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BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART:20210531T131500Z
DTEND:20210531T151500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-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:20210601T000000Z
DTEND:20210601T011500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5715@indico.ipmu.jp
DESCRIPTION:Speakers: Ling Long (Louisiana State U.)\n\nA well-known formu
la 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 unde
rlying hypergeometric data $HD$\, to which there are also associated hyper
geometric character sums and Galois representations. We explain a special
structure behind Whipple's formula when the hypergeometric data $HD$ are p
rimitive and defined over rationals. As a consequence\, the values of the
corresponding hypergeometric character sums can be explicitly expressed in
terms of Fourier coefficients of certain modular forms. We further relat
e the hypergeometric values $_7F_6(1)$ in Whipple's formula to the perio
ds of modular forms.\n\nhttps://indico.ipmu.jp/event/387/contributions/571
5/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5715/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modularity\, Integrability\, and Logarithmic Invariants
DTSTART:20210603T013000Z
DTEND:20210603T024500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5729@indico.ipmu.jp
DESCRIPTION:Speakers: Sergei Gukov (Caltech)\n\nThe goal of the talk is to
explain new ways in which exotic types of modularity\, associated with lo
g-CFT's\, appear in 3d supersymmetric theories\, 3-manifold topology\, and
lattice integrable models.\n\nhttps://indico.ipmu.jp/event/387/contributi
ons/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:20210531T100000Z
DTEND:20210531T111500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5712@indico.ipmu.jp
DESCRIPTION:Speakers: Dimitrii Galakhov (Kavli IPMU\, U. Tokyo)\n\nWe conc
entrate on a treatment of a Higgs-Coulomb duality as an absence of manifes
t phase transition between ordered and disordered phases of 2d N=(2\,2) th
eories. We consider these examples of QFTs in the Schrödinger picture and
identify Hilbert spaces of BPS states with morphisms in triangulated Abel
ian categories of D-brane boundary conditions. As a result of Higgs-Coulom
b duality D-brane categories on IR vacuum moduli spaces are equivalent\, t
his resembles an analog of homological mirror symmetry. Following construc
tion ideas behind the Gaiotto-Moore-Witten algebra of the infrared one is
able to introduce interface defects in these theories and associate them t
o D-brane parallel transport functors. We concentrate on surveying simple
examples\, analytic when possible calculations\, numerical estimates and s
imple physical picture behind curtains of geometric objects. Categorificat
ion of hypergeometric series analytic continuation is derived as an Atiyah
flop of the conifold. Finally we arrive to an interpretation of the braid
group action on the derived category of coherent sheaves on cotangent bun
dles to flag varieties as a categorification of Berry connection on the Fa
yet-Illiopolous parameter space of a sigma-model with a quiver variety tar
get space. The talk is based on arXiv:2105.07602\n\nhttps://indico.ipmu.jp
/event/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:20210531T030000Z
DTEND:20210531T041500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5709@indico.ipmu.jp
DESCRIPTION:Speakers: Brandon Rayhaun (Stanford U.)\n\nThe classification
of finite simple groups is a remarkable theorem of modern mathematics whic
h says that every such group either a) belongs to one of three infinite fa
milies\, or b) is one of 26 exceptional cases\, which are called the spora
dic groups. Of these 26 outliers\, 20 of them appear as subquotients insid
e of the largest\, which is called the monster. It is natural to ask what
objects these groups act on by symmetries. In the case of the monster\, it
is a cherished result of mathematical physics that it arises as the autom
orphism group of a certain meromorphic conformal field theory of central c
harge 24: the moonshine module. We show that the method of coset conformal
field theory can be effectively used to obtain chiral algebras which furn
ish several of the other sporadic groups as their symmetries. Moreover\, t
hese chiral algebras embed into one another in the same way as do their au
