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BEGIN:VEVENT
SUMMARY:Bin Gui (Rutgers University)
DTSTART:20201106T170000Z
DTEND:20201106T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/1
DESCRIPTION:Title: Convergence of sewing conformal blocks\n
by Bin Gui (Rutgers University) as part of Rutgers Lie Group/Quantum Mathe
matics Seminar\n\n\nAbstract\nConformal blocks (i.e. chiral correlation fu
nctions) are central objects of chiral CFT. Given a VOA V and a compact Ri
emann surface C with marked points\, one can define conformal blocks to be
linear functionals on tensor products of V-modules satisfying certain (co
)invariance properties related to V and C. For instance\, the vertex opera
tor of a VOA V\, or more generally\, an intertwining operator of V\, is a
conformal block associated to V and the genus 0 Riemann surface with 3 mar
ked points. Taking contractions/q-traces is a main way of constructing hig
her genus conformal blocks from low genus ones\, and it has been conjectur
ed for a long time that the contractions always converge. In this talk\, I
will report recent work on a solution of this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Gemünden (ETH Zürich)
DTSTART:20201120T170000Z
DTEND:20201120T180000Z
DTSTAMP:20260404T100033Z
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 Zürich) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\
n\nAbstract\nHolomorphic vertex operator algebras at central charges up to
24 have been almost fully classified and it appears that they can all be
constructed as cyclic orbifolds of lattice vertex operator algebras. At th
e same time\, very little is known about the situation at higher central c
harge. Intuition from physics tells us that higher central charge analogue
s of the moonshine vertex operator algebra may exist\, but so far all atte
mpts at their construction have failed. The goal of this work is to explor
e the set of holomorphic vertex operator algebras at higher central charge
using non-abelian orbifold theory.\nI will begin the talk with a review o
f the orbifold theory of strongly rational vertex operator algebras. Then
I will develop a theory of holomorphic extensions of metacyclic orbifolds
as a generalisation of the cyclic theory.\n\nFinally\, I will prove the ex
istence of a holomorphic vertex operator algebra at central charge 72 that
cannot be constructed as a cyclic orbifold of a lattice vertex operator a
lgebra. If there is time I will discuss some of the challenges arising in
trying to construct analogues of the moonshine module.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_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:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/3
DESCRIPTION:Title: Complete pro-unipotent automorphism group fo
r the monster Lie algebra\nby Lisa Carbone (Rutgers University and Ins
titute for Advanced Study\, School of Natural Science) as part of Rutgers
Lie Group/Quantum Mathematics Seminar\n\n\nAbstract\nWe construct a comple
te pro-unipotent group of automorphisms for a completion of the monster Li
e algebra. We also construct an analog of the exponential map and Adjoint
representation. This gives rise to some useful identities involving imagin
ary root vectors.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Li (SUNY-Albany)
DTSTART:20210129T170000Z
DTEND:20210129T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/4
DESCRIPTION:Title: Arc spaces\, vertex algebras and principal s
ubspaces\nby Hao Li (SUNY-Albany) as part of Rutgers Lie Group/Quantum
Mathematics Seminar\n\n\nAbstract\nArc spaces were originally introduced
in algebraic geometry to study singularities. More recently they show in c
onnections to vertex algebras. There is a closed embedding from the singul
ar support of a vertex algebra V into the arc space of associated scheme o
f V. We call a vertex algebra "classically free" if this embedding is an i
somorphism. In this introductory survey talk\, we will first introduce arc
spaces and some of its backgrounds. Then we will provide several examples
of classically free vertex algebras including Feigin-Stoyanovsky principa
l subspaces\, and explain their applications in differential algebras\, $q
$-series identities\, etc. In particular\, we will show the classically fr
eeness of principal subspaces of type A at level 1 by using a method of fi
