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SUMMARY:Omar Kidwai (University of Tokyo)
DTSTART:20210630T120000Z
DTEND:20210630T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/1
DESCRIPTION:Title: Topological recursion and uncoupled BPS structures for hy
pergeometric spectral curves\nby Omar Kidwai (University of Tokyo) as
part of Number theory\, Arithmetic and Algebraic Geometry\, and Physics\n\
n\nAbstract\nThe notion of BPS structure formalizes many of the structures
appearing in the study of four-dimensional $\\mathcal N=2$ QFTs by Gaiott
o-Moore-Neitzke as well as Bridgeland's spaces of stability conditions and
the generalized Donaldson-Thomas (equivalently\, BPS) invariants. We outl
ine a correspondence which relates the BPS invariants\, central charges\,
and solutions to certain Riemann-Hilbert problems with the topological rec
ursion free energies and Voros symbols of corresponding quantum curves\, w
hich we have shown for the special case of spectral curves of "hypergeomet
ric type". This is joint work with K. Iwaki\, arXiv:2010.05596 + ongoing.\
n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioana Coman (University of Amsterdam)
DTSTART:20210728T120000Z
DTEND:20210728T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/2
DESCRIPTION:Title: Quantum modularity of 3-manifold invariants and higher de
pth extensions\nby Ioana Coman (University of Amsterdam) as part of Nu
mber theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstrac
t\nA recently proposed class of topological 3-manifold invariants $\\hat{Z
}[M_3]$ which admit series expansions with integer coefficients has been t
he focal point of intense research over the past few years. Their definiti
on has its origins in the computation of the BPS spectrum of the 3d $\\mat
hcal{N}=2$ theory $T[M_3]$ which is associated to $M_3$ by the compactific
ation on this 3-manifold of the 6d $\\mathcal{N}=(2\,0)$ SCFT living on a
stack of $N$ M5 branes and\, under the 3d-3d correspondence\, the $\\hat{Z
}$-invariants are therefore related to the WRT invariant of $M_3$. Subsequ
ently\, $\\hat{Z}[M_3]$ have also been shown to possess interesting number
-theoretic features\, proving themselves to be quantum modular forms in th
e case where $T[M_3]$ has gauge group $SU(2)$. After reviewing these devel
opments\, here we explore certain extensions to higher rank cases and feat
ures of the corresponding $\\hat{Z}$ invariants.\n\nZoom link available on
research seminars. For queries\, please contact abhiram(dot)kidambi(at)ip
mu(dot)jp\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Beneish (McGill & Berkeley)
DTSTART:20210811T120000Z
DTEND:20210811T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/3
DESCRIPTION:Title: Three perspectives on $M_{24}$ moonshine in weight 2\
nby Lea Beneish (McGill & Berkeley) as part of Number theory\, Arithmetic
and Algebraic Geometry\, and Physics\n\n\nAbstract\nIn this talk\, I will
describe three ways of repackaging the mock modular forms of $M_{24}$ moon
shine into forms of weight two. In the first case\, I will describe quasim
odular forms as trace functions whose integralities are seen to be equival
ent to divisibility conditions on the number of $\\mathbb{F}_p$ points on
the Jacobians of modular curves. In the second case\, for certain subgroup
s of $M_{24}$\, I will describe vertex operator algebraic module construct
ions whose associated trace functions are meromorphic Jacobi forms\, thus
giving explicit realizations of the divisibility conditions. In the third
case\, I will describe an association of weakly holomorphic modular forms
to elements of $M_{24}$ with connections to the Monster group.\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Raum (Chalmers)
DTSTART:20210825T120000Z
DTEND:20210825T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/4
DESCRIPTION:Title: Divisibility questions on the partition function and thei
r connection to modular forms\nby Martin Raum (Chalmers) as part of Nu
mber theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstrac
t\nThe partition function records the number of ways an integer can be wri
tten as a sum of positive integers. Already studied by Euler\, it has turn
ed out to be a great source of inspiration in the theory of modular forms
over the course of the past century. This development was ignited by Raman
ujan. At at a time when it was a challenge to merely calculate values of t
he partition function\, he anticipated divisibility properties of astonish
ing regularity. We will explain some of the ideas that emerged from Ramanu
jan's conjectures and some of their modern manifestations. Many of these a
re connected to modular forms and via these to Galois representations. The
y help us to understand in an increasingly precise sense how frequently Ra
manujan's divisibility patterns and their generalizations occur.\n\nZoom l
ink available now\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenz Eberhardt (IAS)
DTSTART:20210922T113000Z
DTEND:20210922T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/5
DESCRIPTION:Title: Worldsheet correlators in AdS$_3$ and Hurwitz theory\
nby Lorenz Eberhardt (IAS) as part of Number theory\, Arithmetic and Algeb
raic Geometry\, and Physics\n\n\nAbstract\nWe revisit the computation of s
tring correlation functions in AdS$_3$ with pure NS-NS flux from a worldsh
eet point of view. These correlators contain all the perturbative informat
ion about the spacetime CFT and the existence of winding strings in AdS$_3
$ makes them very rich. We propose a solution to the problem of computing
these correlators. The winding correlators encode information about branch
ed covering maps from the worldsheet to the boundary of AdS$_3$. Consisten
cy of this proposal leads to many new and non-trivial relations for branch
ed covering maps.\n\nZoom link available\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter/Dalhousie)
DTSTART:20201006T120000Z
DTEND:20201006T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/6
DESCRIPTION:by Theo Johnson-Freyd (Perimeter/Dalhousie) as part of Number
theory\, Arithmetic and Algebraic Geometry\, and Physics\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter/Dalhousie)
DTSTART:20211006T120000Z
DTEND:20211006T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/7
DESCRIPTION:Title: A menagerie of N = 1 SVOAs\nby Theo Johnson-Freyd (Pe
rimeter/Dalhousie) as part of Number theory\, Arithmetic and Algebraic Geo
metry\, and Physics\n\n\nAbstract\nThe Conway Moonshine module $V^{f\\natu
ral}$ is specific "N=1" supersymmetric vertex operator algebra\; its name
reflects that its automorphism group is the Conway sporadic group $\\mathr
m{Co}_1$. It is a supersymmetric analogue of the Monstrous Moonshine modul
e\, and a quantum analogue of the Leech lattice. I will tell you about som
e interesting subalgebras of $V^{f\\natural}$\, which seem to correspond t
o some interesting subgroups of $\\mathrm{Co}_1$. Some of these subalgebra
s fit within a theorem about WZW algebras\, and others fit within a conjec
ture about umbral moonshine. Along the way\, I will highlight some of the
techniques for building and analyzing SVOAs and superconformal field theor
ies.\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (LIMS/Oxford U.)
