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BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART;VALUE=DATE-TIME:20210531T131500Z
DTEND;VALUE=DATE-TIME:20210531T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5714@indico.ipmu.jp
DESCRIPTION:Hosted on Gather Town\n\nhttps://indico.ipmu.jp/event/387/cont
ributions/5714/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5714/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Whipple formula revisited
DTSTART;VALUE=DATE-TIME:20210601T000000Z
DTEND;VALUE=DATE-TIME:20210601T011500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5715@indico.ipmu.jp
DESCRIPTION:Speakers: Ling Long (Louisiana State U.)\nA well-known formula
of Whipple relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)
$. In this paper we revisit this relation from the viewpoint of the underl
ying hypergeometric data $HD$\, to which there are also associated hyperge
ometric character sums and Galois representations. We explain a special st
ructure behind Whipple's formula when the hypergeometric data $HD$ are pri
mitive and defined over rationals. As a consequence\, the values of the co
rresponding hypergeometric character sums can be explicitly expressed in t
erms of Fourier coefficients of certain modular forms. We further relate
the hypergeometric values $_7F_6(1)$ in Whipple's formula to the periods
of modular forms.\n\nhttps://indico.ipmu.jp/event/387/contributions/5715/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5715/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modularity\, Integrability\, and Logarithmic Invariants
DTSTART;VALUE=DATE-TIME:20210603T013000Z
DTEND;VALUE=DATE-TIME:20210603T024500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5729@indico.ipmu.jp
DESCRIPTION:Speakers: Sergei Gukov (Caltech)\nThe goal of the talk is to e
xplain new ways in which exotic types of modularity\, associated with log-
CFT's\, appear in 3d supersymmetric theories\, 3-manifold topology\, and l
attice integrable models.\n\nhttps://indico.ipmu.jp/event/387/contribution
s/5729/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5729/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Supersymmetric Interface Defects\, Brane Parallel Transport and
Higgs-Coulomb Duality
DTSTART;VALUE=DATE-TIME:20210531T100000Z
DTEND;VALUE=DATE-TIME:20210531T111500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5712@indico.ipmu.jp
DESCRIPTION:Speakers: Dimitrii Galakhov (Kavli IPMU\, U. Tokyo)\nWe concen
trate on a treatment of a Higgs-Coulomb duality as an absence of manifest
phase transition between ordered and disordered phases of 2d N=(2\,2) theo
ries. We consider these examples of QFTs in the Schrödinger picture and i
dentify Hilbert spaces of BPS states with morphisms in triangulated Abelia
n categories of D-brane boundary conditions. As a result of Higgs-Coulomb
duality D-brane categories on IR vacuum moduli spaces are equivalent\, thi
s resembles an analog of homological mirror symmetry. Following constructi
on ideas behind the Gaiotto-Moore-Witten algebra of the infrared one is ab
le to introduce interface defects in these theories and associate them to
D-brane parallel transport functors. We concentrate on surveying simple ex
amples\, analytic when possible calculations\, numerical estimates and sim
ple physical picture behind curtains of geometric objects. Categorificatio
n of hypergeometric series analytic continuation is derived as an Atiyah f
lop of the conifold. Finally we arrive to an interpretation of the braid g
roup action on the derived category of coherent sheaves on cotangent bundl
es to flag varieties as a categorification of Berry connection on the Faye
t-Illiopolous parameter space of a sigma-model with a quiver variety targe
t space. The talk is based on arXiv:2105.07602\n\nhttps://indico.ipmu.jp/e
vent/387/contributions/5712/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5712/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiral algebras with exceptional finite symmetry groups
DTSTART;VALUE=DATE-TIME:20210531T030000Z
DTEND;VALUE=DATE-TIME:20210531T041500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5709@indico.ipmu.jp
DESCRIPTION:Speakers: Brandon Rayhaun (Stanford U.)\nThe classification of
finite simple groups is a remarkable theorem of modern mathematics which
says that every such group either a) belongs to one of three infinite fami
lies\, or b) is one of 26 exceptional cases\, which are called the sporadi
