensions or spin topological field
theories\, but they are usually tricky to find. In this talk\, we will ex
plain how to generalize a result by Ostrik and Natale on algebra objects i
n categories related to lattice VOAs to the case of so-called group-theore
tical fusion categories. The algebra objects we find for these also have v
ery good properties that we will describe in detail. We will assume little
knowledge of categories. Joint work with the WINART2 team Y. Morales\, M.
Mueller\, J. Plavnik\, A. Tabiri and C. Walton\n\nThe password is the uni
versal central extension of the Witt algebra V*******\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Keller (University of Arizona)
DTSTART:20210204T200000Z
DTEND:20210204T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/18
DESCRIPTION:Title: Holographic Families of VOAs\nby Christoph Keller (University
of Arizona) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nPh
ysicists are interested in holographic families of VOAs. These are\nfamili
es of VOAs that on the one hand have dim $V_n$ `small' for `small'\nn\, an
d on the other hand have some kind of large central charge limit.\nI will
discuss the motivation behind these requirements and the\nconnection to ex
tremal VOAs. I will then discuss some attempts at\nconstructing such famil
ies\, namely permutation orbifold VOAs and\nlattice orbifold VOAs. This ta
lk is based on joint work with Thomas\nGemuenden.\n\nLink to join and pass
word can be found in the seminar's webpage.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Arakawa (Kyoto University)
DTSTART:20210211T230000Z
DTEND:20210212T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/19
DESCRIPTION:Title: 4D/2D duality and VOA theory\nby Tomoyuki Arakawa (Kyoto Unive
rsity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe 4D/
2D duality discovered by Beem et at in physics gives a remarkable connecti
on between 4D N=2 SCFTs and VOAs. \nIt gives not only many new interesting
examples of VOAs but also new perspectives to known VOAs\, such as Frenke
l-Styrkas’s modified regular representation of the Virasoro algebra and
Adamovic’s realization of N=4 small superconformal algebra.\nIn this tal
k I will discuss the 4D/2D duality from the VOA perspective\, starting fro
m these examples.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20210218T200000Z
DTEND:20210218T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/20
DESCRIPTION:Title: Conjugation and positivity of conformal blocks\nby Bin Gui (Ru
tgers University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nGiven a strongly rational unitary VOA $V$\, a Hermitian form on the sp
ace of its intertwining operators was introduced recently to understand th
e unitarity of the representation modular tensor category $Rep(V)$. It was
actually shown that\, along with some natural assumptions\, if this Hermi
tian form (which is necessarily non-degenerate) is positive\, namely\, if
it is an inner product\, then $Rep(V)$ is unitary. The crucial step of thi
s story is to prove the positivity of the Hermitian form. In this talk\, I
give a geometric interpretation of this positivity problem using the idea
(self)conjugate Riemann surfaces and (self)conjugate conformal blocks.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McRae (Tsinghua University)
DTSTART:20210226T000000Z
DTEND:20210226T010000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/21
DESCRIPTION:Title: On semisimplicity of modules for C_2-cofinite vertex operator alge
bras\nby Robert McRae (Tsinghua University) as part of Rocky Mountain
Rep Theory Seminar\n\n\nAbstract\nI will discuss work in progress related
to proving semisimplicity of the module category for a suitable positive-e
nergy\, 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 al
gebra of V is a semisimple algebra. The idea for proving this is to show t
hat the braided tensor category of V-modules is rigid with a non-degenerat
e braiding\, using tensor-categorical methods combined with the modular in
variance methods used by Huang to prove the Verlinde conjecture for ration
al vertex operator algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Wood (Cardiff University)
DTSTART:20210304T160000Z
DTEND:20210304T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/22
DESCRIPTION:Title: There is always more that can be learnt from the free boson\nb
y Simon Wood (Cardiff University) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nVertex operator algebras exhibit a feature much like L
ie\nalgebras in that they admit too many modules for the category of all\n
their modules to exhibit nice structure. However\, good choices of module\
ncategory can lead to categories with very rich structure. For example\nth
e categories of admissible modules over rational vertex operator\nalgebras
are modular tensor categories\, as proved by Huang. I will\npresent some
recent work on making the study of vertex operator algebra\nmodule categor
ies more tractable by replacing them by Hopf algebras\, an\narguably simpl
er algebraic structure. The guiding example will be the\nfree boson.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mamoru Ueda (Kyoto University)
DTSTART:20210326T000000Z
DTEND:20210326T010000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/23
DESCRIPTION:Title: Affine super Yangians and rectangular W-superalgebras.\nby Mam
oru Ueda (Kyoto University) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nMotivated by the generalized AGT conjecture in this talk I w
ill construct surjective homomorphisms from the affine super Yangians to t
he universal enveloping algebras of rectangular $W$-superalgebras. This re
sult is a super affine analogue of a result of Ragoucy and Sorba\, which g
ave surjective homomorphisms from finite Yangians of type $A$ to rectangul
ar finite $W$-algebras of type $A$.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20210429T190000Z
DTEND:20210429T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/24
DESCRIPTION:Title: A remark on $\\mathbb{N}$-graded vertex algebras\nby Gaywalee
Yamskulna (Illinois State University) as part of Rocky Mountain Rep The
ory Seminar\n\n\nAbstract\nIn this talk\, I will discuss an impact of Leib
niz algebras on the algebraic structure of $\\mathbb{N}$-graded vertex alg
ebras. Along the way\, I will provide easy ways to characterize several ty
pes of $\\mathbb{N}$-graded vertex algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Lu (University of Denver)
DTSTART:20210311T200000Z
DTEND:20210311T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/25
DESCRIPTION:Title: Skew representations of super Yangian.\nby Kang Lu (University
of Denver) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nSk
ew representations (corresponding to skew Young diagrams) of Yangian and q
uantum affine algebra of type A were introduced by Cherednik and extensive
ly studied by Nazarov and Tarasov. In this talk\, we will discuss some kno
wn results about skew representations of super Yangian of type A such as J
acobi-Trudi identities\, Drinfeld functor\, irreducibility conditions of t
ensor products\, and extended T-systems. We also discuss some open problem
s related to tame modules of super Yangian. Some essential differences com
paring to the even case will be discussed as well.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Möller (Kyoto University)
DTSTART:20210401T230000Z
DTEND:20210402T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/26
DESCRIPTION:Title: Classification of Holomorphic VOAs in Central Charge 24\nby Sv
en Möller (Kyoto University) as part of Rocky Mountain Rep Theory Seminar
\n\n\nAbstract\nI shall summarise recent results (and ongoing work) regard
ing the classification of strongly rational\, holomorphic VOAs (or CFTs) o
f central charge 24 (together with Jethro van Ekeren\, Gerald Höhn\, Chin
g Hung Lam\, Nils Scheithauer and Hiroki Shimakura). First\, we show that
there is an abstract bijection (without classifying either side) between t
hese VOAs and the generalised deep holes of the Leech lattice VOA. The pro
of uses a dimension formula obtained by pairing the VOA character with a v
ector-valued Eisenstein series and an averaged version of Kac's Lie theore
tic "very strange formula". This is a quantum analogue of the beautiful re
sult by Conway\, Parker and Sloane (and Borcherds) that the deep holes of
the Leech lattice are in natural bijection with the Niemeier lattices. The
n\, we explain how this can be used to classify the (exactly 70) strongly
rational\, holomorphic VOAs of central charge 24 with non-zero weight-one
space. (The case of zero weight-one space\, which includes the Moonshine m
odule\, is more difficult and still open.)\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Tsuchioka (Tokyo Institute of Technology)
DTSTART:20210408T230000Z
DTEND:20210409T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/27
DESCRIPTION:Title: A proof of conjectured partition identities of Nandi.\nby Shun
suke Tsuchioka (Tokyo Institute of Technology) as part of Rocky Mountain R
ep Theory Seminar\n\n\nAbstract\nWe generalize the theory of linked partit
ion ideals due to Andrews using finite automata in formal language theory
and apply it to prove three Rogers-Ramanujan type identities of modulo 14
that were posed by Nandi through vertex operator theoretic construction of
the level 4 standard modules of the affine Lie algebra $A^{(2)}_{2}$. Thi
s is a joint work with Motoki Takigiku.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Kontrec (University of Zagreb)
DTSTART:20210415T160000Z
DTEND:20210415T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/28
DESCRIPTION:Title: Bershadsky-Polyakov vertex algebras at positive integer levels and
duality\nby Ana Kontrec (University of Zagreb) as part of Rocky Mount
ain Rep Theory Seminar\n\n\nAbstract\nOne of the simplest examples of $\\m
athcal{W}$-algebras is the Bershadsky-Polyakov vertex algebra $\\mathcal{W
