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BEGIN:VEVENT
SUMMARY:Andrew Linshaw (Denver University)
DTSTART;VALUE=DATE-TIME:20200910T190000Z
DTEND;VALUE=DATE-TIME:20200910T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20200924T190000Z
DTEND;VALUE=DATE-TIME:20200924T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201001T210000Z
DTEND;VALUE=DATE-TIME:20201001T220000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201008T190000Z
DTEND;VALUE=DATE-TIME:20201008T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201015T190000Z
DTEND;VALUE=DATE-TIME:20201015T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201119T160000Z
DTEND;VALUE=DATE-TIME:20201119T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201105T200000Z
DTEND;VALUE=DATE-TIME:20201105T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201029T190000Z
DTEND;VALUE=DATE-TIME:20201029T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201112T200000Z
DTEND;VALUE=DATE-TIME:20201112T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201022T190000Z
DTEND;VALUE=DATE-TIME:20201022T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201203T200000Z
DTEND;VALUE=DATE-TIME:20201203T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201210T200000Z
DTEND;VALUE=DATE-TIME:20201210T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201217T200000Z
DTEND;VALUE=DATE-TIME:20201217T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20201126T000000Z
DTEND;VALUE=DATE-TIME:20201126T010000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210114T200000Z
DTEND;VALUE=DATE-TIME:20210114T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210122T000000Z
DTEND;VALUE=DATE-TIME:20210122T010000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210128T160000Z
DTEND;VALUE=DATE-TIME:20210128T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210204T200000Z
DTEND;VALUE=DATE-TIME:20210204T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210211T230000Z
DTEND;VALUE=DATE-TIME:20210212T000000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210218T200000Z
DTEND;VALUE=DATE-TIME:20210218T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210226T000000Z
DTEND;VALUE=DATE-TIME:20210226T010000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210304T160000Z
DTEND;VALUE=DATE-TIME:20210304T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210326T000000Z
DTEND;VALUE=DATE-TIME:20210326T010000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210429T190000Z
DTEND;VALUE=DATE-TIME:20210429T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210311T200000Z
DTEND;VALUE=DATE-TIME:20210311T210000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210401T230000Z
DTEND;VALUE=DATE-TIME:20210402T000000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210408T230000Z
DTEND;VALUE=DATE-TIME:20210409T000000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210415T160000Z
DTEND;VALUE=DATE-TIME:20210415T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210422T190000Z
DTEND;VALUE=DATE-TIME:20210422T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210506T220000Z
DTEND;VALUE=DATE-TIME:20210506T230000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210513T190000Z
DTEND;VALUE=DATE-TIME:20210513T200000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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;VALUE=DATE-TIME:20210520T220000Z
DTEND;VALUE=DATE-TIME:20210520T230000Z
DTSTAMP;VALUE=DATE-TIME:20210804T230317Z
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
END:VCALENDAR