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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:20201101T012234Z
UID:RockyRepTheory/1
DESCRIPTION:Title: Trialities of W-algebras\nby Andrew Linshaw (Denver Uni
versity) as part of Rocky Mountain Rep Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinwei Yang (University of Alberta)
DTSTART;VALUE=DATE-TIME:20200924T190000Z
DTEND;VALUE=DATE-TIME:20200924T200000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/2
DESCRIPTION:Title: Recent progress on tensor categories of vertex operator
algebras.\nby Jinwei Yang (University of Alberta) as part of Rocky Mounta
in Rep Theory Seminar\n\n\nAbstract\nTensor categories of vertex operator
algebras play an important role in the study of vertex operator algebras a
nd conformal field theories. A central problem of tensor category theory o
f Huang-Lepowsky-Zhang is the existence of the vertex tensor category stru
cture. We develop a few general methods to establish the existence of tens
or structure on module categories for vertex operator algebras\, especiall
y for non-rational and non-C_2 cofinite vertex operator algebras. As appli
cations\, we obtain the tensor structure of affine Lie algebras at various
levels\, affine Lie superalgebra gl(1|1)\, the Virasoro algebra at all ce
ntral charges as well as the singlet algebras. We also study important pr
operties\, including constructions of projective covers\, fusion rules and
the rigidity of these tensor categories. This talk is based on joint work
with T. Creutzig\, Y.-Z. Huang\, F. Orosz Hunziker\, C. Jiang\, R. McRae
and D. Ridout.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART;VALUE=DATE-TIME:20201001T210000Z
DTEND;VALUE=DATE-TIME:20201001T220000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/3
DESCRIPTION:Title: The singular support of the Ising model\nby Reimundo He
luani (IMPA) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nW
e prove a new Fermionic quasiparticle sum expression for the character of
the Ising model vertex algebra\, related to the Jackson-Slater q-series id
entity of Rogers-Ramanujan type. We find\, as consequences\, an explicit m
onomial basis for the Ising model\, and a description of its singular supp
ort. We find that the ideal sheaf of the latter\, defining it as a subsche
me of the arc space of its associated scheme\, is finitely generated as a
differential ideal. We prove three new q-series identities of the Rogers-R
amanujan-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
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro Van Ekeren (UFF)
DTSTART;VALUE=DATE-TIME:20201008T190000Z
DTEND;VALUE=DATE-TIME:20201008T200000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/4
DESCRIPTION:Title: Schellekens list\, the Leech lattice and the very stran
ge Formula.\nby Jethro Van Ekeren (UFF) as part of Rocky Mountain Rep Theo
ry Seminar\n\n\nAbstract\n(joint work with Lam\, Moeller and Shimakura) If
V is a holomorphic vertex algebra of central charge 24 then its weight on
e space V_1 is known to be a reductive Lie algebra which is either trivial
\, abelian of dimension 24 (in which case V is the Leech lattice vertex al
gebra) or else one of 69 semisimple Lie algebras first determined by Schel
lekens in 1993. Until now the only known proof of Schelekens result was a
heavily computational one involving case analysis and difficult integer pr
ogramming problems. Recently Moeller and Scheithauer have established a bo
und on the dimension of the weight one space of a holomorphic orbifold ver
tex algebra\, using the Deligne bound on the growth of coefficients of wei
ght 2 cusp forms. In this talk I will describe how the dimension bound tog
ether with Kac's very strange formula implies that all holomorphic vertex
algebras of central charge 24 and nontrivial weight one space are orbifold
s 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 in this way.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Genra (University of Alberta)
DTSTART;VALUE=DATE-TIME:20201015T190000Z
DTEND;VALUE=DATE-TIME:20201015T200000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/5
DESCRIPTION:Title: Screenings and applications\nby Naoki Genra (University
of Alberta) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nS
creening operators are useful tools to characterize free field realization
s of vertex algebras\, and give new perspectives in the structures of them
. We explain screening operators of the beta-gamma system\, affine vertex
(super)algebras and W-(super)algebras. We also explain the applications to
the coset constructions\, representations and trialities of W-algebras.\
n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Paris-Saclay university)
DTSTART;VALUE=DATE-TIME:20201119T160000Z
DTEND;VALUE=DATE-TIME:20201119T170000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/6
DESCRIPTION:by Anne Moreau (Paris-Saclay university) as part of Rocky Moun
tain Rep Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Zhi Huang (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201105T200000Z
DTEND;VALUE=DATE-TIME:20201105T210000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/7
DESCRIPTION:Title: Associative algebra and the representation theory of gr
ading-restricted vertex algebras.\nby Yi-Zhi Huang (Rutgers University) as
part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nI will introduce
an associative algebra $A^{∞}(V)$ constructed using infinite matrices w