}^k(\\mathfrak{g}\, f_{min})$\, associated to $\\mathfrak{g} = sl(3)$ and
the minimal nilpotent element $f_{min}$.\nWe study the simple Bershadsky
-Polyakov algebra $\\mathcal W_k$ at positive integer levels and obtain a
classification of their irreducible modules.\nIn the case $k=1$\, we sho
w 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://researchseminars.org/talk/RockyRepTheory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Qi (University of Manitoba)
DTSTART:20210422T190000Z
DTEND:20210422T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/29
DESCRIPTION:Title: Bosonic and fermionic constructions of meromorphic open-string ver
tex algebras.\nby Fei Qi (University of Manitoba) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nMeromorphic open-string vertex alg
ebras (abbre. MOSVAs) is a noncommutative generalization of the usual vert
ex algebra defined by Yi-Zhi Huang in 2012. Vertex operators still satisfy
the associativity but do not necessarily satisfy commutativity. In this t
alk I will illustrate nontrivial examples of MOSVAs and modules we know so
far\, including the universal bosonic construction\, the universal fermio
nic construction\, and the example from the geometry over constant curvatu
re manifolds.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ridout (University of Melbourne)
DTSTART:20210506T220000Z
DTEND:20210506T230000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/30
DESCRIPTION:Title: Weight modules for $\\mathfrak{sl}_3$ minimal models\nby David
Ridout (University of Melbourne) as part of Rocky Mountain Rep Theory Sem
inar\n\n\nAbstract\nMinimal models are simple vertex operator algebras (VO
As) for\nwhich the structure of the associated universal VOA is somehow ma
ximally\ndegenerate. Some minimal models are rational and $C_2$-cofinite\
, 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 minima
l\nmodels associated with $\\mathfrak{sl}_3$. The novelty here is the fac
t\nthat the rank of the associated algebra is not $1$.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cris Negron (University of North Carolina)
DTSTART:20210513T190000Z
DTEND:20210513T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/31
DESCRIPTION:Title: Quantum SL(2) and logarithmic vertex operator algebras at (p\,1)-c
entral charge\nby Cris Negron (University of North Carolina) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will discuss joint wo
rk with Terry Gannon in which we provide a ribbon tensor equivalence betwe
en the representation category of small quantum SL(2)\, at parameter q=exp
(pi i/p)\, and the representation category of the triplet vertex operator
algebra at integral parameter p>1. We provide similar quantum group equiva
lences for representation categories associated to the Virasoro\, and sing
let vertex operator algebras at central charge c=1-6(p-1)^2/p.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ZacharyFehily (University of Melbourne)
DTSTART:20210520T220000Z
DTEND:20210520T230000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/32
DESCRIPTION:Title: Subregular W-algebras\nby ZacharyFehily (University of Melbour
ne) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nWhile regu
lar W-algebras have enjoyed many years of study and attention\, recent dev
elopments in physics have the less popular subregular W-algebras playing a
n important role. Moreover\, these subregular W-algebras appear at levels
where the corresponding conformal field theory is likely non-rational. Thi
s necessitates a deeper understanding of the representation theory of such
vertex operator algebras at non-rational levels. In type $A_n$\, only the
n=1 ($sl_2$) and n=2 (Bershadsky-Polyakov algebra) cases are particularly
well-understood. In both cases an 'inverse reduction-by-stages' approach\
, first described for sl_2 in vertex operator algebra language by D. Adamo
vic\, relates much of the representation theory to that of the correspondi
ng regular W-algebra. In this talk\, I will describe how to generalise thi
s approach to all type A_n subregular W-algebras using screening operators
developed by N. Genra.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20210930T190000Z
DTEND:20210930T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/33
DESCRIPTION:Title: The category O of affine osp(1|2n) at admissible level\nby Tho
mas Creutzig (University of Alberta) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nosp(1|2n) behaves in many respects similar to finit
e 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 ca
tegory O at admissible level.\nI will explain how to construct the univers
al affine vertex superalgebra of osp(1|2n) by translating the equivariant
CDO of sp(2n). This construction gives valuable information about the simp
le affine vertex superalgebra at admissible level\, in particular we 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 an
d password to join the talk.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Yale University)
DTSTART:20211007T190000Z
DTEND:20211007T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/34
DESCRIPTION:Title: The Drinfeld--Sokolov reduction of admissible representations of a
ffine Lie algebras\nby Gurbir Dhillon (Yale University) as part of Roc
ky Mountain Rep Theory Seminar\n\n\nAbstract\nFix an affine Lie algebra ̂
gκ with associated principal affine W-algebra Wκ. A basic conjecture of
Frenkel–Kac–Wakimoto asserts that Drinfeld–Sokolov reduction sends a
dmissible ̂gκ-modules to zero or cohomological shifts of minimal series
Wκ-modules. In recent work\, we proved this conjecture and a natural gene
ralization to the spectrally flowed Drinfeld–Sokolov reduction functors
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 his
tory and statement of the conjecture\, discuss the form the answer takes\,
and highlight a few ingredients of its proof which may be of use elsewher
e.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rupert (Utah State University)
DTSTART:20211014T150000Z
DTEND:20211014T160000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/35
DESCRIPTION:Title: Uprolling Unrolled Quantum Groups\nby Matthew Rupert (Utah Sta
te University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\
nI will discuss joint work with Thomas Creutzig where we construct familie
s of commutative (super) algebra objects in the category of weight modules
for unrolled restricted quantum groups of a simple Lie algebra at roots o
f unity. We study their categories of local modules and derive conditions
for these categories being finite\, non-degenerate\, and ribbon. Based on
motivation from the rank one examples\, we expect that these categories sh
ould be equivalent to module categories for vertex operator algebras\, and
we present conjectures for the structure of module categories for the hig
her rank Triplet and Bp vertex operator algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronika Pedić (University of Zagreb)
DTSTART:20211021T150000Z
DTEND:20211021T160000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/36
DESCRIPTION:Title: Representation theory and fusion rules for Weyl vertex algebras an
d beyond\nby Veronika Pedić (University of Zagreb) as part of Rocky M
ountain Rep Theory Seminar\n\n\nAbstract\nWeyl vertex algebra is an intere
sting example of a non-rational and non C2-cofinite vertex algebra. We des
cribe fusion rules in the category of Weyl vertex algebra weight modules a
nd explicitly construct the intertwining operators appearing in these equa
tions. We describe applications of our methods to other VOAs\, in particul
ar the M(p) singlet. We present a result which relates irreducible weight
modules for the Weyl vertex algebra to the irreducible modules of the affi
ne Lie superalgebra gl(1|1). This part of the talk is based on joint work
with D. Adamović.\n\nIn the second part we present results of a joint pro
ject with D. Addabbo\, K. Barron\, K. Batistelli\, F. Orosz Hunziker and G
. Yamskulna. Among other things we calculate the first Zhu algebra of the
Weyl vertex algebra.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villareal (North Carolina State)
DTSTART:20211028T150000Z
DTEND:20211028T160000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/37
DESCRIPTION:Title: Logarithmic vertex algebras.\nby Juan Villareal (North Carolin
a State) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIn th
is talk\, I want to explain a generalization of vertex algebras called log
arithmic vertex algebras\, which is a vertex algebra with logarithmic sing
ularities in the operator product expansion of quantum fields. In this wor
k\, we develop a framework that allows many results about vertex algebras
to be extended to logarithmic vertex algebras. Finally\, I will mention on
e example which is motivated by physics\, this example exhibits some unex
pected new features that are peculiar to the logarithmic case. This is joi
nt work with Bojko Bakalov.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathrin Bringmann (University of Cologne)
DTSTART:20211111T160000Z
DTEND:20211111T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/39
DESCRIPTION:Title: Modularity of class number generating function\nby Kathrin Bri
ngmann (University of Cologne) as part of Rocky Mountain Rep Theory Semina
r\n\n\nAbstract\nI my talk I will speak about various results related to t
he modularity of the class number generating function and some application
s.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20211123T200000Z
DTEND:20211123T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/40
DESCRIPTION:Title: Borcherds identity in logarithmic coordinates.\nby Reimundo He
luani (IMPA) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nT
he exponential change of coordinates z = exp(t) induces an automorphism on
every conformal vertex algebra. Vertex operators in these new coordinates
play an essential role in Zhu's proof of modularity of conformal blocks.