ltrations and identities from quantum dilogarithm or quiver representation
s. As a result\, we obtain new presentations and graded dimensions of the
principal subspaces of type A at level 1\, which can be thought of as the
continuation of previous works by Calinescu\, Lepowsky and Milas. The clas
sically freeness of some principal subspaces which possess free fields rea
lisation will also be discussed. Most of the talk is based on the joint wo
rk with A. Milas.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilit Martirosyan (University of North Carolina\, Wilmington)
DTSTART:20210205T170000Z
DTEND:20210205T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/5
DESCRIPTION:Title: Braided rigidity for path algebras (joint wo
rk with Hans Wenzl)\nby Lilit Martirosyan (University of North Carolin
a\, Wilmington) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n
\n\nAbstract\nPath algebras are a convenient way of describing decompositi
ons of tensor powers of an object in a tensor category. If the category is
braided\, 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 t
he path algebra and the representations of B2. We show that besides the kn
own classical cases also the braid representations for the path algebra fo
r the 7-dimensional representation of G2 satisfies the rigidity condition\
, provided B3 generates End(V^{⊗3}). We obtain a complete classification
of ribbon tensor categories with the fusion rules of g(G2) if this condit
ion is satisfied.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Sergel (Rutgers University - New Brunswick)
DTSTART:20210212T170000Z
DTEND:20210212T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/6
DESCRIPTION:Title: Positivity of interpolation polynomials\
nby Emily Sergel (Rutgers University - New Brunswick) as part of Rutgers L
ie Group/Quantum Mathematics Seminar\n\n\nAbstract\nThe interpolation poly
nomials are a family of inhomogeneous symmetric polynomials characterized
by simple vanishing properties. In 1996\, Knop and Sahi showed that their
top homogeneous components are Jack polynomials. For this reason these pol
ynomials are sometimes called interpolation Jack polynomials\, shifted Jac
k polynomials\, or Knop-Sahi polynomials.\nWe prove Knop and Sahi's main c
onjecture from 1996\, which asserts that\, after a suitable normalization\
, the interpolation polynomials have positive integral coefficients. This
result generalizes Macdonald's conjecture for Jack polynomials that was pr
oved by Knop and Sahi in 1997. Moreover\, we give a combinatorial expansio
n for the interpolation polynomials that exhibits the desired positivity p
roperty.\n\nThis is joint work with Y. Naqvi and S. Sahi.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antun Milas (SUNY - Albany)
DTSTART:20210219T170000Z
DTEND:20210219T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/7
DESCRIPTION:Title: Graph q-series\, graph schemes\, and 4d/2d c
orrespondences\nby Antun Milas (SUNY - Albany) as part of Rutgers Lie
Group/Quantum Mathematics Seminar\n\n\nAbstract\nTo any graph with n nodes
we associate two n-fold q-series\, with single and double poles\, closely
related to Nahm's sum associated to a positive definite symmetric bilinea
r form.\nQuite remarkably series with "double poles" sometimes capture Sch
ur's indices of 4d N = 2 superconformal field theories (SCFTs) and thus\,
under 2d/4d correspondence\, they give new character formulas of certain v
ertex operator algebras.\nIf poles are simple\, they arise in algebraic ge
ometry as Hilbert-Poincare series of "graph" arc algebras. These q-series
are poorly understood and seem to exhibit peculiar modular transformation
behavior.\nIn this talk\, we explain how these "counting" functions arise
in different areas of mathematics and physics. This talk will be fairly ac
cessible\, assuming minimal background. No familiarity with concepts like
vertex algebras and 4d N=2 SCFT is needed.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haisheng Li (Rutgers University at Camden)
DTSTART:20210409T160000Z
DTEND:20210409T170000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/8
DESCRIPTION:Title: Deforming vertex algebras by module and como
dule actions of vertex bialgebras\nby Haisheng Li (Rutgers University
at Camden) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n\nA
bstract\nPreviously\, we introduced a notion of vertex bialgebra and a not