c groups. Of these 26 outliers\, 20 of them appear as subquotients inside
of the largest\, which is called the monster. It is natural to ask what ob
jects these groups act on by symmetries. In the case of the monster\, it i
s a cherished result of mathematical physics that it arises as the automor
phism group of a certain meromorphic conformal field theory of central cha
rge 24: the moonshine module. We show that the method of coset conformal f
ield theory can be effectively used to obtain chiral algebras which furnis
h several of the other sporadic groups as their symmetries. Moreover\, the
se chiral algebras embed into one another in the same way as do their auto
morphism groups\; that is to say\, we have discovered a functorial assignm
ent of subalgebras of the moonshine module to certain privileged subgroups
of the monster.\n\nhttps://indico.ipmu.jp/event/387/contributions/5709/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5709/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borcherds Algebras and 2d String Theory
DTSTART;VALUE=DATE-TIME:20210604T120000Z
DTEND;VALUE=DATE-TIME:20210604T131500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5713@indico.ipmu.jp
DESCRIPTION:Speakers: Sarah Harrison (McGill U.)\nBorcherds Kac-Moody (BKM
) algebras are a generalization of familiar Kac-Moody algebras with imagin
ary simple roots. On the one hand\, they were invented by Borcherds in his
proof of the monstrous moonshine conjectures and have many interesting co
nnections to new moonshines\, number theory and the theory of automorphic
forms. On the other hand\, there is an old conjecture of Harvey and Moore
that BPS states in string theory form an algebra that is in some cases a B
KM algebra and which is based on certain signatures of BKMs observed in 4d
threshold corrections and black hole physics. I will talk about the const
ruction of new BKMs superalgebras arising from self-dual vertex operator a
lgebras of central charge 12\, and comment on their relation to physical s
tring theories in 2 dimensions. Based on work with N. Paquette\, D. Persso
n\, and R. Volpato.\n\nhttps://indico.ipmu.jp/event/387/contributions/5713
/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5713/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arborescent and non-arborescent knots & links
DTSTART;VALUE=DATE-TIME:20210604T070000Z
DTEND;VALUE=DATE-TIME:20210604T081500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5737@indico.ipmu.jp
DESCRIPTION:Speakers: Ramadevi Pichai (IIT Mumbai)\nFinding colored HOMFLY
-PT invariants for knots carrying arbitrary colors still needs new ideas.
I will briefly discuss the computational methods of obtaining colored HOM
FLY-PT invariants of arborescent knots/links and non-arborescent knots/li
nks and their limitations. Some of our recent works on mutant knots and hy
brid weaving knots will also be presented.\n\nhttps://indico.ipmu.jp/event
/387/contributions/5737/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5737/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Interpolation\, integrals\, and indices
DTSTART;VALUE=DATE-TIME:20210604T083000Z
DTEND;VALUE=DATE-TIME:20210604T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5738@indico.ipmu.jp
DESCRIPTION:Speakers: Andrei Okounkov (Columbia U.)\nThere is an interesti
ng topology behind such classical questions as interpolation and solving l
inear q-difference equations by integrals. It has to do with counting alge
braic curves in some very specific geometries\, which can be also phrased
as computing indices in certain (2+1) dimensional supersymmetric QFTs. The
talk will be an introduction to this circle of ideas.\n\nhttps://indico.i
pmu.jp/event/387/contributions/5738/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5738/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chern-Simons Invariants from Ensemble Averages
DTSTART;VALUE=DATE-TIME:20210603T030000Z
DTEND;VALUE=DATE-TIME:20210603T041500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5730@indico.ipmu.jp
DESCRIPTION:Speakers: Matthew Dodelson (Kavli IPMU\, U. Tokyo)\nI will dis
cuss the holographic duality between a free boson CFT associated with an i
ntegral lattice and Chern-Simons theory. The boundary CFT has a moduli spa
ce\, and averaging over the moduli space reproduces the partition function
of Chern-Simons theory in the bulk\, as a result of a theorem derived by
Siegel. For odd lattices the bulk theory is given by a spin Chern-Simons t