In this talk we'll take a look at a version of Borcherds formula for these
operators. Unlike the usual formula involving Laurent expansions of ratio
nal functions\, this formula uses Fourier expansion and explicit domains o
f convergence.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Wang (Xiamen University)
DTSTART:20211202T230000Z
DTEND:20211203T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/41
DESCRIPTION:Title: Trigonometric Lie algebras\, affine Lie algebras\, and vertex alge
bras\nby Qing Wang (Xiamen University) as part of Rocky Mountain Rep T
heory Seminar\n\n\nAbstract\nWe present natural connections among trigonom
etric Lie algebras\, affine Lie algebras\, and vertex algebras. More speci
fically\, we prove that restricted modules for trigonometric Lie algebras
naturally correspond to equivariant quasi modules for the affine vertex al
gebra. Furthermore\, we prove that every quasi-finite unitary highest weig
ht irreducible module of type A trigonometric Lie algebra gives rise 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://researchseminars.org/talk/RockyRepTheory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niklas Garner (University of Washington)
DTSTART:20211209T200000Z
DTEND:20211209T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/42
DESCRIPTION:Title: Non-semisimple 3d TQFTs for the Feigen-Tipunin algebras and quantu
m groups\nby Niklas Garner (University of Washington) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nI will describe a class of phy
sical 3d QFTs that conjecturally serve as non-semisimple\, derived general
izations of Chern-Simons theory with compact gauge group SU(n). These 3d Q
FTs admit two different boundary conditions furnishing VOAs\, one of which
being a Feigen-Tipunin algebra\, and we conjecture a novel logarithmic le
vel-rank-like duality that relates them. Modules for the Feigen-Tipunin al
gebra are expected to be related to modules for the quantum group via a lo
garithmic Kazhdan-Lusztig-like correspondence\, thereby connecting our phy
sical QFT to mathematical TQFTs built from modules of the quantum group. O
ur proposed physical QFT offers a new perspective on these VOAs and mathem
atical TQFTs and allows for the use of techniques in supersymmetric QFT to
analyze their properties. This is based on joint work with T. Creutzig\,
T. Dimofte\, and N. Geer.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haisheng Li (Rutgers University)
DTSTART:20211216T200000Z
DTEND:20211216T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/43
DESCRIPTION:Title: Deforming vertex algebras by module and comodule actions of vertex
bialgebras.\nby Haisheng Li (Rutgers University) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nPreviously\, we studied a notion o
f vertex bialgebra and a notion of module vertex algebra for a vertex bial
gebra\, and gave a smash product construction of nonlocal vertex algebras
. Here\, we introduce a notion of right comodule vertex algebra for a ver
tex 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 deformations
of the lattice vertex algebras. This is based on a joint work with Naihua
n Jing\, Fei Kong\, and Shaobin Tan.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Linshaw (University of Denver)
DTSTART:20220127T200000Z
DTEND:20220127T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/44
DESCRIPTION:Title: Vertex algebras and arc spaces\nby Andrew Linshaw (University
of Denver) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nVer
tex algebras are certain noncommutative\, nonassociative algebraic structu
res that arose out of physics in the 1980s. They were axiomatized by Borch
erds in his proof of the Moonshine Conjecture\, and in the last 35 years t
hey have become important in a diverse range of subjects. A fruitful persp
ective is that many vertex algebras can be viewed as quantizations of coor
dinate rings of arc spaces. In this talk\, I will give an introduction to
vertex algebras\, arc spaces\, and their interconnections. This is based o
n joint work with Bailin Song.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirko Primc (University of Zagreb)
DTSTART:20220203T200000Z
DTEND:20220203T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/45
DESCRIPTION:Title: New partition identities from $C_l^{(1)}$-modules\nby Mirko Pr
imc (University of Zagreb) as part of Rocky Mountain Rep Theory Seminar\n\
n\nAbstract\nIn joint work with S. Capparelli\, A. Meurman\, and A. Primc
(arXiv:2106.06262) we conjecture combinatorial Rogers-Ramanujan type ident
ities for colored partitions\, related to standard representations of symp
lectic affine Lie algebras. The conjecture is stated in purely combinatori
al terms\, and it is supported by numerical evidence. In my talk\, I will
state the conjecture and then explain the representation theory background
.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schweigert (University of Hamburg)
DTSTART:20220210T200000Z
DTEND:20220210T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/46
DESCRIPTION:Title: Rigidity in conformal field theory and vertex algebras beyond rigi
dity\nby Christoph Schweigert (University of Hamburg) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nRigidity of tensor categories
plays an important role\, in quantum topology\nand in the representation t
heory of many algebraic objects\, in particular of\nHopf algebras and vert
ex algebras. In this talk\, we discuss inherent restrictions of the notion
of rigidity. We then explain why rigidity is so useful in the study of bu
lk fields of conformal field theories.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uhi Rinn Suh (Seoul National University)
DTSTART:20220224T230000Z
DTEND:20220225T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/47
DESCRIPTION:Title: N=1 Supersymmetric (SUSY) W-algebras\nby Uhi Rinn Suh (Seoul N
ational University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbst
ract\nAs a SUSY analogue of vertex algebras\, Heluani and Kac introduced S
USY vertex algebras. On the other hand\, in physics literature\, SUSY coun
terpart of Toda theory has been studied. In particular\, Madsen and Ragouc
y described an N=1 SUSY analogue of the quantum Drinfeld-Sokolov reduction
. In this talk\, I will explain the SUSY Hamiltonian reduction process in
terms of supersymmetric vertex algebras. This is based on the joint work w
ith Molev and Ragoucy.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Yu (Xiamen University)
DTSTART:20220303T230000Z
DTEND:20220304T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/48
DESCRIPTION:Title: Fusion products of twisted modules in permutation orbifolds\nb
y Nina Yu (Xiamen University) as part of Rocky Mountain Rep Theory Seminar
\n\n\nAbstract\nThe orbifold theory studies a vertex operator algebra unde
r the action of a finite group. The goal is to understand the representati
on theory for the fixed point vertex operator subalgebra. The main feature
in orbifold theory is the appearance of the twisted modules. The permutat
ion orbifolds study the action of the symmetric group of degree k on the k
-tensor product of a vertex operator algebra. In [Dong-Li-Xu-Yu\; 2019]\,
we determined the fusion product of any untwisted module with any twisted
module for permutation orbifolds. In this talk I will talk about fusion pr
oducts of twisted modules for permutation orbifolds. This is a joint work
with C. Dong and F. Xu.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Williams (University of Edinburgh)
DTSTART:20220310T200000Z
DTEND:20220310T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/49
DESCRIPTION:Title: Exceptional super Lie algebras and their representations from M-th
eory\nby Brian Williams (University of Edinburgh) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nRecently\, a program for mathemati
cally realizing a ubiquitous relationship in physics called holography in
terms of Koszul duality has been proposed. In this talk I will explain how
three exceptional super Lie algebras appear in a (twisted) version of thi
s correspondence in the context of M-theory. One of these Lie algebras\, w
hich Kac calls E(3|6)\, plays a particular important role related to the A
GT correspondence and we will argue how its representation theory sheds li
ght on the holographic story and beyond.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20220818T190000Z
DTEND:20220818T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/50
DESCRIPTION:Title: Factorization resolutions\nby Angela Gibney (University of Pen
nsylvania) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIn
recent work with Damiolini and Tarasca\, extending previous results\, we h
ave shown that simple modules over a vertex operator algebra V of CFT-type
determine sheaves of coinvariants\, and dual sheaves of conformal blocks
on certain moduli spaces of stable pointed curves. If V is strongly ration
al\, these are vector bundles\, with Chern classes in the tautological rin
g. The factorization formula\, which relies on rationality of V\, played a
crucial role in proving these results. In this talk I will discuss recent
work with Damiolini and Krashen\, where we introduce factorization presen
tations\, applicable to C_1-cofinite V. As I'll explain\, this new perspec
tive simplifies the original proof of factorization and gives evidence tha
t modules over strongly finite VOAs may determine vector bundles.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20220331T190000Z
DTEND:20220331T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/51
DESCRIPTION:Title: On the cohomology of vertex algebras and Poisson vertex algebras.<
/a>\nby Bojko Bakalov (North Carolina State University) as part of Rocky M
ountain Rep Theory Seminar\n\n\nAbstract\nFollowing Beilinson and Drinfeld
\, we describe vertex algebras as Lie\nalgebras for a certain operad of $n
$-ary chiral operations. This\nallows us to introduce the cohomology of a
vertex algebra $V$ as a Lie\nalgebra cohomology. When $V$ is equipped with
a good filtration\, its\nassociated graded is a Poisson vertex algebra. W
e relate the\ncohomology of $V$ to the variational Poisson cohomology stud
ied\npreviously by De Sole and Kac. This talk is based on joint work with\
nAlberto De Sole\, Reimundo Heluani\, Victor Kac\, and Veronica Vignoli.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenjun Niu (University of California\, Davis)
DTSTART:20220407T190000Z
DTEND:20220407T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/52
DESCRIPTION:Title: Beta-gamma VOA and 3d mirror symmetry\nby Wenjun Niu (Universi
ty of California\, Davis) as part of Rocky Mountain Rep Theory Seminar\n\n
\nAbstract\nIn this talk\, I will explain our study of the category of mod
ules of the beta-gamma VOA from the point of view of 3d mirror symmetry. I
will introduce a category of modules of the beta-gamma VOA\, containing t
he category studied by Ridout-Wood and Allen-Wood. We propose that this ca
tegory is the category of line operators for a twisted 3d N=4 theory. I wi
ll explain that using a relation of beta-gamma and affine Lie superalgebra
of \\mathfrak{gl}(1|1)\, we can show that this category has the structure
of a braided tensor category. This relation is an example of 3d abelian m
irror symmetry. If time permits\, I will talk about a relation to matrix f
actorizations. This is based on joint work with Andrew Ballin.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Rozhkovskaya (Kansas State University)
DTSTART:20220414T190000Z
DTEND:20220414T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/53
DESCRIPTION:Title: Transformations of Vertex operators of Hall-Littlewood Polynomials
\nby Natalia Rozhkovskaya (Kansas State University) as part of Rocky M
ountain Rep Theory Seminar\n\n\nAbstract\nWe study the effect of linear tr
ansformations on quantum fields\, with the main example of application to
vertex operator presentations of Hall-Littlewood polynomials. The construc
tion is illustrated with examples that include certain versions of m
ultiparameter symmetric functions\, dual Grothendieck polynomials\, defor
mations by cyclotomic polynomials\, and some other variations of Schur sym
metric functions that exist in the literature. Linear transformations of q
uantum fields effectively describe preservation of commutation relations
of operators\, stability of symmetric polynomials\, polynomial tau functio
ns of the KP and the BKP hierarchy.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chongying Dong (University of California Santa Cruz)
DTSTART:20220428T220000Z
DTEND:20220428T230000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/54
DESCRIPTION:Title: Pointed modular tensor category\nby Chongying Dong (University
of California Santa Cruz) as part of Rocky Mountain Rep Theory Seminar\n\
n\nAbstract\nA modular tensor category is pointed if every simple object i
s a simple current. We show that any pointed modular tensor category is e
quivalent to the module category of a lattice vertex operator algebra. Mor
eover\, if the pointed modular tensor category C is the module category of
a twisted Drinfeld double associated to a finite abelian group G and a 3-
cocycle with coefficients in U(1)\, then there exists a self dual positi
ve definite even lattice L such that G can be realized an automorphism gro
up of lattice vertex operator algebra $V_L\,$ $V_L^G$ is also a lattice v
ertex 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://researchseminars.org/talk/RockyRepTheory/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Linshaw (University of Denver)
DTSTART:20220505T190000Z
DTEND:20220505T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/55
DESCRIPTION:Title: Global sections of the chiral de Rham complex for Calabi-Yau and h
yperkahler manifolds.\nby Andrew Linshaw (University of Denver) as par
t of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFor any complex mani
fold M\, the chiral de Rham complex is a sheaf of vertex algebras on M tha
t was introduced in 1998 by Malikov\, Schechtman\, and Vaintrob. It is N-g
raded by conformal weight\, and the weight zero piece coincides with the o
rdinary de Rham sheaf. When M is a Calabi-Yau manifold with holonomy group
SU(d)\, it was shown by Ekstrand\, Heluani\, Kallen and Zabzine that the
algebra of global sections $\\Omega^{ch}(M)$ contains a certain vertex alg
ebra defined by Odake which is an extension of the N=2 superconformal alge
bra. When M is a hyperkahler manifold\, it was shown by Ben-Zvi\, Heluani\
, and Szczesny that $\\Omega^{ch}(M)$ contains the small N=4 superconforma
l algebra. In this talk\, we will show that in both cases\, these subalgeb
ras are actually the full algebras of global sections. In an earlier work\
, Bailin Song has shown that the global section algebra can be identified
with a certain subalgebra of a free field algebra which is invariant under
the action of an infinite-dimensional Lie algebra of Cartan type. They ke
y observation is that this algebra can be described using the arc space an
alogue of Weyl's first and second fundamental theorems of invariant theory
for the special linear and symplectic groups. This is a joint work with B
ailin Song.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20220901T190000Z
DTEND:20220901T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/56
DESCRIPTION:Title: Vertex tensor categories and C_1 cofiniteness\nby Thomas Creut
zig (University of Alberta) as part of Rocky Mountain Rep Theory Seminar\n
\n\nAbstract\nA major challenge in VOA theory is to show that a given cate
gory of modules admits a vertex tensor category structure. It turns out th
at C_1-cofiniteness plus a few additional conditions is sufficient to ensu
re the existence of vertex tensor category. I will illustrate this in exam
ples and explain its use beyond C_1-cofinite modules.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20220908T190000Z
DTEND:20220908T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/57
DESCRIPTION:Title: Frobenius exact symmetric tensor categories.\nby Victor Ostrik
(University of Oregon) as part of Rocky Mountain Rep Theory Seminar\n\n\n
Abstract\nI will report on a joint work with K.Coulembier and P.Etingof. W
e give a characterization of symmetric tensor categories over fields of po
sitive characteristic which admit an exact tensor functor to the Verlinde
category\; in particular we give a characterization of Tannakian categorie
s. A crucial ingredient of this characterization is exactness of the Frobe
nius twist functor which mimics the Frobenius twist for representations of
algebraic groups. We will also discuss some applications to modular repre
sentation theory.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (Indiana University-Purdue University Indianapolis)
DTSTART:20221013T190000Z
DTEND:20221013T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/58
DESCRIPTION:Title: Extensions of deformed W-algebras.\nby Evgeny Mukhin (Indiana
University-Purdue University Indianapolis) as part of Rocky Mountain Rep T
heory Seminar\n\n\nAbstract\nI will discuss the combinatorics of qq-charac
ters as a tool for constructing deformed W-algebras and their extensions.