ion of module vertex algebra for a vertex bialgebra\, and gave a smash pro
duct construction of nonlocal vertex algebras. Here\, we introduce a notio
n of right comodule vertex algebra for a vertex bialgebra. Then we give a
construction of quantum vertex algebras from vertex algebras with a right
comodule vertex algebra structure and a compatible (left) module vertex al
gebra structure for a vertex bialgebra. As an application\, we obtain a fa
mily of deformations of the lattice vertex algebras. This is based on a jo
int work with Naihuan Jing\, Fei Kong\, and Shaobin Tan.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_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:20260404T100033Z
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://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Sadowski (Ursinus College)
DTSTART:20210423T160000Z
DTEND:20210423T170000Z
DTSTAMP:20260404T100033Z
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://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Carbone (Rutgers University and Institute for Advanced Study)
DTSTART:20210312T170000Z
DTEND:20210312T180000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/11
DESCRIPTION:Title: Imaginary root strings and Chevalley-Steinb
erg group commutators for hyperbolic Kac--Moody algebras\nby Lisa Carb
one (Rutgers University and Institute for Advanced Study) as part of Rutge
rs Lie Group/Quantum Mathematics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Saied (Rutgers University—New Brunswick)
DTSTART:20210326T160000Z
DTEND:20210326T170000Z
DTSTAMP:20260404T100033Z
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 Group/Quantum Mathematics Seminar\n\n\nAbstract\nMacdonald polynomial
s are homogeneous polynomials that generalize many important representatio
n-theoretic families of polynomials\, such as Jack polynomials\, Hall-Litt
lewood polynomials\, affine Demazure characters\, and Whittaker functions
of GL_r(F) (where F is a non-Archimedean field). They may be constructed u
sing the basic representation of the corresponding double affine Hecke alg
ebra (DAHA): a particular commutative subalgebra of the DAHA acts semisimp
ly on the space of polynomials\, and the (nonsymmetric) Macdonald polynomi
als are the simultaneous eigenfunctions. In 2018\, Sahi\, Stokman\, and Ve
nkateswaran constructed a generalization of this DAHA action\, recovering
the metaplectic Weyl group action of Chinta and Gunnells. As a consequence
\, they discovered a new family of polynomials\, called SSV polynomials\,
that generalize both Macdonald polynomials and Whittaker functions of meta
plectic covers of GL_r(F). We will give a combinatorial formula for these
SSV polynomials in terms of alcove walks\, generalizing Ram and Yip's form
ula for Macdonald polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (Rutgers University—New Brunswick)
DTSTART:20210402T160000Z
DTEND:20210402T170000Z
DTSTAMP:20260404T100033Z
UID:Rutgers_Lie_Group_Quantum_Math/13
DESCRIPTION:Title: Geometric properties of sheaves of coinvari
ants and conformal blocks\nby Chiara Damiolini (Rutgers University—N
ew Brunswick) as part of Rutgers Lie Group/Quantum Mathematics Seminar\n\n
\nAbstract\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 m
aps to projective spaces. An effective way to produce such vector bundles
is through representations of vertex operator algebras: more precisely att
ached to n simple modules over a vertex opearator algebra of CohFT type\,
we can construct sheaves of coinvariants over the space of stable n-pointe
d curves. This generalizes the construction of coinvariants associated wit
h representations of affine Lie algebras. In this talk I will focus on som
e geometric properties of these sheaves\, especially on global generation.
Investigating this property we can see phenomena that did not occur for c
oinvariants associated with affine Lie algebra representations. This is ba
sed on joint work with A. Gibney and N. Tarasca and ongoing work with A. G
ibney.\n
LOCATION:https://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abid Ali (Rutgers University—New Brunswick)
DTSTART:20210430T160000Z
DTEND:20210430T170000Z
DTSTAMP:20260404T100033Z
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://stable.researchseminars.org/talk/Rutgers_Lie_Group_Quantu
m_Math/14/
END:VEVENT
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