tomorphism groups\; that is to say\, we have discovered a functorial assig
nment of subalgebras of the moonshine module to certain privileged subgrou
ps 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:20210604T120000Z
DTEND:20210604T131500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5713@indico.ipmu.jp
DESCRIPTION:Speakers: Sarah Harrison (McGill U.)\n\nBorcherds Kac-Moody (B
KM) algebras are a generalization of familiar Kac-Moody algebras with imag
inary simple roots. On the one hand\, they were invented by Borcherds in h
is proof of the monstrous moonshine conjectures and have many interesting
connections to new moonshines\, number theory and the theory of automorphi
c forms. On the other hand\, there is an old conjecture of Harvey and Moor
e that BPS states in string theory form an algebra that is in some cases a
BKM algebra and which is based on certain signatures of BKMs observed in
4d threshold corrections and black hole physics. I will talk about the con
struction of new BKMs superalgebras arising from self-dual vertex operator
algebras of central charge 12\, and comment on their relation to physical
string theories in 2 dimensions. Based on work with N. Paquette\, D. Pers
son\, and R. Volpato.\n\nhttps://indico.ipmu.jp/event/387/contributions/57
13/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5713/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arborescent and non-arborescent knots & links
DTSTART:20210604T070000Z
DTEND:20210604T081500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5737@indico.ipmu.jp
DESCRIPTION:Speakers: Ramadevi Pichai (IIT Mumbai)\n\nFinding colored HOMF
LY-PT invariants for knots carrying arbitrary colors still needs new idea
s. I will briefly discuss the computational methods of obtaining colored H
OMFLY-PT invariants of arborescent knots/links and non-arborescent knots/
links and their limitations. Some of our recent works on mutant knots and
hybrid weaving knots will also be presented.\n\nhttps://indico.ipmu.jp/eve
nt/387/contributions/5737/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5737/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Interpolation\, integrals\, and indices
DTSTART:20210604T083000Z
DTEND:20210604T094500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5738@indico.ipmu.jp
DESCRIPTION:Speakers: Andrei Okounkov (Columbia U.)\n\nThere is an interes
ting topology behind such classical questions as interpolation and solving
linear q-difference equations by integrals. It has to do with counting al
gebraic curves in some very specific geometries\, which can be also phrase
d as computing indices in certain (2+1) dimensional supersymmetric QFTs. T
he talk will be an introduction to this circle of ideas.\n\nhttps://indico
.ipmu.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:20210603T030000Z
DTEND:20210603T041500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5730@indico.ipmu.jp
DESCRIPTION:Speakers: Matthew Dodelson (Kavli IPMU\, U. Tokyo)\n\nI will d
iscuss the holographic duality between a free boson CFT associated with an
integral lattice and Chern-Simons theory. The boundary CFT has a moduli s
pace\, and averaging over the moduli space reproduces the partition functi
on of Chern-Simons theory in the bulk\, as a result of a theorem derived b
y Siegel. For odd lattices the bulk theory is given by a spin Chern-Simons
theory.\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:20210601T013000Z
DTEND:20210601T024500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5716@indico.ipmu.jp
DESCRIPTION:Speakers: Edward Frenkel (U.C. Berkeley)\n\nThe Langlands corr
espondence for complex curves has been traditionally formulated in terms o
f sheaves rather than functions. Together with Pavel Etingof and David Kaz
hdan (arXiv:1908.09677\, arXiv:2103.01509)\, we have formulated an analyti
c (or function-theoretic) version as a spectral problem for an algebra of
commuting 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
global differential operators on Bun_G (holomorphic and anti-holomorphic
quantum Hitchin Hamiltonians) as well as integral operators\, which are an
alytic analogues of the Hecke operators of the classical Langlands corresp
ondence. We conjecture that the joint spectrum of this algebra (properly u
nderstood) can be identified with the set of opers for the Langlands dual
group of G whose monodromy is in the split real form (up to conjugation).