\nThis is a report on a joint work in progress with B. Feigin and M. Jimb
o.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Sadowski (Ursinus College)
DTSTART:20221020T190000Z
DTEND:20221020T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/59
DESCRIPTION:Title: Weight-one elements of vertex operator algebras and automorphisms
of categories of generalized twisted modules\nby Chris Sadowski (Ursin
us College) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nGi
ven a weight-one element u of a vertex operator algebra V \, we construct
an automorphism of the category of generalized g-twisted modules for autom
orphisms of g fixing u. We apply these results to the case that V is an af
fine vertex algebra to obtain explicit results on these automorphisms of c
ategories. In particular\, we give explicit constructions of certain gener
alized twisted modules from generalized twisted modules associated to diag
ram automorphisms of finite-dimensional simple Lie algebras and generalize
d (untwisted) modules. This talk is based on a joint work with Yi-Zhi Huan
g.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Genra (Kavli IMPU)
DTSTART:20220922T230000Z
DTEND:20220923T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/60
DESCRIPTION:Title: Coset constructions of W-superalgebras of type B\nby Naoki Gen
ra (Kavli IMPU) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract
\nWe talk about coset constructions of principal W-superalgebras of osp(1|
2n)\, which are analogs of coset constructions of principal W-algebras of
type ADE by Arakawa-Creutzig-Linshaw. The cosets are useful not only to st
udy the category of modules at non-degenerate admissible levels\, but also
to prove the existence of embeddings of the affine vertex superalgebras o
f osp(1|2n) into the equivariant W-algebras of sp(2n) times 2n+1 free ferm
ions. This leads to the rigidity of the category O of affine sp(2n) at adm
issible levels as a corollary. This is joint work with Thomas Creutzig and
Andrew Linshaw.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University)
DTSTART:20220825T190000Z
DTEND:20220825T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/61
DESCRIPTION:Title: Zesting link invariants\nby Julia Plavnik (Indiana University)
as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIt was conjec
tured that modular categories were determined by its modular data (S- and
T-matrices). In 2017\, Mignard and Schauenburg presented a family of count
erexamples to this conjecture\, which led to the study of link invariants
beyond modular data to distinguish these categories. In this talk we will
discuss ribbon zesting\, which is a construction of modular categories\, a
nd how it is related to the family of Mignard-Schauenburg counterexamples.
To better understand this relation\, we look into how zesting affects lin
k invariants such as the W-matrix and the B-tensor. This talk is based on
joint work with Colleen Delaney and Sung Kim (https://arxiv.org/abs/2107.1
1374).\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20220915T190000Z
DTEND:20220915T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/62
DESCRIPTION:Title: Duality of hook-type W-superalgebras via convolution operations\nby Shigenori Nakatsuka (University of Alberta) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nHook type W-superalgebras are W-supera
lgebras whose affine cosets appear at junctions of supersymmetric interfac
es in N = 4 Super Yang Mills gauge theory. Their affine cosets enjoy a Fei
gin-Frenkel type duality as proven by Creutzig and Linshaw by the uniquene
ss property of these algebras. I will explain how this duality is enhanced
to a reconstruction theorem for the W-superalgebra themselves via convolu
tion operation with ``shifted" chiral differential operators. If time perm
its\, I will talk about its representation theoretic applications and modu
le characters. The talk is based on my joint work with Thomas Creutzig\, A
ndrew Linshaw and Ryo Sato.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinwei Yang (Shanghai Jiao Tong University)
DTSTART:20220929T230000Z
DTEND:20220930T000000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/63
DESCRIPTION:Title: Ribbon categories for the singlet algebras and their extensions.\nby Jinwei Yang (Shanghai Jiao Tong University) as part of Rocky Mounta
in Rep Theory Seminar\n\n\nAbstract\nIn this talk\, we summarize our recen
t work on the tensor categories for the singlet algebras\, including the t
ensor structure on the category of the atypical modules\, as well as on th
e full category of C_1-cofinite modules. We will also apply these results
to study representation theory of vertex algebras that are extensions of t
he singlet algebras\, especially the B_p-algebra. This talk is based on a
series of joint work with T. Creutzig and R. McRae.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McRae (YMSC\, Tsinghua University)
DTSTART:20221111T000000Z
DTEND:20221111T010000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/64
DESCRIPTION:Title: Non-rigid Kazhdan-Lusztig tensor categories for affine sl_2 at adm
issible levels and quantum groups.\nby Robert McRae (YMSC\, Tsinghua U
niversity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI w
ill present upcoming joint work with Jinwei Yang on the non-semisimple Kaz
hdan-Lusztig categories KL^k(sl_2) of affine sl_2 at admissible levels 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 level k wh
ose composition factors are irreducible highest-weight modules whose highe
st weights are dominant integral for the finite-dimensional subalgebra sl_
2. We show that KL^k(sl_2) admits the\nvertex algebraic braided tensor cat
egory structure of Huang-Lepowsky-Zhang\, but that it is not rigid. Instea
d\, an object of KL^k(sl_2) is rigid if and only if it is projective and\,
moreover\, KL^k(sl_2) has enough projectives\; most of the indecomposable
projective objects are logarithmic modules\, which means that the Virasor
o L(0) operator acts non-semisimply. We show also that the monoidal subcat
egory of rigid and projective objects is tensor equivalent to tilting modu
les for quantum sl_2 at the root of unity e^{pi i/(k+2)}. This leads to a
universal property for KL^k(sl_2)\, which allows us to construct an essent
ially surjective (but not fully faithful) exact tensor functor from KL^k(s
l2) to the category of finite-dimensional weight modules for quantum sl_2
at e^{pi i/(k+2)}.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20221208T200000Z
DTEND:20221208T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/65
DESCRIPTION:Title: From N-graded vertex algebras to Leibniz algebras and back.\nb
y Gaywalee Yamskulna (Illinois State University) as part of Rocky Mountain
Rep Theory Seminar\n\n\nAbstract\nA large portion of the literature in bo
th mathematics and physics is concerned with vertex algebras V that are of
CFT-type and rational. It is natural to ask whether there are other signi
ficant classes of vertex algebras that well-behaved from the representatio
n theoretic point of view such as \n\nNon CFT-type\, and rational for som
e category of modules or \n\nNon CFT-type and irrational but the module c
ategory has other nice properties such as C_2-condition. \n\nFor this tal
k\, I will focus on a study of representation theory of N-graded vertex al
gebras. To be precise\, I will describe an algebraic structure of rational
N-graded vertex algebras\, provide some tools to determine when N-graded
vertex algebras are irrational and describe roles of Leibniz algebras on t
he study of N-graded vertex algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (Weizmann Institute of Science)
DTSTART:20221117T180000Z
DTEND:20221117T190000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/66
DESCRIPTION:Title: Linkage classes for Kac-Moody superalgebras and the Duflo-Serganov
a functors\nby Maria Gorelik (Weizmann Institute of Science) as part o
f Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIn this talk\, I will p
resent a uniform description of the linkage classes for finite dimensional
and affine Kac-Moody superalgebras. These linkage classes are then used t
o parametrize the blocks in the category O. I will describe the interacti
on between these linkage classes and the Duflo-Serganova functors. The lat
ter are homological functors from the category of representations of a Lie
superalgebra to the category of representations of a Lie superalgebra of
the same type\, but smaller rank.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (University of Melbourne)
DTSTART:20221103T190000Z
DTEND:20221103T200000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/67
DESCRIPTION:Title: Rationality of subregular W-algebras of type B.\nby Justine Fa
squel (University of Melbourne) as part of Rocky Mountain Rep Theory Semin
ar\n\n\nAbstract\nIn this talk\, we present several results on the rationa
lity of W-algebras associated with subregular nilpotent elements of the Li
e algebra so(2n+1) as well as applications to W-superalgebras of type osp(
2|2n). The case n=2 was studied in my thesis\; the generalization for high
er ranks and the « super » cases is an on going work with Shigenori Naka
tsuka (Alberta).\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20230309T210000Z
DTEND:20230309T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/68
DESCRIPTION:Title: Quantum groups and VOAs\nby Thomas Creutzig (University of Alb
erta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThere ar
e two natural sources of braided tensor categories: categories of modules
of VOAs and quantum groups. Jointly with Matt Rupert and Simon Lentner\, w
e are developing a theory on relating the two and in this talk I will expl
ain that under suitable conditions a VOA category is a relative Drinfeld c
enter\, while this is always true for quantum groups. This implies nice co
rrespondences as e.g. the one between singlet algebra and unrolled small q
uantum group of sl(2) at root of unity.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryam Khaqan (Stockholm University)
DTSTART:20230316T170000Z
DTEND:20230316T180000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/69
DESCRIPTION:Title: Vertex operators for imaginary gl2-subalgebras in the Monster Lie
algebra.\nby Maryam Khaqan (Stockholm University) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nThe Monster Lie algebra is a quoti
ent of the physical space of the vertex algebra tensor product of a specif
ic rank-2 lattice vertex algebra with the Moonshine module of Frenkel\, Le
powsky\, and Meurman. \n\nIn this talk\, I will describe elements in the t
ensor product vertex algebra that project onto generators of gl2-subalgebr
as corresponding to each imaginary simple root of the Monster Lie algebra.