heory.\n\nhttps://indico.ipmu.jp/event/387/contributions/5730/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5730/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytic Langlands correspondence for complex curves
DTSTART;VALUE=DATE-TIME:20210601T013000Z
DTEND;VALUE=DATE-TIME:20210601T024500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5716@indico.ipmu.jp
DESCRIPTION:Speakers: Edward Frenkel (U.C. Berkeley)\nThe Langlands corres
pondence for complex curves has been traditionally formulated in terms of
sheaves rather than functions. Together with Pavel Etingof and David Kazhd
an (arXiv:1908.09677\, arXiv:2103.01509)\, we have formulated an analytic
(or function-theoretic) version as a spectral problem for an algebra of co
mmuting operators acting on half-densities on the moduli space Bun_G of G-
bundles over a complex algebraic curve. This algebra is generated by the g
lobal differential operators on Bun_G (holomorphic and anti-holomorphic qu
antum Hitchin Hamiltonians) as well as integral operators\, which are anal
ytic analogues of the Hecke operators of the classical Langlands correspon
dence. We conjecture that the joint spectrum of this algebra (properly und
erstood) can be identified with the set of opers for the Langlands dual gr
oup of G whose monodromy is in the split real form (up to conjugation). Fu
rthermore\, we give an explicit formula relating the eigenvalues of the He
cke operators and the global differential operators.\n\nhttps://indico.ipm
u.jp/event/387/contributions/5716/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5716/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART;VALUE=DATE-TIME:20210603T144500Z
DTEND;VALUE=DATE-TIME:20210603T154500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5819@indico.ipmu.jp
DESCRIPTION:https://indico.ipmu.jp/event/387/contributions/5819/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5819/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polyakov Path Integral as Modular Parametrization (?): CM Elliptic
Curves as Target Spaces
DTSTART;VALUE=DATE-TIME:20210601T070000Z
DTEND;VALUE=DATE-TIME:20210601T081500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5717@indico.ipmu.jp
DESCRIPTION:Speakers: Taizan Watari (Kavli IPMU\, U. Tokyo)\nAn L-function
is defined for an algebraic variety with defining equations written only
with algebraic numbers as coefficients. For some classes of such varieties
\, a correspondence between those L-functions and modular forms has been o
bserved as pure mathematics. It is a natural question whether the modular
transformation in g=1 string-theory amplitudes has something to do with th
is phenomenon. \n\nWe argue for the class of varieties called elliptic cur
ves of Shimura type (implying complex multiplication) that the modular tra
nsformation can indeed be regarded as that of the g=1 world sheet\, and th
at certain class of g=1 correlation functions yield functions on the compl
ex upper half plane\, just like the theory of modular parametrization does
. Roles played by choice of the target space metric\, arithmetic model dep
endence\, and the needs for average within the ideal class group will also
be discussed along the way. \n\nThis presentation is based on two joint
works with Satoshi Kondo: \nhttps://arxiv.org/abs/1912.13294 and https:/
/arxiv.org/abs/1801.07464\n\nhttps://indico.ipmu.jp/event/387/contribution
s/5717/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5717/
END:VEVENT
BEGIN:VEVENT
SUMMARY:3D rank-0 N=4 SCFTs and non-unitary TQFTs
DTSTART;VALUE=DATE-TIME:20210531T070000Z
DTEND;VALUE=DATE-TIME:20210531T081500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5710@indico.ipmu.jp
DESCRIPTION:Speakers: Dongmin Gang (Seoul Natl. U & APCTP)\nI will talk ab
out a recently proposed correspondence between 3D rank-0 N=4 SCFTs and 3D
non-unitary TQFTs. Using the basic dictionaries of correspondence\, we de
rive the lower bound on F (3-sphere free energy)\, F >= -1/2 log((5-\\sqr
t{5})/10)=0.6429. The talk is based on arXiv:2103.09283.\n\nhttps://indico
.ipmu.jp/event/387/contributions/5710/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5710/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathieu Moonshine: Quarter BPS states at the Kummer point and near
by
DTSTART;VALUE=DATE-TIME:20210603T083000Z
DTEND;VALUE=DATE-TIME:20210603T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5731@indico.ipmu.jp