Furthermore\, we give an explicit formula relating the eigenvalues of the
Hecke operators and the global differential operators.\n\nhttps://indico.i
pmu.jp/event/387/contributions/5716/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5716/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion session
DTSTART:20210603T144500Z
DTEND:20210603T154500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-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:20210601T070000Z
DTEND:20210601T081500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5717@indico.ipmu.jp
DESCRIPTION:Speakers: Taizan Watari (Kavli IPMU\, U. Tokyo)\n\nAn L-functi
on is defined for an algebraic variety with defining equations written onl
y with algebraic numbers as coefficients. For some classes of such varieti
es\, a correspondence between those L-functions and modular forms has been
observed as pure mathematics. It is a natural question whether the modula
r transformation in g=1 string-theory amplitudes has something to do with
this phenomenon. \n\nWe argue for the class of varieties called elliptic c
urves of Shimura type (implying complex multiplication) that the modular t
ransformation can indeed be regarded as that of the g=1 world sheet\, and
that certain class of g=1 correlation functions yield functions on the com
plex upper half plane\, just like the theory of modular parametrization do
es. Roles played by choice of the target space metric\, arithmetic model d
ependence\, and the needs for average within the ideal class group will al
so be discussed along the way. \n\nThis presentation is based on two joi
nt works with Satoshi Kondo: \nhttps://arxiv.org/abs/1912.13294 and https
://arxiv.org/abs/1801.07464\n\nhttps://indico.ipmu.jp/event/387/contributi
ons/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:20210531T070000Z
DTEND:20210531T081500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5710@indico.ipmu.jp
DESCRIPTION:Speakers: Dongmin Gang (Seoul Natl. U & APCTP)\n\nI will talk
about a recently proposed correspondence between 3D rank-0 N=4 SCFTs and
3D non-unitary TQFTs. Using the basic dictionaries of correspondence\, we
derive the lower bound on F (3-sphere free energy)\, F >= -1/2 log((5-\\s
qrt{5})/10)=0.6429. The talk is based on arXiv:2103.09283.\n\nhttps://indi
co.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:20210603T083000Z
DTEND:20210603T094500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5731@indico.ipmu.jp
DESCRIPTION:Speakers: Anne Taormina (Durham U.)\n\nThe construction of $\\
mathbb{Z}_2$ orbifolds of toroidal conformal field theories (CFTs) is indu
ced by the Kummer construction of a K3 surface. These theories provide a v
antage point from which to study the quarter BPS states of K3 theories whi
ch are at the heart of the Mathieu Moonshine phenomenon. In this talk\, w
e argue that a non-trivial SU(2) action on a subspace of quarter BPS state
s in these orbifold CFTs governs the pairing of states that lift from the
BPS bound upon a given type of deformation.\n\nhttps://indico.ipmu.jp/even
t/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:20210602T120000Z
DTEND:20210602T131500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5726@indico.ipmu.jp
DESCRIPTION:Speakers: Atish Dabholkar (ICTP Trieste)\n\nMock theta functio
ns were introduced by Ramanujan in his famous last letter to Hardy in 1920
but were properly understood only recently with the work of Zwegers in 20
02. I will describe three manifestations of this apparently exotic mathema
tics in three important physical contexts of holography\, topology and d
uality where mock modularity has come to play in important role. \n \nIn p
articular\, I will derive a holomorphic anomaly equation for the indexed
partition function of a two-dimensional CFT2 dual to AdS3 that counts the
black hole degeneracies\, and for Vafa-Witten partition function for twis
ted four dimensional N=4 super Yang-Mills theory on CP2 for the gauge grou
p SO(3) that counts instantons. The holomorphic kernel of this equation i
s not modular but `mock modular’ and one obtains correct modular propert
ies only after including certain `anomalous’ nonholomorphic boundary co
ntributions. This phenomenon can be related to the holomorphic anomaly of
the elliptic genus of a two-dimensional noncompact supersymmetric sigma m
odel\, and in a simpler context of quantum mechanics to the Atiyah-Patodi-
Singer eta invariant. \n \nMock modularity is thus essential to exhibit m
odular symmetries expected from the AdS3/CFT2 holographic equivalence in
quantum gravity and the S-duality symmetry of four-dimensional quantum
gauge 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:20210601T083000Z
DTEND:20210601T094500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5718@indico.ipmu.jp
DESCRIPTION:Speakers: Beatrix Mühlmann (U. Amsterdam)\n\nWe explore the t
wo-sphere partition function in two-dimensional quantum gravity coupled to
conformal matter and the relation to matrix integrals. We discuss how suc
h two-dimensional models may shed light on Euclidean gravity with a positi
ve cosmological constant.\n\nhttps://indico.ipmu.jp/event/387/contribution
s/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:20210603T100000Z
DTEND:20210603T111500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5732@indico.ipmu.jp
DESCRIPTION:Speakers: Katrin Wendland (Freiburg U.)\n\nThis talk will focu
s on the notion of a "generic space of states" of K3 theories\, which can
serve 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:20210603T000000Z
DTEND:20210603T011500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5728@indico.ipmu.jp
DESCRIPTION:Speakers: Kazuhiro Hikami (Kyushu U.)\n\nWe will review some p
roperties of colored Jones polynomial and WRT invariants from the viewpoin
t of the volume conjecture based on Habiro's expansion.\n\nhttps://indico.