Furthermore\, for a fixed imaginary simple root\, I will illustrate how t
he action of the Monster simple group on the Moonshine module induces an o
rbit of each gl2-subalgebra of the Monster Lie algebra constructed in this
way. We conjecture that this Monster action is non-trivial. \n\nThis talk
is based on joint work with Darlayne Addabbo\, Lisa Carbone\, Elizabeth J
urisich\, and Scott H. Murray.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ole Warnaar (The University of Queensland)
DTSTART:20230413T210000Z
DTEND:20230413T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/71
DESCRIPTION:Title: Cylindric partitions and character formulas for W algebras\nby
Ole Warnaar (The University of Queensland) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nCylindric partitions are an affine analogue
of plane partitions. In this talk I will explain the role cylindric partit
ions have played in recent years in the computation of characters of the v
ertex operator algebra W_r(p\,p').\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Hekmati (University of Auckland)
DTSTART:20230420T200000Z
DTEND:20230420T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/72
DESCRIPTION:Title: Distributional characters on toric contact manifolds.\nby Pedr
am Hekmati (University of Auckland) as part of Rocky Mountain Rep Theory S
eminar\n\n\nAbstract\nToric contact manifolds have a nice combinatorial de
scription in terms of their moment cones. This paves the way for an explic
it computation of their various invariants\, such as the fundamental group
\, cohomology ring and contact homology. In this talk\, I will discuss the
transverse Dirac operator on these manifolds. It features notably in cert
ain supersymmetric gauge theories and its T-equivariant index character de
termines a distribution on the torus T\, for which we derive a simple and
explicit formula.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Valeri (Sapienza University of Rome)
DTSTART:20230427T170000Z
DTEND:20230427T180000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/73
DESCRIPTION:Title: Deformations of W-algebras and differential-difference equations\nby Daniele Valeri (Sapienza University of Rome) as part of Rocky Mount
ain Rep Theory Seminar\n\n\nAbstract\nIn this talk I will review some resu
lts about q-deformations of W-algebras and their relations with differenti
al-difference equations.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lachowska (EPFL Lausanne)
DTSTART:20230504T170000Z
DTEND:20230504T180000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/74
DESCRIPTION:Title: The small quantum group and related geometry\nby Anna Lachowsk
a (EPFL Lausanne) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nLet $u_q(g)$ denote the small quantum group associated to a semisimple
complex Lie algebra g and a root of unity q. \n\nI will describe some rec
ent results on the structure of the center of u_q(g) and discuss its relat
ion to the geometry of the Springer resolution and the affine Springer fib
ers. \n\nA lower bound on the dimension of the center of $u_q(g)$ suggests
a connection with the representation theory \n\nof the rational Cherednik
algebra.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Lentner (University of Hamburg)
DTSTART:20230511T200000Z
DTEND:20230511T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/75
DESCRIPTION:Title: A theory of logarithmic Kazhdan-Lusztig correspondences.\nby S
imon Lentner (University of Hamburg) as part of Rocky Mountain Rep Theory
Seminar\n\n\nAbstract\nWe want to understand braided tensor categories U t
hat have a\ncommutative algebra and a known braided tensor category C of l
ocal\nmodules. Our first result is that U is a relative Drinfeld center of
the\ncategory B of twisted modules\, our second result is that in good ca
ses\nwe can understand B in terms of a Hopf algebra in C and we develop\nm
ethods to determine this Hopf algebra. Hence we can determine U\nexplicitl
y.\n\nIn particular we can prove that if U is equivalent as an abelian\nca
tegory to representations of a quantum group\, or certain\ngeneralizations
\, and if it has a commutative algebra as above\, then it\nis equivalent a
lready 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. In this
case the latter gives\nby construction a commutative algebra with known C
and conjecturally the\nHopf algebra above should be the Nichols algebra of
screenings. With our\nresults above we can prove in some cases braided ca
tegory equivalences\nto certain quantum groups\, which are instances of lo
garithmic Kazhdan\nLusztig conjectures.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivana Vukorepa (University of Zagreb)
DTSTART:20230525T180000Z
DTEND:20230525T190000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/76
DESCRIPTION:Title: Tensor category $KL_k(sl_{2n})$ via minimal affine $W$--algebras a
t the non-admissible level $k=-\\frac{2n+1}{2}$\nby Ivana Vukorepa (Un
iversity of Zagreb) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbst
ract\nRepresentation theory of simple affine vertex algebra $L_k(\\mathfra
k{g})$\, for arbitrary simple Lie algebra $\\mathfrak{g}$ and general leve
l $k \\in \\mathbb{C}$\, is a very important direction in the theory of ve
rtex algebras. Some of the best understood cases are non-negative integer
levels $k \\in \\mathbb{Z}_{\\geq 0}$ and so-called admissible levels. \n\
nIn the present talk we consider special non-admissible levels for $\\math
frak{g} = \\mathfrak{sl}_m$. We prove that $KL_k(\\mathfrak{sl}_m)$ is a s
emi-simple\, rigid braided tensor category for all even $m \\geq 4$\, and
$k=-\\frac{m+1}{2}$. Moreover\, all modules in $KL_k(\\mathfrak{sl}_m)$ ar
e simple-currents and they appear in the decomposition of conformal embedd
ings $\\mathfrak{gl}_m \\hookrightarrow \\mathfrak{sl}_{m+1}$ at level $k=
-\\frac{m+1}{2}$. For this we inductively identify minimal affine $W$--alg
ebra $W_{k-1}(\\mathfrak{sl}_{m+2}\,\\theta)$ as simple current extension
of $L_k(\\mathfrak{sl}_m) \\otimes \\mathcal{H} \\otimes \\mathcal{M}$\, w
here $\\mathcal{H}$ is the rank one Heisenberg vertex algebra\, and $\\mat
hcal{M}$ 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://researchseminars.org/talk/RockyRepTheory/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumah Al-Ali (Saudi Electronic University)
DTSTART:20230601T160000Z
DTEND:20230601T170000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/77
DESCRIPTION:Title: Orbifolds of Gaiotto-Rapčák Y-algebras\nby Masoumah Al-Ali (
Saudi Electronic University) as part of Rocky Mountain Rep Theory Seminar\
n\n\nAbstract\nGaiotto and Rapčák introduced an important family of vert
ex 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 universal
two-parameters $W_\\infty$-algebra and serve as building blocks for many
interesting vertex algebras. The universal two parameters $W_\\infty$-alge
bra has a full automorphism group $Z_2$ and these algebras inherit this ac
tion. We shall study the structure of their orbifolds. Regardless of the e
xtremal cases\, we show that these orbifolds are generated by a single fie
ld of weight four\, and we give strong finite generating set.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jehanne Dousse (University of Geneva)
DTSTART:20230608T200000Z
DTEND:20230608T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/78
DESCRIPTION:Title: Characters of level 1 $C_n^{(1)}$-modules\, integer partitions\, a
nd the Capparelli-Meurman-Primc-Primc conjecture\nby Jehanne Dousse (U
niversity of Geneva) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbs
tract\nA partition of a positive integer n is a non-increasing sequence of
positive integers whose sum is n.\nSince Lepowsky\, Milne\, and Wilson's
seminal work in the 1980's\, several connections have been established bet
ween integer partitions and characters of standard modules of affine Lie a
lgebras. 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 study
ing crystal bases of the modules to obtain character formulas which 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 sev
eral expressions for their characters as generating functions for generali
sed partitions. Doing this\, we prove a recent conjecture of Capparelli-Me
urman-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 Isaac Konan.\
n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20230406T200000Z
DTEND:20230406T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/79
DESCRIPTION:Title: On Feigin-Tipunin type extension of W-algebras\nby Shigenori N
akatsuka (University of Alberta) as part of Rocky Mountain Rep Theory Semi
nar\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 irrati
onal VOA. Feigin and Tipunin gave a construction and generalization of thi
s algebra to simply-laced principal W-algebras by using VOA bundles over f
lag varieties. In this talk\, we'll generalize their construction for all
the W-algebras and then explain their properties for $sl(2)$. The talk is
based on my on-going joint work with Thomas Creutzig and Shoma Sugimoto.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Kanade (University of Denver)
DTSTART:20230914T200000Z
DTEND:20230914T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/80
DESCRIPTION:Title: Invariants of torus links and characters of VOAs.\nby Shashank
Kanade (University of Denver) as part of Rocky Mountain Rep Theory Semina
r\n\n\nAbstract\nI will explain how the characters of various rational and
non-rational VOAs of type A are obtained from sl_r invariants of torus \n
links. Specifically\, we will consider principal W algebras\, (1\,p) singl
et and\n(1\,p) triplet VOAs.\n\nThe password is the central extension of t
he Witt algebra V*******\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marijana Butorac (University of Rijeka)
DTSTART:20230921T200000Z
DTEND:20230921T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/81
DESCRIPTION:Title: Combinatorial construction of standard modules for affine Lie alge
bras.\nby Marijana Butorac (University of Rijeka) as part of Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nIn this talk I will present the co
nstruction of combinatorial bases of standard modules with rectangular hig
hest weights for affine Lie algebras\, which relies on the construction of
quasi--particle bases of the Feigin--Stoyanovsky principal subspaces. Th
is talk is based on a joint project with S. Kožić and M. Primc.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Qi (University of Denver)
DTSTART:20230928T200000Z
DTEND:20230928T210000Z
DTSTAMP:20260422T225827Z
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 Mountain
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 Huang's co
homology 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 satisfying a tec
hnical convergence condition. Then\, we will explain that the technical co
nvergence condition automatically holds if $V$ contains a nice subalgebra
$V_0$\, such that $W_1$ and $W_2$ are semisimple $V_0$-modules\, and the p
roducts of intertwining operators converge. Here $V_0$ is not required to
be conformally embedded into $V$. Nor will we need $V$-modules to form a t
ensor category. The result leads to a new method for computing $\\text{Ext
}^1(W_1\, W_2)$.\n
LOCATION:https://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:20260422T225827Z
UID:RockyRepTheory/83
DESCRIPTION:Title: Supersymmetric Vertex Algebras and Killing Spinors\nby Andoni
de Arriba de la Hera (Instituto de Ciencias Matemáticas) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nThe goal of the talk is to con
struct embeddings of the N=2 superconformal vertex algebra\, motivated by
mirror symmetry\, into the chiral de Rham complex\, provided that we have
solutions to the Killing spinor equations. Our approach to the chiral de R