DESCRIPTION:Speakers: Anne Taormina (Durham U.)\nThe construction of $\\ma
thbb{Z}_2$ orbifolds of toroidal conformal field theories (CFTs) is induce
d by the Kummer construction of a K3 surface. These theories provide a van
tage point from which to study the quarter BPS states of K3 theories which
are at the heart of the Mathieu Moonshine phenomenon. In this talk\, we
argue that a non-trivial SU(2) action on a subspace of quarter BPS states
in these orbifold CFTs governs the pairing of states that lift from the BP
S bound upon a given type of deformation.\n\nhttps://indico.ipmu.jp/event/
387/contributions/5731/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5731/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Three Avatars of Mock Modularity
DTSTART;VALUE=DATE-TIME:20210602T120000Z
DTEND;VALUE=DATE-TIME:20210602T131500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5726@indico.ipmu.jp
DESCRIPTION:Speakers: Atish Dabholkar (ICTP Trieste)\nMock theta functions
were introduced by Ramanujan in his famous last letter to Hardy in 1920 b
ut were properly understood only recently with the work of Zwegers in 2002
. I will describe three manifestations of this apparently exotic mathemati
cs in three important physical contexts of holography\, topology and dua
lity where mock modularity has come to play in important role. \n \nIn par
ticular\, I will derive a holomorphic anomaly equation for the indexed pa
rtition function of a two-dimensional CFT2 dual to AdS3 that counts the bl
ack hole degeneracies\, and for Vafa-Witten partition function for twiste
d four dimensional N=4 super Yang-Mills theory on CP2 for the gauge group
SO(3) that counts instantons. The holomorphic kernel of this equation is
not modular but `mock modular’ and one obtains correct modular propertie
s only after including certain `anomalous’ nonholomorphic boundary cont
ributions. This phenomenon can be related to the holomorphic anomaly of t
he elliptic genus of a two-dimensional noncompact supersymmetric sigma mod
el\, and in a simpler context of quantum mechanics to the Atiyah-Patodi-Si
nger eta invariant. \n \nMock modularity is thus essential to exhibit mod
ular symmetries expected from the AdS3/CFT2 holographic equivalence in q
uantum gravity and the S-duality symmetry of four-dimensional quantum ga
uge theories.\n\nhttps://indico.ipmu.jp/event/387/contributions/5726/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5726/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matrix integrals & the two-sphere partition function
DTSTART;VALUE=DATE-TIME:20210601T083000Z
DTEND;VALUE=DATE-TIME:20210601T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5718@indico.ipmu.jp
DESCRIPTION:Speakers: Beatrix Mühlmann (U. Amsterdam)\nWe explore the two
-sphere partition function in two-dimensional quantum gravity coupled to c
onformal matter and the relation to matrix integrals. We discuss how such
two-dimensional models may shed light on Euclidean gravity with a positive
cosmological constant.\n\nhttps://indico.ipmu.jp/event/387/contributions/
5718/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5718/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Towards a generic space of BPS states for K3
DTSTART;VALUE=DATE-TIME:20210603T100000Z
DTEND;VALUE=DATE-TIME:20210603T111500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5732@indico.ipmu.jp
DESCRIPTION:Speakers: Katrin Wendland (Freiburg U.)\nThis talk will focus
on the notion of a "generic space of states" of K3 theories\, which can se
rve as an ingredient of the symmetry surfing idea in Mathieu Moonshine.\n\
nhttps://indico.ipmu.jp/event/387/contributions/5732/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5732/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum invariants\, q-series\, DAHA
DTSTART;VALUE=DATE-TIME:20210603T000000Z
DTEND;VALUE=DATE-TIME:20210603T011500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5728@indico.ipmu.jp
DESCRIPTION:Speakers: Kazuhiro Hikami (Kyushu U.)\nWe will review some pro
perties of colored Jones polynomial and WRT invariants from the viewpoint
of the volume conjecture based on Habiro's expansion.\n\nhttps://indico.ip
mu.jp/event/387/contributions/5728/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5728/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Narain to Narnia
DTSTART;VALUE=DATE-TIME:20210601T100000Z
DTEND;VALUE=DATE-TIME:20210601T111500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5719@indico.ipmu.jp