ipmu.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:20210601T100000Z
DTEND:20210601T111500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5719@indico.ipmu.jp
DESCRIPTION:Speakers: Ida Zadeh (ICTP Trieste)\n\nRecently\, a new hologra
phic correspondence was discovered between an ensemble average of toroidal
conformal field theories in two dimensions and an abelian Chern-Simons th
eory in three dimensions coupled to topological gravity. I will discuss a
generalisation of this duality for three families of conformal field theor
ies and show that the correspondence works for toroidal orbifolds but not
for K3/Calabi-Yau sigma-models and not always for the minimal models. For
toroidal orbifolds\, the holographic correspondence is extended to correla
tion functions of twist operators by using topological properties of ratio
nal tangles in the three-dimensional ball.\n\nhttps://indico.ipmu.jp/event
/387/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:20210602T013000Z
DTEND:20210602T024500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5723@indico.ipmu.jp
DESCRIPTION:Speakers: Chantal David (Concordia U.)\n\nKatz and Sarnak conj
ectured that statistics on zeroes of a family of L-functions on the critic
al line should match statistics on eigenvalues of characteristic polynomia
ls of a group of random matrices\, where the group is chosen according to
the properties of the family. For example\, the family of L-functions atta
ched to quadratic Dirichlet characters corresponds to symplectic matrices\
, and evidence for the conjecture of Katz and Sarnak was obtained by prov
ing that the one-level density of zeroes of quadratic Dirichlet L-function
s matches the one-level density for eigenvalues of characteristic polynomi
als of symplectic matrices\,\nfor special test functions (with limited sup
port of the Fourier transform) by Ozluk and Snyder in 1999. Since the sup
port of the Fourier transform of the test function is large enough\, they
can deduce that more than $93.75 \\%$ of the L-functions attached to quadr
atic Dirichlet characters are such that $L(1/2\, \\chi) \\neq 0$\, giving
evidence for a well-known conjecture of Chowla. The full conjecture of Kat
z-Sarnak\n(without any restrictions on the support of the Fourier transfor
m) implies that $100 \\%$ of the L-functions attached to quadratic Dirichl
et characters are such that $L(1/2\, \\chi) \\neq 0$.\n\nWe will review th
ose results and consider the case of L-functions attached to cubic Dirich
let characters. We prove the first result towards the Katz and Sarnak conj
ecture for test functions with support of the Fourier transform large enou
gh to obtain a positive proportion of L-functions attached to cubic Diric
hlet characters such that $L(1/2\, \\chi) \\neq 0$.\n\nJoint work with Ahm
et 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:20210603T120000Z
DTEND:20210603T131500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5733@indico.ipmu.jp
DESCRIPTION:Speakers: Miranda Cheng (U. Amsterdam)\n\nOften it is useful t
o study the "boundary condition"\, namely the behaviour near the cusps\, o
f functions on the upper-half plane. This leads naturally to the concept o
f quantum modular forms\, which are functions on rational numbers that hav
e rather mysterious weak modular properties generalizing modular forms and
mock modular forms. In this talk I will discuss how considerations of bou
ndary conditions lead to interesting application of quantum modular forms
in the inter-connected subjects of moonshine\, physics and topology.\n\nht
tps://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:20210531T000000Z
DTEND:20210531T011500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5707@indico.ipmu.jp
DESCRIPTION:Speakers: Mina Aganagic (U.C. Berkeley)\n\nKhovanov showed\, m
ore than 20 years ago\, that there is a deeper theory underlying the Jones
polynomial. The knot categorification problem is to find a uniform descri
ption of this theory\, for all gauge groups\, which originates from physic
s. I found two solutions to this problem\, related by a version of two dim
ensional homological mirror symmetry. They are based on two descriptions o
f the theory that lives on defects of the six dimensional (0\,2) CFT\, whi
ch are supported on a link times time. \n\nThe theory turns out to be solv
able explicitly. It is also more efficient\, often exponentially so\, than
Khovanov's original approach.\n\nhttps://indico.ipmu.jp/event/387/contrib
utions/5707/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5707/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantization by Branes And Geometric Langlands
DTSTART:20210601T120000Z
DTEND:20210601T131500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5720@indico.ipmu.jp
DESCRIPTION:Speakers: Edward Witten (IAS\, Princeton)\n\nhttps://indico.ip
mu.jp/event/387/contributions/5720/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5720/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discussion
DTSTART:20210601T131500Z