ham complex is based on the universal construction by Bressler and Heluani
\, which applies to any Courant algebroid over a smooth manifold. The Kill
ing spinor equations that are considered come from the approach to special
holonomy based on Courant algebroids in generalized geometry and are insp
ired by the physics of heterotic supergravity and string theory. The embed
dings are given in two different set-ups. Firstly\, for equivariant Couran
t algebroids over homogeneous manifolds\, where the construction reduces t
o embeddings into the superaffinization of a quadratic Lie algebra\, and t
he Killing spinor equations become purely algebraic conditions that can be
checked on explicit examples. As an application\, we present the first ex
amples of (0\,2) mirror symmetry on compact non-Kähler complex manifolds.
These results are included in axiv:2012.01851\, recently published in Int
ernational Mathematical Research Notices. Secondly\, for transitive Couran
t algebroids over complex manifolds\, where these equations are equivalent
to the Hull-Strominger system\, with origins in the heterotic sigma-model
studied by physicists. Several examples have been studied where the obtai
ned results are applied. These results are included in arxiv:2305.06836. T
his talk is based on my PhD thesis\, and is a joint work with Luis Álvare
z-Cónsul and Mario Garcia-Fernandez.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Caradot (Henan University)
DTSTART:20231012T200000Z
DTEND:20231012T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/84
DESCRIPTION:Title: The cohomological variety of a vertex operator algebra.\nby An
toine Caradot (Henan University) as part of Rocky Mountain Rep Theory Semi
nar\n\n\nAbstract\nGiven a vertex operator algebra V\, one can attach a gr
aded Poisson algebra called the C2-algebra. The associated Poisson variety
is an important invariant for V and is known as the associated variety of
V. In this talk\, we will introduce the cohomological variety of a vertex
operator algebra\, a notion cohomologically dual to that of the associate
d variety. First\, we will motivate and define this variety\, as well as g
ive 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 constructed fr
om the Virasoro Lie algebra and finite dimensional simple Lie algebras. Th
is is a joint work with Cuipo Jiang (Shanghai Jiao Tong University) and Zo
ngzhu Lin (Kansas State University).\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdi Huang
DTSTART:20231026T200000Z
DTEND:20231026T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/85
DESCRIPTION:Title: Weighted Poisson polynomial rings and their Poisson valuations
\nby Hongdi Huang as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstra
ct\nA commutative algebra $A$ together with a Lie bracket satisfying the L
eibniz rule is called a Poisson algebra\, which is named in honor of Simé
on Denis Poisson. Poisson structures appear in many contexts\, including s
tring theory\, classical (quantum) mechanics\, and differential geometry.
In this talk\, we will talk about Poisson structure on weighted polynomial
rings and introduce Poisson valuations. Furthermore\, we will see that t
he Poisson valuations play an important role in characterizing the Poisson
automorphism groups of certain Poisson algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART:20231102T200000Z
DTEND:20231102T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/86
DESCRIPTION:Title: Going to the other side\nby Sergei Gukov (California Institute
of Technology) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract
\nAt its core\, this talk will be about a relation between characters of m
odules of logarithmic vertex algebras in the positive and negative Kazhdan
-Lusztig (KL) zones. The main concrete result will be an easy-to-use step-
by-step computational algorithm that produces a character of a log-VOA\, s
ay\, in the positive KL zone from the expression in the negative KL zone\,
and vice versa. An equally (if not more!) valuable conceptual message of
this talk will be an explanation that the same bijective relation plays an
important role in very different areas of mathematics (and even physics)
under other guises.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agustina Czenky (University of Oregon)
DTSTART:20231116T210000Z
DTEND:20231116T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/87
DESCRIPTION:Title: Low rank symmetric fusion categories in positive characteristic.\nby Agustina Czenky (University of Oregon) as part of Rocky Mountain Re
p Theory Seminar\n\n\nAbstract\nIn this talk\, we look at the classificati
on problem for symmetric fusion categories in positive characteristic. We
recall the second Adams operation on the Grothendieck ring and use its pro
perties to obtain some classification results. In particular\, we show tha
t the Adams operation is not the identity for any non-trivial symmetric fu
sion category. We also give lower bounds for the rank of a (non-super-Tann
akian) symmetric fusion category in terms of the characteristic of the fie
ld. 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://researchseminars.org/talk/RockyRepTheory/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Kovalchuk (University of Denver)
DTSTART:20231130T210000Z
DTEND:20231130T220000Z
DTSTAMP:20260422T225827Z
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 Rocky Mou
ntain Rep Theory Seminar\n\n\nAbstract\nW-(super)algebras have generated g
reat interest in recent years due to their numerous applications in mathem
atics and physics. The process of Hamiltonian reduction in stages suggests
that W-(super)algebras often arise as extensions of tensor products basic
building blocks. In type A\, we expect that the building blocks are the G
aiotto-Rapcak Y-algebras which arise as 1-parameter quotients of the unive
rsal 2-parameter VOA of type W(2\,3\,…). For types B\, C\, and D\, the q
uotients of the universal 2-parameter VOA of type W(2\,4\,…) provide som
e\, but not all\, of the necessary building blocks. In this talk we discus
s 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 building bloc
ks for W-(super)algebras of types B\, C\, and D. There are 8 infinite fami
lies of such quotients\, which are analogues of the Gaiotto-Rapcak Y-algeb
ras. We will explain the process behind the construction of this universal
two-parameter VOA and discuss several applications. This is a join work w
ith Thomas Creutzig and Andrew Linshaw.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (University of Alberta)
DTSTART:20231019T200000Z
DTEND:20231019T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/89
DESCRIPTION:Title: On unimodularity in the theory of tensor categories\nby Harshi
t Yadav (University of Alberta) as part of Rocky Mountain Rep Theory Semin
ar\n\n\nAbstract\nUnimodularity a classical notion shows up in various are
as like linear algebra\, lattices\, Poisson algebras\, etc. In this talk\,
we focus on unimodular Hopf algebras and unimodular tensor categories. We
will introduce unimodular module categories and use them to construct Fro
benius algebras and unimodular tensor categories. These ideas will be illu
strated with examples drawn from Hopf algebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University)
DTSTART:20240125T210000Z
DTEND:20240125T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/90
DESCRIPTION:Title: Reflective centers of module categories and quantum K-matrices
\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 Laugwi
tz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtaining sol
utions to the quantum reflection equation (qRE). To start\, given a braide
d monoidal category C and C-module category M\, we introduce a version of
the Drinfeld center Z(C) of C adapted for M. We refer to this category 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 canonical brai
ded module category attached to M. We will also discuss the case when C is
the category of modules over a quasitriangular Hopf algebra H\, and show
how quantum K-matrices arise in this setting (thus yielding solutions to t
he qRE).\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (University of Alberta)
DTSTART:20240201T210000Z
DTEND:20240201T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/91
DESCRIPTION:Title: A family of rational VOAs as type C cosets\nby Thomas Creutzig
(University of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\
nAbstract\nVladimir Kovalchuk constructed a two parameter family of VOA th
at have an affine sp(2) as subalgebra and in each even positive conformal
weight a singlet and at each odd one an sp(2)-triplet. This structure is
the third universal family of W-algebras after the W-infinity algebra and
its even spin analogue and quotients of one-parameter subfamilies of Vladi
mir algebras are often realized by cosets of certain W-algebras of orthosy
mplectic type. Very much like in the W-infinity case and in the even 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 n
ovel family of rational and lisse cosets. This is joint work with Vlad Kov
alchuk and Andy Linshaw.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto (Tsinghua University)
DTSTART:20240208T210000Z
DTEND:20240208T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/92
DESCRIPTION:Title: Feigin-Tipunin algorithm\nby Shoma Sugimoto (Tsinghua Universi
ty) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe Feigin
-Tipunin algorithm is a combinatorial and iterative algorithm introduced b
y the speaker recently to construct and study log VA(-module)s that have t
he q-series valued quantum invariant of 3-mfds called homological block in
troduced 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 use
d as in the usual Feigin-Tipunin construction\, so that the representation
theory of the log-VA can be studied without having to examine its complic
ated algebraic structure.\nIn this talk\, after describing the speaker's p
revious work\, it will be explained that if the FT algorithm can be applie
d to a certain lattice VOA-module\, we can construct a log VA-module with
the homological block of the (N+2)-Seifert 3-mfd as its character.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Alberta)
DTSTART:20240215T210000Z
DTEND:20240215T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/93
DESCRIPTION:Title: On the structure of W-algebras in type A\nby Shigenori Nakatsu
ka (University of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\
n\nAbstract\nIn physics\, the webs of W-algebras are introduced as the ver
tex algebras associated with the (p\, q)-webs of interfaces in the topolog
ically twisted N = 4 super Yang-Mills theory. This class of vertex algebra
s are generalizations and extensions of the so-called vertex algebras at t
he corner\, or equivalently the affine cosets of hook-type W-algebras in t
ype A. Although not proven yet in general\, it has recently been noticed t
hat the webs of W-algebras actually recover the general W-algebras in type
A through the ``reduction by stages". In this talk\, I will present the f
irst non-trivial examples and some interesting phenomena found in the cour
se both in rational and irrational cases. The talk is based on a joint wor
k with T. Creutzig\, J. Fasquel\, and A. Linshaw.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Angiono (Universidad Nacional de Córdoba)
DTSTART:20240229T210000Z
DTEND:20240229T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/95
DESCRIPTION:Title: Contragredient Lie algebras in symmetric tensor categories\nby
Iván Angiono (Universidad Nacional de Córdoba) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nDue to a celebrated result by Deligne\
, symmetric tensor categories of moderate growth over (algebraically close
d) fields of characteristic zero correspond to categories of representatio