DESCRIPTION:Speakers: Ida Zadeh (ICTP Trieste)\nRecently\, a new holograph
ic correspondence was discovered between an ensemble average of toroidal c
onformal field theories in two dimensions and an abelian Chern-Simons theo
ry in three dimensions coupled to topological gravity. I will discuss a ge
neralisation of this duality for three families of conformal field theorie
s and show that the correspondence works for toroidal orbifolds but not fo
r K3/Calabi-Yau sigma-models and not always for the minimal models. For to
roidal orbifolds\, the holographic correspondence is extended to correlati
on functions of twist operators by using topological properties of rationa
l tangles in the three-dimensional ball.\n\nhttps://indico.ipmu.jp/event/3
87/contributions/5719/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5719/
END:VEVENT
BEGIN:VEVENT
SUMMARY:One-Level density for cubic characters over the Eisenstein field
DTSTART;VALUE=DATE-TIME:20210602T013000Z
DTEND;VALUE=DATE-TIME:20210602T024500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5723@indico.ipmu.jp
DESCRIPTION:Speakers: Chantal David (Concordia U.)\nKatz and Sarnak conjec
tured that statistics on zeroes of a family of L-functions on the critical
line should match statistics on eigenvalues of characteristic polynomials
of a group of random matrices\, where the group is chosen according to th
e properties of the family. For example\, the family of L-functions attach
ed to quadratic Dirichlet characters corresponds to symplectic matrices\,
and evidence for the conjecture of Katz and Sarnak was obtained by provin
g that the one-level density of zeroes of quadratic Dirichlet L-functions
matches the one-level density for eigenvalues of characteristic polynomial
s of symplectic matrices\,\nfor special test functions (with limited suppo
rt of the Fourier transform) by Ozluk and Snyder in 1999. Since the suppo
rt of the Fourier transform of the test function is large enough\, they ca
n deduce that more than $93.75 \\%$ of the L-functions attached to quadrat
ic Dirichlet characters are such that $L(1/2\, \\chi) \\neq 0$\, giving ev
idence for a well-known conjecture of Chowla. The full conjecture of Katz-
Sarnak\n(without any restrictions on the support of the Fourier transform)
implies that $100 \\%$ of the L-functions attached to quadratic Dirichlet
characters are such that $L(1/2\, \\chi) \\neq 0$.\n\nWe will review thos
e results and consider the case of L-functions attached to cubic Dirichle
t characters. We prove the first result towards the Katz and Sarnak conjec
ture for test functions with support of the Fourier transform large enough
to obtain a positive proportion of L-functions attached to cubic Dirichl
et characters such that $L(1/2\, \\chi) \\neq 0$.\n\nJoint work with Ahmet
M. Guloglu.\n\nhttps://indico.ipmu.jp/event/387/contributions/5723/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5723/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taking the Limit: Quantum Modular Forms in Moonshine\, Physics and
Topology
DTSTART;VALUE=DATE-TIME:20210603T120000Z
DTEND;VALUE=DATE-TIME:20210603T131500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5733@indico.ipmu.jp
DESCRIPTION:Speakers: Miranda Cheng (U. Amsterdam)\nOften it is useful to
study the "boundary condition"\, namely the behaviour near the cusps\, of
functions on the upper-half plane. This leads naturally to the concept of
quantum modular forms\, which are functions on rational numbers that have
rather mysterious weak modular properties generalizing modular forms and m
ock modular forms. In this talk I will discuss how considerations of bound
ary conditions lead to interesting application of quantum modular forms in
the inter-connected subjects of moonshine\, physics and topology.\n\nhttp
s://indico.ipmu.jp/event/387/contributions/5733/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5733/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khovanov Homology from Mirror Symmetry
DTSTART;VALUE=DATE-TIME:20210531T000000Z
DTEND;VALUE=DATE-TIME:20210531T011500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5707@indico.ipmu.jp
DESCRIPTION:Speakers: Mina Aganagic (U.C. Berkeley)\nKhovanov showed\, mor
e than 20 years ago\, that there is a deeper theory underlying the Jones p
olynomial. The knot categorification problem is to find a uniform descript
ion of this theory\, for all gauge groups\, which originates from physics.