DTEND:20210601T151500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-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:20210604T000000Z
DTEND:20210604T011500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5735@indico.ipmu.jp
DESCRIPTION:Speakers: Richard Nally (Stanford U.)\n\nMany familiar constru
ctions in string theory are rooted in the complex geometry of the compact
dimensions. On the other hand\, many recent advances in mathematics come f
rom arithmetic geometry\, where we consider the properties of varieties ov
er smaller fields such as Q. In this talk\, following recent work (arXiv:2
001.06022\, arXiv:2010.07285) with S. Kachru and W. Yang\, I will explain
how string theory can be related to arithmetic. In particular\, I will arg
ue that supersymmetric flux vacua admit arithmetic structures closely rela
ted to those of elliptic curves\, and moreover that these arithmetic struc
tures are related to the geometry of the F-theory description of the flux
compactification.\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:20210602T083000Z
DTEND:20210602T094500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5724@indico.ipmu.jp
DESCRIPTION:Speakers: Sanjaye Ramgoolam (QMUL & U. Witwatersrand)\n\nI des
cribe a family of algebras $K(n)$\, one for every positive integer n\, rel
ated to the group algebra of the symmetric group $S_n$. These algebras hav
e a basis labelled by bi-partite ribbon graphs with $n$ edges. They also h
ave a decomposition into matrix blocks labelled by triples of Young diagr
ams with $n$ boxes\, with matrix block size equal to the Kronecker coeffic
ient $C$ 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 matric
es. Some of the algorithms are realised in quantum mechanical systems wher
e the quantum states are bipartite ribbon graphs. Using the known connecti
ons between bipartite ribbon graphs and Belyi maps\, these quantum systems
have an interpretation as models of quantum membranes.\n\nhttps://indico.
ipmu.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:20210604T100000Z
DTEND:20210604T111500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5739@indico.ipmu.jp
DESCRIPTION:Speakers: Xenia de la Ossa (Oxford U.)\n\nIn this seminar I wi
ll discuss the arithmetic of Calabi-Yau 3-folds. The main goal is to explo
re whether there are questions of common interest in this context to physi
cists\, number theorists and geometers. The main quantities of interest i
n the arithmetic context are the numbers of points of the manifold conside
red as a variety over a finite field. We are interested in the computation
of these numbers and their dependence on the moduli of the variety. The
surprise for a physicist is that the numbers of points over a finite field
are also given by expression that involve the periods of a manifold. The
number of points are encoded in the local zeta function\, about which much
is known in virtue of the Weil conjectures. I will discuss interesting
topics related to the zeta function and the appearance of modularity for
one parameter families of Calabi-Yau manifolds.\nA topic I will stress is
that for these families there are values of the parameter for which the ma
nifold becomes singular and for these values the zeta function degenerates
and exhibits modular behaviour. I will report (on joint work with Phil
ip Candelas\, Mohamed Elmi and Duco van Straten) on an example for which t
he quartic numerator of the zeta function factorises into two quadrics at
special values of the parameter which satisfy an algebraic equation with c
oefficients in Q (so independent of any particular prime)\, and for which
the underlying manifold is smooth. We note that these factorisations are
due to a splitting of the Hodge structure and that these special values of
the parameter are rank two attractor points in the sense of type IIB supe
rgravity. Modular groups and modular forms arise in relation to these att
ractor points.\nTo our knowledge\, the rank two attractor points that were
found by the application of these number theoretic techniques\, provide t
he first explicit examples of such points for Calabi-Yau manifolds of full
SU(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:20210531T083000Z
DTEND:20210531T094500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5711@indico.ipmu.jp
DESCRIPTION:Speakers: Wei Li (ITP\, Chinese Academy of Sciences)\n\nI will
first explain how to construct BPS algebras for string theory on general
toric Calabi-Yau threefolds\, based on the 3D colored crystals that descri
be BPS states of the system. The resulting algebras are shifted quiver Yan
gians Y(Q\,W) that are associated with the quiver and the superpotential o
f the theory. Then I will show how to construct representations of a shift
ed quiver Yangian from general subcrystals of the canonical crystal\, and
how the shape of the subcrystal determines the framing of the quiver.\n\nh
ttps://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:20210604T013000Z
DTEND:20210604T024500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5736@indico.ipmu.jp
