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BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20201106T170000Z
DTEND:20201106T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/1
DESCRIPTION:Title: Convergence of sewing conformal blocks\nby Bin
Gui (Rutgers University) as part of Rutgers Lie Group/Quantum Mathematics
Seminar\n\n\nAbstract\nConformal blocks (i.e. chiral correlation functions
) are central objects of chiral CFT. Given a VOA V and a compact Riemann s
urface C with marked points\, one can define conformal blocks to be linear
functionals on tensor products of V-modules satisfying certain (co)invari
ance properties related to V and C. For instance\, the vertex operator of
a VOA V\, or more generally\, an intertwining operator of V\, is a conform
al block associated to V and the genus 0 Riemann surface with 3 marked poi
nts. Taking contractions/q-traces is a main way of constructing higher gen
us conformal blocks from low genus ones\, and it has been conjectured for
a long time that the contractions always converge. In this talk\, I will r
eport recent work on a solution of this conjecture.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Gemünden (ETH Zürich)
DTSTART:20201120T170000Z
DTEND:20201120T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/2
DESCRIPTION:Title: Non-abelian orbifold theory and holomorphic vertex
operator algebras at higher central charge\nby Thomas Gemünden (ETH Z
ürich) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n\nAbst
ract\nHolomorphic vertex operator algebras at central charges up to 24 hav
e been almost fully classified and it appears that they can all be constru
cted as cyclic orbifolds of lattice vertex operator algebras. At the same
time\, very little is known about the situation at higher central charge.
Intuition from physics tells us that higher central charge analogues of th
e moonshine vertex operator algebra may exist\, but so far all attempts at
their construction have failed. The goal of this work is to explore the s
et of holomorphic vertex operator algebras at higher central charge using
non-abelian orbifold theory.\nI will begin the talk with a review of the o
rbifold theory of strongly rational vertex operator algebras. Then I will
develop a theory of holomorphic extensions of metacyclic orbifolds as a ge
neralisation of the cyclic theory.\n\nFinally\, I will prove the existence
of a holomorphic vertex operator algebra at central charge 72 that cannot
be constructed as a cyclic orbifold of a lattice vertex operator algebra.
If there is time I will discuss some of the challenges arising in trying
to construct analogues of the moonshine module.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Carbone (Rutgers University and Institute for Advanced Study\
, School of Natural Science)
DTSTART:20210122T170000Z
DTEND:20210122T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/3
DESCRIPTION:Title: Complete pro-unipotent automorphism group for the m
onster Lie algebra\nby Lisa Carbone (Rutgers University and Institute
for Advanced Study\, School of Natural Science) as part of Rutgers Lie Gro
up/Quantum Mathematics Seminar\n\n\nAbstract\nWe construct a complete pro-
unipotent group of automorphisms for a completion of the monster Lie algeb
ra. We also construct an analog of the exponential map and Adjoint represe
ntation. This gives rise to some useful identities involving imaginary roo
t vectors.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Li (SUNY-Albany)
DTSTART:20210129T170000Z
DTEND:20210129T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/4
DESCRIPTION:Title: Arc spaces\, vertex algebras and principal subspace
s\nby Hao Li (SUNY-Albany) as part of Rutgers Lie Group/Quantum Mathem
atics Seminar\n\n\nAbstract\nArc spaces were originally introduced in alge
braic geometry to study singularities. More recently they show in connecti
ons to vertex algebras. There is a closed embedding from the singular supp
ort of a vertex algebra V into the arc space of associated scheme of V. We
call a vertex algebra "classically free" if this embedding is an isomorph
ism. In this introductory survey talk\, we will first introduce arc spaces
and some of its backgrounds. Then we will provide several examples of cla
ssically free vertex algebras including Feigin-Stoyanovsky principal subsp
aces\, and explain their applications in differential algebras\, $q$-serie
s identities\, etc. In particular\, we will show the classically freeness
of principal subspaces of type A at level 1 by using a method of filtratio
ns and identities from quantum dilogarithm or quiver representations. As a