ns of affine algebraic supergroups. Once we move to positive characteristi
c\, we need to take into account the Verlinde category Ver_p: Coulembier-E
tingof-Ostrik proved recently that every such symmetric tensor category is
the one of representations of an algebraic group in Ver_p\, under some re
strictions. Thus\, we wonder how to describe algebraic groups in Ver_p\, w
hich in turn correspond to pairs of usual algebraic groups and Lie algebra
s 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 algebras
. We prove the existence of contragredient Lie algebras in symmetric tenso
r algebras generalizing Kac-Moody construction of Lie (super) algebras\, w
hich at the same time give a description of some examples obtained previou
sly by 'semi simplifying' usual Lie algebras and provide new Lie algebras
in Ver_p.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Argyres (University of Cincinnati)
DTSTART:20240307T210000Z
DTEND:20240307T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/96
DESCRIPTION:Title: The extended vertex algebra of 4-dimensional N=2 superconformal fi
eld theories\nby Philip Argyres (University of Cincinnati) as part of
Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe local operators of a
unitary 4d N=2 SCFT in twisted Schur cohomology form a vertex operator alg
ebra (VOA). By "local operator" we mean one associated with a point in sp
ace-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 proper su
balgebra. The new vertex operators of this larger vertex algebra are asso
ciated with certain extended operators (line\, surface\, etc.) in twisted
Schur cohomology. Though we can compute some partial results in simple SC
FTs\, the structure of these extended vertex algebras is still largely mys
terious.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Université Paris-Saclay)
DTSTART:20240314T150000Z
DTEND:20240314T160000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/97
DESCRIPTION:Title: On a series of simple affine VOAs at non-admissible level arising
from rank one 4D SCFTs.\nby Anne Moreau (Université Paris-Saclay) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIt is known by th
e works of Adamović and Perše that the affine simple vertex algebras ass
ociated 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 Arakawa\, X
uanzhong Dai\, Justine Fasquel\, Bohan Li on the classification to the irr
educible highest weight modules of these vertex algebras. \nI will also de
scribe their associated varieties: it turns out that the associated variet
y of that corresponding to G2 is the orbifold of the associated variety 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 interesting e
xample of associated variety satisfying a number of conjectures in the con
text of orbifold vertex algebras. It is interesting to notice that these v
ertex algebra also appear as the vertex operator algebras corresponding to
rank one Argyres–Douglas theories in four dimension with flavour symmet
ry G2 and B3.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rupert (University of Saskatchewan)
DTSTART:20240321T200000Z
DTEND:20240321T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/98
DESCRIPTION:Title: Constructing Quantum Vertex (Co)-Algebras associated to Yangians\nby Matthew Rupert (University of Saskatchewan) as part of Rocky Mounta
in Rep Theory Seminar\n\n\nAbstract\nQuantum vertex algebras are deformati
ons of vertex algebras introduced by Etingof and Kazhdan in 1998. They are
families of vertex operators with relations deformed by a solution of the
quantum Yang-Baxter equation. There is also a dual notion of quantum vert
ex coalgebras which deform vertex coalgebras. In this talk I will explain
how to construct two distinct structures of a quantum vertex coalgebra on
the Yangian associated to any simple finite-dimensional complex Lie algebr
a\, and how to induce quantum vertex algebra structures on the dual Yangia
n. This talk is based on ongoing work with Alex Weekes and Curtis Wendland
t.\n\nQuantum vertex algebras are deformations of vertex algebras introduc
ed by Etingof and Kazhdan in 1998. They are families of vertex operators w
ith relations deformed by a solution of the quantum Yang-Baxter equation.
There is also a dual notion of quantum vertex coalgebras which deform vert
ex coalgebras. In this talk I will explain how to construct two distinct s
tructures of a quantum vertex coalgebra on the Yangian associated to any s
imple finite-dimensional complex Lie algebra\, and how to induce quantum v
ertex algebra structures on the dual Yangian. This talk is based on ongoin
g work with Alex Weekes and Curtis Wendlandt.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Raymond (Université Laval)
DTSTART:20240404T200000Z
DTEND:20240404T210000Z
DTSTAMP:20260422T225827Z
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\nAbs
tract\nIn this talk\, I want to give a pedagogical overview of Zhu's algeb
ras and then describe an alternative approach to understanding their algeb
raic structure that has resurfaced in 3D-2D correspondences. First\, I wil
l introduce the approach to Zhu's algebras in physics and the resulting ca
lculational framework. Following that\, I'll describe the link between Zhu
's algebras and Yangians and briefly discuss how these links are realised
in physics if time permits.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Castellan (University of Glasgow)
DTSTART:20240411T200000Z
DTEND:20240411T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/100
DESCRIPTION:Title: Chiralization of star products\nby Simone Castellan (Universi
ty of Glasgow) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\
nA star-product on a Poisson algebra $\\mathcal{A}$ is an associative prod
uct * such that ${\\bf A}:= (\\mathcal{A}\, *)$ is a (formal) quantization
of$\\mathcal{A}$. Famous examples are the Moyal-Weyl and Gutt star produc
t\, which quantize the symmetric algebra of a symplectic vector space and
of a Lie algebra\, respectively. Suppose that we can realize $\\mathcal{A
}$ and ${\\bf A}$ as the Zhu algebras of a Poisson vertex algebra $\\mathc
al{V}$ and of a vertex algebra ${\\bf V}$\, respectively. A chiralization
of * is a deformation of the Poisson vertex algebra structure on $\\mathc
al{V}$\, that becomes the star-product * after applying the Zhu-functor. I
n this talk\, I will explain the general framework and some general result
s on the problem\, and then I’ll show how to compute some explicit formu
lae for the chiralization of some classical star-products\, like the Moyal
-Weyl and Gutt star products. This talk is based on arXiv:2308.13412\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ridout (University of Melbourne)
DTSTART:20240328T200000Z
DTEND:20240328T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/101
DESCRIPTION:Title: Inverse quantum hamiltonian reduction for beginners.\nby Davi
d Ridout (University of Melbourne) as part of Rocky Mountain Rep Theory Se
minar\n\n\nAbstract\nQuantum hamiltonian reduction refers to a collection
of\nfunctors that map the module category of a given affine vertex algebra
\nto those of its associated W-algebras.\nSome of these functors are reaso
nably well understood and then the\nrepresentation theory of the W-algebra
is accessible.\nBut some are not.\nInverse quantum hamiltonian reduction
is a recent discovery that there\n(sometimes) exist functors in the opposi
te direction: from a given\nW-algebra module category to that of another W
-algebra\, which may be the\naffine vertex algebra itself.\nI will give an
overview of the simplest example\, which connects the\nmodule categories
of the Virasoro and sl2 minimal model vertex operator\nalgebras.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mamoru Ueda (University of Alberta)
DTSTART:20240418T200000Z
DTEND:20240418T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/102
DESCRIPTION:Title: Affine Yangians and W-algebras\nby Mamoru Ueda (University of
Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nCreu
tzig-Diaconescu-Ma conjectured that there exists a homomorphism from the s
hifted affine Yangian to the universal enveloping algebra of an iterated W
-algebra. They also conjectured that this homomorphism will induce a resol
ution of the generalized AGT conjecture. In this talk\, I will explain how
to construct a homomorphism from the affine Yangian of type A to the univ
ersal enveloping algebra of a W-algebra including the non-rectangular W-al
gebra. I expect that this homomorphism can be extended to the shifted affi
ne Yangian.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University)
DTSTART:20240222T210000Z
DTEND:20240222T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/103
DESCRIPTION:Title: On the classification of rigid Frobenius algebras in Dijkgraaf-Wi
tten categories.\nby Ana Ros Camacho (Cardiff University) as part of R
ocky Mountain Rep Theory Seminar\n\n\nAbstract\nThe study and classificati
on of algebra objects in modular tensor categories has a strong motivation
from the conformal field theoretical point of view\, these objects being
related to e.g. full theories [Fuchs-Runkel-Schweigert] and extensions of
vertex operator algebras [Huang-Kirillov-Lepowsky\, Creutzig-Kanade-McRae
for superalgebras]. In this talk\, I will present a classification of rigi
d\, Frobenius algebras in the so-called Dijkgraaf-Witten categories\, whic
h we achieved using Frobenius monoidal functors. Joint work with Robert La
ugwitz and Sam Hannah\, based on SIGMA 19 (2023)\, 075\, 42 pages.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaywalee Yamskulna (Illinois State University)
DTSTART:20241003T200000Z
DTEND:20241003T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/104
DESCRIPTION:Title: On the algebraic structure of $N$-Graded Vertex Algebras $V=\\opl
us_{n=0}^{\\infty}V_n$ when $V_0$ is a Gorenstein ring and Their Relation
to vertex algebras of CFT-Type\nby Gaywalee Yamskulna (Illinois State
University) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nIn
this talk\, I will explore the algebraic properties of an $\\mathbb{N}$-g
raded vertex algebra associated with Gorenstein rings. Through this framew
ork\, 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://researchseminars.org/talk/RockyRepTheory/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Tarasca (Virginia Commonwealth University)
DTSTART:20241205T210000Z
DTEND:20241205T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/106
DESCRIPTION:Title: Coinvariants of metaplectic representations and abelian varieties
\nby Nicola Tarasca (Virginia Commonwealth University) as part of Roc
ky Mountain Rep Theory Seminar\n\n\nAbstract\nSpaces of coinvariants have
classically been constructed by assigning representations of affine Lie al
gebras\, and more generally\, vertex operator algebras\, to pointed algebr
aic curves. Removing curves out of the picture\, I will construct spaces o
f coinvariants at abelian varieties with respect to the action of an infin
ite-dimensional Lie algebra. I will show how these spaces globalize to twi
sted D-modules on moduli of abelian varieties\, extending the classical pi
cture from moduli of curves. This is based on the preprint arXiv:2301.1322
7.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harshit Yadav (University of Alberta)
DTSTART:20241010T200000Z
DTEND:20241010T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/107
DESCRIPTION:Title: Rigidity of vertex tensor categories.\nby Harshit Yadav (Univ
ersity of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstr
act\nThanks to the advances over the last decade\, we now have a reasonabl
e understanding of when a vertex operator algebra (VOA) admits a vertex te
nsor category that is braided monoidal. However\, rigidity of such categor
ies is often quite difficult to establish and is proven by ad hoc methods.