DESCRIPTION:Speakers: Meng-Chwan Tan (NUS Singapore)\n\nWe unravel the gro
und states and left-excited states of the A_{k-1} N=(2\,0) little string t
heory. Via a theorem by Atiyah\, these sectors can be captured by a supers
ymmetric quasi-topological sigma model on CP^1 with target space the based
loop group of SU(k). The ground states\, described by L^2-cohomology clas
ses\, form modules over an affine Lie algebra\, while the left-excited sta
tes\, described by chiral differential operators\, form modules over a tor
oidal Lie algebra. We also apply our results to unravel the 1/2 and 1/4 BP
S sectors of the M5-brane worldvolume theory\, which spectrum we find to b
e captured by cousins of modular and automorphic forms\, respectively\, th
at reveal an intrinsic S- and T-duality of the worldvolume theory.\n\nhttp
s://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:20210603T133000Z
DTEND:20210603T144500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5708@indico.ipmu.jp
DESCRIPTION:Speakers: Jeffrey Harvey (U. Chicago)\n\nAmong other things I
will discuss the relationship between Thompson moonshine at weight 1/2 and
Generalized Monstrous Moonshine at weight zero.\n\nhttps://indico.ipmu.jp
/event/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:20210602T000000Z
DTEND:20210602T011500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5722@indico.ipmu.jp
DESCRIPTION:Speakers: Gregory Moore (Rutgers)\n\nWe review how supersymmet
ric quantum mechanics naturally leads to several \nstandard constructions
in homological algebra. We apply these ideas to 2d Landau-Ginzburg \nmodel
s with (2\,2) supersymmetry to discuss wall-crossing. Some aspects of the
web formalism \nare reviewed and applied to the categorification of the Ce
cotti-Vafa wall-crossing formula for \nBPS invariants. We then sketch the
generalization to include twisted masses. In the final part of \nthe talk
we sketch how some of these ideas give a natural framework for understandi
ng a \nrecent conjecture of Garoufalidis\, Gu\, and Marino and lead to pot
entially new knot invariants. \nThe talk is based on work done with Ahsan
Khan and recent discussions with Ahsan Khan\, Davide \nGaiotto\, and Fei Y
an.\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:20210531T120000Z
DTEND:20210531T131500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5740@indico.ipmu.jp
DESCRIPTION:Speakers: Kim Klinger-Logan (Rutgers)\n\nGreen\, Russo\, and V
anhove have shown that the scattering amplitude for gravitons (hypothetica
l particles of gravity represented by massless string states) is closely r
elated to automorphic forms through differential equations. Green\, Miller
\, Russo\, Vanhove\, Pioline\, and K-L have used a variety of methods to s
olve eigenvalue problems for the invariant Laplacian on different moduli s
paces to compute the coefficients of the scattering amplitude of four grav
itons. We will examine two methods for solving the most complicated of the
se differential equations on $SL_2(\\mathbb{Z})\\backslash\\mathfrak{H}$.
Time permitting\, we will discuss recent work with S. Miller to improve up
on his original method for solving this equation.\n\nhttps://indico.ipmu.j
p/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:20210602T100000Z
DTEND:20210602T111500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5725@indico.ipmu.jp
DESCRIPTION:Speakers: Tudor Dimofte (U.C. Davis & Edinburg U.)\n\nThirty y
ears ago\, work of Witten and Reshetikhin-Turaev activated the study of qu
antum invariants of links and three-manifolds. A cornerstone of subsequent
developments\, leading up to our current knot-homology conference\, was a
three-pronged approach involving 1) quantum field theory (Chern-Simons)\;
2) rational VOA's (WZW)\; and 3) semisimple representation theory of quan
tum groups. The second and third perspectives have since been extended\, t
o logarithmic VOA's and related non-semisimple quantum-group categories. I
will propose a family of 3d quantum field theories that similarly extend
the first perspective to a non-semisimple (and more so\, derived) regime.
They support boundary VOA's whose module categories equivalent to modules
for 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 o
f Gukov-Hsin-Nakajima-Park-Pei-Sopenko.\n\nhttps://indico.ipmu.jp/event/38
7/contributions/5725/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5725/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Opening comments
DTSTART:20210530T235000Z
DTEND:20210530T235500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-5706@indico.ipmu.jp
DESCRIPTION:Speakers: Abhiram Kidambi (Kavli IPMU\, U. Tokyo)\n\nhttps://i
ndico.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:20210604T131500Z
DTEND:20210604T151500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-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:20210602T131500Z
DTEND:20210602T151500Z
DTSTAMP:20241015T070300Z
UID:indico-contribution-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