result\, we obtain new presentations and graded dimensions of the princip
al subspaces of type A at level 1\, which can be thought of as the continu
ation of previous works by Calinescu\, Lepowsky and Milas. The classically
freeness of some principal subspaces which possess free fields realisatio
n will also be discussed. Most of the talk is based on the joint work with
A. Milas.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilit Martirosyan (University of North Carolina\, Wilmington)
DTSTART:20210205T170000Z
DTEND:20210205T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/5
DESCRIPTION:Title: Braided rigidity for path algebras (joint work with
Hans Wenzl)\nby Lilit Martirosyan (University of North Carolina\, Wil
mington) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n\nAbs
tract\nPath algebras are a convenient way of describing decompositions of
tensor powers of an object in a tensor category. If the category is braide
d\, one obtains representations of the braid groups Bn for all n in N. We
say that such representations are rigid if they are determined by the path
algebra and the representations of B2. We show that besides the known cla
ssical cases also the braid representations for the path algebra for the 7
-dimensional representation of G2 satisfies the rigidity condition\, provi
ded B3 generates End(V^{⊗3}). We obtain a complete classification of rib
bon tensor categories with the fusion rules of g(G2) if this condition is
satisfied.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Sergel (Rutgers University - New Brunswick)
DTSTART:20210212T170000Z
DTEND:20210212T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/6
DESCRIPTION:Title: Positivity of interpolation polynomials\nby Emi
ly Sergel (Rutgers University - New Brunswick) as part of Rutgers Lie Grou
p/Quantum Mathematics Seminar\n\n\nAbstract\nThe interpolation polynomials
are a family of inhomogeneous symmetric polynomials characterized by simp
le vanishing properties. In 1996\, Knop and Sahi showed that their top hom
ogeneous components are Jack polynomials. For this reason these polynomial
s are sometimes called interpolation Jack polynomials\, shifted Jack polyn
omials\, or Knop-Sahi polynomials.\nWe prove Knop and Sahi's main conjectu
re from 1996\, which asserts that\, after a suitable normalization\, the i
nterpolation polynomials have positive integral coefficients. This result
generalizes Macdonald's conjecture for Jack polynomials that was proved by
Knop and Sahi in 1997. Moreover\, we give a combinatorial expansion for t
he interpolation polynomials that exhibits the desired positivity property
.\n\nThis is joint work with Y. Naqvi and S. Sahi.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antun Milas (SUNY - Albany)
DTSTART:20210219T170000Z
DTEND:20210219T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/7
DESCRIPTION:Title: Graph q-series\, graph schemes\, and 4d/2d correspo
ndences\nby Antun Milas (SUNY - Albany) as part of Rutgers Lie Group/Q
uantum Mathematics Seminar\n\n\nAbstract\nTo any graph with n nodes we ass
ociate two n-fold q-series\, with single and double poles\, closely relate
d to Nahm's sum associated to a positive definite symmetric bilinear form.
\nQuite remarkably series with "double poles" sometimes capture Schur's in
dices of 4d N = 2 superconformal field theories (SCFTs) and thus\, under 2
d/4d correspondence\, they give new character formulas of certain vertex o
perator algebras.\nIf poles are simple\, they arise in algebraic geometry
as Hilbert-Poincare series of "graph" arc algebras. These q-series are poo
rly understood and seem to exhibit peculiar modular transformation behavio
r.\nIn this talk\, we explain how these "counting" functions arise in diff
erent areas of mathematics and physics. This talk will be fairly accessibl
e\, assuming minimal background. No familiarity with concepts like vertex
algebras and 4d N=2 SCFT is needed.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haisheng Li (Rutgers University at Camden)
DTSTART:20210409T160000Z
DTEND:20210409T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/8
DESCRIPTION:Title: Deforming vertex algebras by module and comodule ac
tions of vertex bialgebras\nby Haisheng Li (Rutgers University at Camd
en) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n\nAbstract
\nPreviously\, we introduced a notion of vertex bialgebra and a notion of
module vertex algebra for a vertex bialgebra\, and gave a smash product co
nstruction of nonlocal vertex algebras. Here\, we introduce a notion of ri
ght comodule vertex algebra for a vertex bialgebra. Then we give a constru