I found two solutions to this problem\, related by a version of two dimen
sional homological mirror symmetry. They are based on two descriptions of
the theory that lives on defects of the six dimensional (0\,2) CFT\, which
are supported on a link times time. \n\nThe theory turns out to be solvab
le explicitly. It is also more efficient\, often exponentially so\, than K
hovanov's original approach.\n\nhttps://indico.ipmu.jp/event/387/contribut
ions/5707/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5707/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantization by Branes And Geometric Langlands
DTSTART;VALUE=DATE-TIME:20210601T120000Z
DTEND;VALUE=DATE-TIME:20210601T131500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5720@indico.ipmu.jp
DESCRIPTION:Speakers: Edward Witten (IAS\, Princeton)\nhttps://indico.ipmu
.jp/event/387/contributions/5720/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5720/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion
DTSTART;VALUE=DATE-TIME:20210601T131500Z
DTEND;VALUE=DATE-TIME:20210601T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5721@indico.ipmu.jp
DESCRIPTION:Hosted via Gather Town\n\nhttps://indico.ipmu.jp/event/387/con
tributions/5721/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5721/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Supersymmetric Flux Compactifications and Calabi-Yau Modularity
DTSTART;VALUE=DATE-TIME:20210604T000000Z
DTEND;VALUE=DATE-TIME:20210604T011500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5735@indico.ipmu.jp
DESCRIPTION:Speakers: Richard Nally (Stanford U.)\nMany familiar construct
ions in string theory are rooted in the complex geometry of the compact di
mensions. On the other hand\, many recent advances in mathematics come fro
m arithmetic geometry\, where we consider the properties of varieties over
smaller fields such as Q. In this talk\, following recent work (arXiv:200
1.06022\, arXiv:2010.07285) with S. Kachru and W. Yang\, I will explain ho
w string theory can be related to arithmetic. In particular\, I will argue
that supersymmetric flux vacua admit arithmetic structures closely relate
d to those of elliptic curves\, and moreover that these arithmetic structu
res are related to the geometry of the F-theory description of the flux co
mpactification.\n\nhttps://indico.ipmu.jp/event/387/contributions/5735/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5735/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Mechanics of bipartite ribbon graphs and Kronecker coeffic
ients
DTSTART;VALUE=DATE-TIME:20210602T083000Z
DTEND;VALUE=DATE-TIME:20210602T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5724@indico.ipmu.jp
DESCRIPTION:Speakers: Sanjaye Ramgoolam (QMUL & U. Witwatersrand)\nI descr
ibe a family of algebras $K(n)$\, one for every positive integer n\, relat
ed to the group algebra of the symmetric group $S_n$. These algebras have
a basis labelled by bi-partite ribbon graphs with $n$ edges. They also hav
e a decomposition into matrix blocks labelled by triples of Young diagram
s with $n$ boxes\, with matrix block size equal to the Kronecker coefficie
nt $C$ for the triple. This leads to algorithms for the determination of
sub-lattices in the lattice of ribbon graphs\, of dimensions $C^2$ and $
C$\, equipped with bases constructed from null vectors of integer matrices
. Some of the algorithms are realised in quantum mechanical systems where
the quantum states are bipartite ribbon graphs. Using the known connection
s between bipartite ribbon graphs and Belyi maps\, these quantum systems h
ave an interpretation as models of quantum membranes.\n\nhttps://indico.ip
mu.jp/event/387/contributions/5724/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5724/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the arithmetic of Calabi-Yau manifolds: periods\, zeta function
s and attractor varieties
DTSTART;VALUE=DATE-TIME:20210604T100000Z
DTEND;VALUE=DATE-TIME:20210604T111500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5739@indico.ipmu.jp
DESCRIPTION:Speakers: Xenia de la Ossa (Oxford U.)\nIn this seminar I will
discuss the arithmetic of Calabi-Yau 3-folds. The main goal is to explore
whether there are questions of common interest in this context to physici
sts\, number theorists and geometers. The main quantities of interest in
the arithmetic context are the numbers of points of the manifold considere
d as a variety over a finite field. We are interested in the computation o
f these numbers and their dependence on the moduli of the variety. The su