\nI will present recent joint work (https://arxiv.org/abs/2409.14618) with
Thomas Creutzig\, Robert McRae and Kenichi Shimizu where we develop techn
iques for proving rigidity of vertex tensor categories. Namely\, given an
extension of VOAs V ⊂ W\, we establish results that allow us to prove ri
gidity to Rep(V) given rigidity of Rep(W) and vice versa.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Beneish (University of North Texas)
DTSTART:20241024T200000Z
DTEND:20241024T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/108
DESCRIPTION:Title: Replicable functions arising from code-lattice VOAs fixed by auto
morphisms\nby Lea Beneish (University of North Texas) as part of Rocky
Mountain Rep Theory Seminar\n\n\nAbstract\nWe ascertain properties of the
algebraic structures in towers of codes\, lattices\, and vertex operator
algebras (VOAs) by studying the associated subobjects fixed by lifts of co
de automorphisms. In the case of sublattices fixed by subgroups of code au
tomorphisms\, we identify replicable functions that occur as quotients of
the associated theta functions by suitable eta products. We show that thes
e lattice theta quotients can produce replicable functions not associated
to any individual automorphisms. Moreover\, we show that the structure of
the fixed subcode can induce certain replicable lattice theta quotients an
d we provide a general code theoretic characterization of order doubling f
or lifts of code automorphisms to the lattice-VOA. Finally\, we prove resu
lts on the decompositions of characters of fixed subVOAs. This talk is bas
ed on joint work with Jennifer Berg\, Eva Goedhart\, Hussain M. Kadhem\, A
llechar Serrano López\, and Stephanie Treneer.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (University of Melbourne)
DTSTART:20241031T200000Z
DTEND:20241031T210000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/109
DESCRIPTION:Title: Partial and inverse Hamiltonian reductions for W-algebras\nby
Justine Fasquel (University of Melbourne) as part of Rocky Mountain Rep T
heory Seminar\n\n\nAbstract\nW-algebras are vertex algebras obtained form
quantum Hamiltonian reductions of an affine vertex algebra. These reductio
ns are naturally upgraded to functors from the category of modules over th
e affine vertex algebras to the category of the modules over the correspon
ding W-algebras. However\, they are difficult to control in general. Recen
tly\, two approaches have been developed to improve our understanding of t
he functors. One consists in spitting the functor into small pieces that a
re easier to deal with (partial reductions)\, the other aims to reverse th
e quantum Hamiltonian reduction procedure (inverse Hamiltonian reductions)
. In this talk\, I will discuss about recent advances in these complementa
ry approaches. The talk is based on recent papers with T. Creutzig\, A. Li
nshaw and S. Nakatsuka and with Z. Fehily\, E. Fursman and S. Nakatsuka.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lau (Université Laval)
DTSTART:20241212T210000Z
DTEND:20241212T220000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/110
DESCRIPTION:Title: Good filtrations\, Lie algebras representations\, and free Jordan
algebras\nby Michael Lau (Université Laval) as part of Rocky Mountai
n Rep Theory Seminar\n\n\nAbstract\nAffine Lie algebras are universal cent
ral extensions of algebras of matrices over Laurent polynomials. In the
case of sl_2\, the ring of Laurent polynomials can be replaced with any un
ital Jordan algebra. This gives a very large family of Lie algebras. M
otivated by this connection between Lie and Jordan theory\, we describe a
category of Lie algebra weight modules\, whose homological properties are
related to the long-standing open problem of computing graded dimensions o
f free Jordan algebras. No prior knowledge of Jordan algebras will be as
sumed. This talk is based on joint work with Olivier Mathieu.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Creutzig (FAU Erlangen-Nürnberg)
DTSTART:20250327T183000Z
DTEND:20250327T193000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/111
DESCRIPTION:Title: Verlinde's formula in logarithmic CFT\nby Thomas Creutzig (FA
U Erlangen-Nürnberg) as part of Rocky Mountain Rep Theory Seminar\n\n\nAb
stract\nA while ago and with David Ridout a Verlinde formula for the affin
e VOAs of sl(2) at admissible level was conjectured. This is a VOA whose r
epresentation category is neither finite nor semisimple. Our idea was to r
eplace the Verlinde S-matrix by an S-kernel and atypical modules by their
resolutions of typical modules to get a natural Verlinde formula conjectur
e. I will explain why this formalism is true.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arim Song (University of Denver)
DTSTART:20250403T183000Z
DTEND:20250403T193000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/112
DESCRIPTION:Title: Supersymmetric W-algebras vs. W-algebras\nby Arim Song (Unive
rsity of Denver) as part of Rocky Mountain Rep Theory Seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Caradot (Jean Monnet University)
DTSTART:20250417T183000Z
DTEND:20250417T193000Z
DTSTAMP:20260422T225827Z
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 Theory Sem
inar\n\n\nAbstract\nIn order to investigate the representation theory of a
vertex algebra $V$\, a fruitful strategy is to look at the properties of
its $C_2$-algebra $R(V)$. This Poisson algebra reflects interesting proper
ties of the vertex algebra and is often easier to handle than the vertex a
lgebra itself. In this talk\, we are interested in studying vertex algebra
s in a closed monoidal category\, and in providing a description of the du
al versions of $V$ and $R(V)$ when those exist. We introduce vertex algebr
as graded by an abelian group and explain how to "dualize" the definition
to obtain a graded vertex coalgebra. This leads to the notion of the $C_2$
-coalgebra of a vertex coalgebra. We will describe its properties and show
that the duality vertex algebra / vertex coalgebra passes down to a duali
ty $C_2$-algebra / $C_2$-coalgebra. We will also explain how this dualitie
s carry on to the respective modules / comodules.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Villarreal (University of Colorado Boulder)
DTSTART:20250501T183000Z
DTEND:20250501T193000Z
DTSTAMP:20260422T225827Z
UID:RockyRepTheory/115
DESCRIPTION:Title: Intertwiners and filtrations\nby Juan Villarreal (University
of Colorado Boulder) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbs
tract\nIn this talk we introduce a canonical decreasing filtration on inte
rtwiners of a vertex algebra. We study the associated graded spaces. Then\
, we define Poisson vertex intertwiners and Poisson intertwiners. We obtai
n relations between the associated varieties of modules of a vertex algebr
a.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronika Pedić Tomić (University of Zagreb)
DTSTART:20250515T183000Z
DTEND:20250515T193000Z
DTSTAMP:20260422T225827Z
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://researchseminars.org/talk/RockyRepTheory/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Zhang (Tsinghua University)
DTSTART:20250522T150000Z
DTEND:20250522T160000Z
DTSTAMP:20260422T225827Z
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 Theory Semin
ar\n\n\nAbstract\nIn this talk\, I will present a sewing-factorization the
orem for conformal blocks in arbitrary genus associated to a (possibly non
rational) $C_2$-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 some of th
e conjectures by Gainuditnov-Runkel. The relationship between our result a
nd coends will also be discussed. The talk is based on an ongoing project
(arXiv: 2305.10180\, 2411.07707\, 2503.23995) joint with Bin Gui.\n
LOCATION:https://researchseminars.org/talk/RockyRepTheory/117/
END:VEVENT
END:VCALENDAR