ction of quantum vertex algebras from vertex algebras with a right comodul
e vertex algebra structure and a compatible (left) module vertex algebra s
tructure for a vertex bialgebra. As an application\, we obtain a family of
deformations of the lattice vertex algebras. This is based on a joint wor
k with Naihuan Jing\, Fei Kong\, and Shaobin Tan.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corina Calinescu (New York City College of Technology and CUNY Gra
duate Center)
DTSTART:20210416T160000Z
DTEND:20210416T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/9
DESCRIPTION:by Corina Calinescu (New York City College of Technology and C
UNY Graduate Center) as part of Rutgers Lie Group/Quantum Mathematics Semi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Sadowski (Ursinus College)
DTSTART:20210423T160000Z
DTEND:20210423T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/10
DESCRIPTION:by Christopher Sadowski (Ursinus College) as part of Rutgers L
ie Group/Quantum Mathematics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Carbone (Rutgers University and Institute for Advanced Study)
DTSTART:20210312T170000Z
DTEND:20210312T180000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/11
DESCRIPTION:Title: Imaginary root strings and Chevalley-Steinberg gro
up commutators for hyperbolic Kac--Moody algebras\nby Lisa Carbone (Ru
tgers University and Institute for Advanced Study) as part of Rutgers Lie
Group/Quantum Mathematics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Saied (Rutgers University—New Brunswick)
DTSTART:20210326T160000Z
DTEND:20210326T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/12
DESCRIPTION:Title: Combinatorial formula for SSV polynomials\nby
Jason Saied (Rutgers University—New Brunswick) as part of Rutgers Lie Gr
oup/Quantum Mathematics Seminar\n\n\nAbstract\nMacdonald polynomials are h
omogeneous polynomials that generalize many important representation-theor
etic families of polynomials\, such as Jack polynomials\, Hall-Littlewood
polynomials\, affine Demazure characters\, and Whittaker functions of GL_r
(F) (where F is a non-Archimedean field). They may be constructed using th
e basic representation of the corresponding double affine Hecke algebra (D
AHA): a particular commutative subalgebra of the DAHA acts semisimply on t
he space of polynomials\, and the (nonsymmetric) Macdonald polynomials are
the simultaneous eigenfunctions. In 2018\, Sahi\, Stokman\, and Venkatesw
aran constructed a generalization of this DAHA action\, recovering the met
aplectic Weyl group action of Chinta and Gunnells. As a consequence\, they
discovered a new family of polynomials\, called SSV polynomials\, that ge
neralize both Macdonald polynomials and Whittaker functions of metaplectic
covers of GL_r(F). We will give a combinatorial formula for these SSV pol
ynomials in terms of alcove walks\, generalizing Ram and Yip's formula for
Macdonald polynomials.\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (Rutgers University—New Brunswick)
DTSTART:20210402T160000Z
DTEND:20210402T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/13
DESCRIPTION:Title: Geometric properties of sheaves of coinvariants an
d conformal blocks\nby Chiara Damiolini (Rutgers University—New Brun
swick) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n\nAbstr
act\nOne method to study the moduli space of stable pointed curves is via
the study of vector bundles on them as they can yield interesting maps to
projective spaces. An effective way to produce such vector bundles is thro
ugh representations of vertex operator algebras: more precisely attached t
o n simple modules over a vertex opearator algebra of CohFT type\, we can
construct sheaves of coinvariants over the space of stable n-pointed curve
s. This generalizes the construction of coinvariants associated with repre
sentations of affine Lie algebras. In this talk I will focus on some geome
tric properties of these sheaves\, especially on global generation. Invest
igating this property we can see phenomena that did not occur for coinvari
ants associated with affine Lie algebra representations. This is based on
joint work with A. Gibney and N. Tarasca and ongoing work with A. Gibney.\
n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abid Ali (Rutgers University—New Brunswick)
DTSTART:20210430T160000Z
DTEND:20210430T170000Z
DTSTAMP:20260422T212857Z
UID:Rutgers_Lie_Group_Quantum_Math/14
DESCRIPTION:by Abid Ali (Rutgers University—New Brunswick) as part of Ru
tgers Lie Group/Quantum Mathematics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Rutgers_Lie_Group_Quantum_Math/
14/
END:VEVENT
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