ith entries in a grading-restricted vertex algebra V. The Zhu algebra and
its generalizations by Dong-Li-Mason are very special subalgebras of $A^{
∞}(V)$. I will also introduce the new subalgebras $A^{N}(V)$ of $A^{∞}
$(V)\, which can be viewed as obtained from finite matrices with entries i
n V. I will then discuss the relations between lower-bounded generalized V
-modules and suitable modules for these associative algebras. This talk is
based on the paper arXiv:2009.00262.\n
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:20201101T012234Z
UID:RockyRepTheory/8
DESCRIPTION:Title: Kazama-Suzuki coset vertex superalgebras at admissible
levels\nby Ryo Sato (Academia Sinica\, Taipei\, Taiwan) as part of Rocky M
ountain Rep Theory Seminar\n\n\nAbstract\nThe Kazama-Suzuki coset vertex o
perator superalgebra associated with a simple Lie algebra g and its Cartan
subalgebra h is a ``super-analog'' of the parafermion vertex operator alg
ebra associated with g. At positive integer levels\, the coset superalgebr
a turns out to be C_2-cofinite and rational by the general theory of orbif
olds (Miyamoto) and Heisenberg cosets (Creutzig-Kanade-Linshaw-Ridout)\, r
espectively. On the other hand\, at Kac-Wakimoto admissible levels\, the c
oset superalgebra is not C_2-cofinite nor rational. In this talk we discus
s a relationship between the category of weight modules for the admissible
affine vertex algebra associated with g and that for the corresponding Ka
zama-Suzuki coset vertex superalgebra. In our discussion the inverse Kazam
a-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 sim
ple weight modules of the Kazama-Suzuki coset vertex superalgebra and veri
fy the conjectural Verlinde formula in this case (corresponding to Creutzi
g-Ridout's result in the affine side). The last part is based on the joint
work with Shinji Koshida.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antun Milas (SUNY-Albany)
DTSTART;VALUE=DATE-TIME:20201112T200000Z
DTEND;VALUE=DATE-TIME:20201112T210000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/9
DESCRIPTION:by Antun Milas (SUNY-Albany) as part of Rocky Mountain Rep The
ory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darlayne Addabbo (University of Arizona)
DTSTART;VALUE=DATE-TIME:20201022T190000Z
DTEND;VALUE=DATE-TIME:20201022T200000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/10
DESCRIPTION:Title: Higher level Zhu algebras for vertex operator algebras\
nby Darlayne Addabbo (University of Arizona) as part of Rocky Mountain Rep
Theory Seminar\n\n\nAbstract\nI will discuss the level two Zhu algebra fo
r the Heisenberg vertex operator algebra and techniques used in determinin
g its structure. I will also discuss more general results helpful in deter
mining generators and relations for higher level Zhu algebras\, and in par
ticular\, will provide an example to clarify the necessity of an extra con
dition required in the definition of higher level Zhu algebras. (Joint wit
h Katrina Barron.)\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201203T200000Z
DTEND;VALUE=DATE-TIME:20201203T210000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/11
DESCRIPTION:by Chiara Damiolini (Rutgers University) as part of Rocky Moun
tain Rep Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigenori Nakatsuka (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201210T200000Z
DTEND;VALUE=DATE-TIME:20201210T210000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/12
DESCRIPTION:by Shigenori Nakatsuka (University of Tokyo) as part of Rocky
Mountain Rep Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drazen Adamovic (University of Zagreb)
DTSTART;VALUE=DATE-TIME:20201217T160000Z
DTEND;VALUE=DATE-TIME:20201217T170000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/13
DESCRIPTION:by Drazen Adamovic (University of Zagreb) as part of Rocky Mou
ntain Rep Theory Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto (Kyoto University)
DTSTART;VALUE=DATE-TIME:20201125T170000Z
DTEND;VALUE=DATE-TIME:20201125T180000Z
DTSTAMP;VALUE=DATE-TIME:20201101T012234Z
UID:RockyRepTheory/14
DESCRIPTION:Title: On the log W-algebras\nby Shoma Sugimoto (Kyoto Univers
ity) as part of Rocky Mountain Rep Theory Seminar\n\n\nAbstract\nFor a fin
ite dimensional simply-laced simple Lie algebra $g$ and an\ninteger $p\\ge
q 2$\, we can attach the logarithmic $W$-algebra $W(p)_Q$.\nWhen $g=sl_2$\
, $W(p)_Q$ is called the triplet $W$-algebra\, and studied by\nmany people
as one of the most famous examples of $C_2$-cofinite but\nirrational vert
ex operator algebra. However\, apart from the triplet\n$W$-algebra\, not m
uch is known about the log $W$-algebras $W(p)_Q$.\nIn this talk\, after we
construct $W(p)_Q$ and their modules\n$W(p\,\\lambda)_Q$ geometrically al
ong the preprint of Feigin-Tipunin\, first\nwe show the simplicity\, $W_k(
g)$-module structure\, and character formula\nof $W(p\,\\lambda)_Q$ when $
\\sqrt{p}\\bar\\lambda$ is in the closure of the\nfundamental alcove. In p
articular\, for $p\\geq h-1$\, $W(p)_Q$ is simple and\ndecomposed into sim
ple $W_k(g)$-modules.\nSecond we give a purely $W$-algebraic algorithm to
calculate nilpotent\nelements in the Zhu's $C_2$-algebra of $W(p)_Q$ much
easier than\nstraightforward way. Using this algorithm to the cases $g=sl_
3$ and\n$p=2\,3$\, we show that $W(p)_Q$ is $C_2$-cofinite in these cases.
\n
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