rprise for a physicist is that the numbers of points over a finite field a
re also given by expression that involve the periods of a manifold. The nu
mber of points are encoded in the local zeta function\, about which much i
s known in virtue of the Weil conjectures. I will discuss interesting t
opics related to the zeta function and the appearance of modularity for on
e parameter families of Calabi-Yau manifolds.\nA topic I will stress is th
at for these families there are values of the parameter for which the mani
fold becomes singular and for these values the zeta function degenerates a
nd exhibits modular behaviour. I will report (on joint work with Philip
Candelas\, Mohamed Elmi and Duco van Straten) on an example for which the
quartic numerator of the zeta function factorises into two quadrics at sp
ecial values of the parameter which satisfy an algebraic equation with coe
fficients in Q (so independent of any particular prime)\, and for which th
e underlying manifold is smooth. We note that these factorisations are du
e to a splitting of the Hodge structure and that these special values of t
he parameter are rank two attractor points in the sense of type IIB superg
ravity. Modular groups and modular forms arise in relation to these attra
ctor points.\nTo our knowledge\, the rank two attractor points that were f
ound by the application of these number theoretic techniques\, provide the
first explicit examples of such points for Calabi-Yau manifolds of full S
U(3) holonomy.\n\nhttps://indico.ipmu.jp/event/387/contributions/5739/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5739/
END:VEVENT
BEGIN:VEVENT
SUMMARY:BPS (shifted) quiver Yangians and representations from colored cry
stals
DTSTART;VALUE=DATE-TIME:20210531T083000Z
DTEND;VALUE=DATE-TIME:20210531T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5711@indico.ipmu.jp
DESCRIPTION:Speakers: Wei Li (ITP\, Chinese Academy of Sciences)\nI will f
irst explain how to construct BPS algebras for string theory on general to
ric Calabi-Yau threefolds\, based on the 3D colored crystals that describe
BPS states of the system. The resulting algebras are shifted quiver Yangi
ans Y(Q\,W) that are associated with the quiver and the superpotential of
the theory. Then I will show how to construct representations of a shifted
quiver Yangian from general subcrystals of the canonical crystal\, and ho
w the shape of the subcrystal determines the framing of the quiver.\n\nhtt
ps://indico.ipmu.jp/event/387/contributions/5711/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5711/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From Little Strings to M5-branes and Number Theory via a Quasi-Top
ological Sigma Model on Loop Group
DTSTART;VALUE=DATE-TIME:20210604T013000Z
DTEND;VALUE=DATE-TIME:20210604T024500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5736@indico.ipmu.jp
DESCRIPTION:Speakers: Meng-Chwan Tan (NUS Singapore)\nWe unravel the groun
d states and left-excited states of the A_{k-1} N=(2\,0) little string the
ory. Via a theorem by Atiyah\, these sectors can be captured by a supersym
metric quasi-topological sigma model on CP^1 with target space the based l
oop group of SU(k). The ground states\, described by L^2-cohomology classe
s\, form modules over an affine Lie algebra\, while the left-excited state
s\, described by chiral differential operators\, form modules over a toroi
dal Lie algebra. We also apply our results to unravel the 1/2 and 1/4 BPS
sectors of the M5-brane worldvolume theory\, which spectrum we find to be
captured by cousins of modular and automorphic forms\, respectively\, that
reveal an intrinsic S- and T-duality of the worldvolume theory.\n\nhttps:
//indico.ipmu.jp/event/387/contributions/5736/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5736/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Two new avatars of Thompson Moonshine
DTSTART;VALUE=DATE-TIME:20210603T133000Z
DTEND;VALUE=DATE-TIME:20210603T144500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5708@indico.ipmu.jp
DESCRIPTION:Speakers: Jeffrey Harvey (U. Chicago)\nAmong other things I wi
ll discuss the relationship between Thompson moonshine at weight 1/2 and G
eneralized Monstrous Moonshine at weight zero.\n\nhttps://indico.ipmu.jp/e
vent/387/contributions/5708/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5708/
END:VEVENT
BEGIN:VEVENT
SUMMARY:2d Categorical Wall-Crossing With Twisted Masses\, And An Applicat
ion To Knot Invariants
DTSTART;VALUE=DATE-TIME:20210602T000000Z
DTEND;VALUE=DATE-TIME:20210602T011500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5722@indico.ipmu.jp
DESCRIPTION:Speakers: Gregory Moore (Rutgers)\nWe review how supersymmetri
c quantum mechanics naturally leads to several \nstandard constructions in
homological algebra. We apply these ideas to 2d Landau-Ginzburg \nmodels
with (2\,2) supersymmetry to discuss wall-crossing. Some aspects of the we
b formalism \nare reviewed and applied to the categorification of the Ceco
tti-Vafa wall-crossing formula for \nBPS invariants. We then sketch the ge
neralization to include twisted masses. In the final part of \nthe talk we
sketch how some of these ideas give a natural framework for understanding
a \nrecent conjecture of Garoufalidis\, Gu\, and Marino and lead to poten
tially new knot invariants. \nThe talk is based on work done with Ahsan Kh
an and recent discussions with Ahsan Khan\, Davide \nGaiotto\, and Fei Yan
.\n\nhttps://indico.ipmu.jp/event/387/contributions/5722/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5722/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graviton scattering and differential equations in automorphic form
s
DTSTART;VALUE=DATE-TIME:20210531T120000Z
DTEND;VALUE=DATE-TIME:20210531T131500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5740@indico.ipmu.jp
DESCRIPTION:Speakers: Kim Klinger-Logan (Rutgers)\nGreen\, Russo\, and Van
hove have shown that the scattering amplitude for gravitons (hypothetical
particles of gravity represented by massless string states) is closely rel
ated to automorphic forms through differential equations. Green\, Miller\,
Russo\, Vanhove\, Pioline\, and K-L have used a variety of methods to sol
ve eigenvalue problems for the invariant Laplacian on different moduli spa
ces to compute the coefficients of the scattering amplitude of four gravit
ons. We will examine two methods for solving the most complicated of these
differential equations on $SL_2(\\mathbb{Z})\\backslash\\mathfrak{H}$. Ti
me permitting\, we will discuss recent work with S. Miller to improve upon
his original method for solving this equation.\n\nhttps://indico.ipmu.jp/
event/387/contributions/5740/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5740/
END:VEVENT
BEGIN:VEVENT
SUMMARY:QFT's for Non-Semisimple TQFT's
DTSTART;VALUE=DATE-TIME:20210602T100000Z
DTEND;VALUE=DATE-TIME:20210602T111500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5725@indico.ipmu.jp
DESCRIPTION:Speakers: Tudor Dimofte (U.C. Davis & Edinburg U.)\nThirty yea
rs ago\, work of Witten and Reshetikhin-Turaev activated the study of quan
tum invariants of links and three-manifolds. A cornerstone of subsequent d
evelopments\, leading up to our current knot-homology conference\, was a t
hree-pronged approach involving 1) quantum field theory (Chern-Simons)\; 2
) rational VOA's (WZW)\; and 3) semisimple representation theory of quantu
m groups. The second and third perspectives have since been extended\, to
logarithmic VOA's and related non-semisimple quantum-group categories. I w
ill propose a family of 3d quantum field theories that similarly extend th
e first perspective to a non-semisimple (and more so\, derived) regime. Th
ey support boundary VOA's whose module categories equivalent to modules fo
r small quantum groups at even roots of unity. \nThis is joint work with T
. Creutzig\, N. Garner\, and N. Geer\, and also related to recent work of
Gukov-Hsin-Nakajima-Park-Pei-Sopenko.\n\nhttps://indico.ipmu.jp/event/387/
contributions/5725/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5725/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Opening comments
DTSTART;VALUE=DATE-TIME:20210530T235000Z
DTEND;VALUE=DATE-TIME:20210530T235500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5706@indico.ipmu.jp
DESCRIPTION:Speakers: Abhiram Kidambi (Kavli IPMU\, U. Tokyo)\nhttps://ind
ico.ipmu.jp/event/387/contributions/5706/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5706/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART;VALUE=DATE-TIME:20210604T131500Z
DTEND;VALUE=DATE-TIME:20210604T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5741@indico.ipmu.jp
DESCRIPTION:Hosted via Gather Town\n\nhttps://indico.ipmu.jp/event/387/con
tributions/5741/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5741/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART;VALUE=DATE-TIME:20210602T131500Z
DTEND;VALUE=DATE-TIME:20210602T151500Z
DTSTAMP;VALUE=DATE-TIME:20240624T172340Z
UID:indico-contribution-387-5727@indico.ipmu.jp
DESCRIPTION:Hosted via Gather Town\n\nhttps://indico.ipmu.jp/event/387/con
tributions/5727/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5727/
END:VEVENT
END:VCALENDAR