DTSTART:20211110T120000Z
DTEND:20211110T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/8
DESCRIPTION:Title: From String Theory to Machine-Learning Mathematical Struc
tures\nby Yang-Hui He (LIMS/Oxford U.) as part of Number theory\, Arit
hmetic and Algebraic Geometry\, and Physics\n\n\nAbstract\nWe report and s
ummarize some of the recent experiments in machine-learning of various str
uctures from different fields of mathematics\, ranging from the string lan
dscape\, to geometry\, to representation theory\, to combinatorics\, to nu
mber theory. We speculate on a hierarchy of inherent difficulty and where
string theoretic problems tend to reside.\n\nZoom link available\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UC Irvine)
DTSTART:20220126T040000Z
DTEND:20220126T050000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/9
DESCRIPTION:Title: The Ratios Conjecture and negative moments of L-functions
\nby Alexandra Florea (UC Irvine) as part of Number theory\, Arithmeti
c and Algebraic Geometry\, and Physics\n\n\nAbstract\nThe Ratios Conjectur
e is a wide-reaching\, very general conjecture\, predicting asymptotic for
mulas for averages of ratios of L–functions in families. The Ratios Conj
ecture has applications to many questions of interest in number theory\, s
uch as obtaining non-vanishing results for L-functions or computing the n-
level correlations of zeros of L-functions. In this talk\, I will describe
some recent results on the Ratios Conjecture for the family of quadratic
L-functions over function fields. I will also discuss the closely related
problem of obtaining upper bounds for negative moments of L-functions\, wh
ich allows us to prove partial results towards the Ratios Conjecture in th
e case of one over one\, two over two and three over three L-functions. Pa
rt of the work is joint with H. Bui and J. Keating.\n\nZoom link available
\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johanna Knapp (University of Melbourne)
DTSTART:20220302T080000Z
DTEND:20220302T100000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/10
DESCRIPTION:Title: Genus 1 fibered Calabi-Yau 3-folds with 5-sections - A G
LSM perspective\nby Johanna Knapp (University of Melbourne) as part of
Number theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbst
ract\nElliptic and genus one fibered Calabi-Yau spaces play a prominent ro
le in string theory and mathematics. In this talk we will discuss examples
and properties of a class of Calabi-Yau threefolds with 5-sections. These
Calabi-Yaus cannot be constructed by means of toric geometry. One way to
obtain them is as vacuum manifolds of gauged linear sigma models (GLSMs) w
ith non-abelian gauge groups. This approach makes it possible to find conn
ections between different genus one fibrations with 5-sections that fit in
to the framework of homological projective duality. Furthermore we briefly
discuss applications in topological string theory and M-/F-theory. This i
s joint work with Emanuel Scheidegger and Thorsten Schimannek.\n\nZoom lin
k available\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Cesana (University of Cologne)
DTSTART:20220406T120000Z
DTEND:20220406T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/12
DESCRIPTION:Title: Asymptotic equidistribution for partition statistics and
topological invariants\nby Giulia Cesana (University of Cologne) as p
art of Number theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n
\nAbstract\nThroughout mathematics\, the equidistribution properties of ce
rtain objects are a central theme studied by many authors. In my talk I am
going to speak about a joint project with William Craig and Joshua Males\
, where we provide a general framework for proving asymptotic equidistribu
tion\, convexity\, and log-concavity of coefficients of generating functio
ns on arithmetic progressions.\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suresh Govindarajan (IIT Madras)
DTSTART:20220504T090000Z
DTEND:20220504T100000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/13
DESCRIPTION:Title: Siegel modular forms for Mathieu moonshine\nby Sures
h Govindarajan (IIT Madras) as part of Number theory\, Arithmetic and Alge
braic Geometry\, and Physics\n\n\nAbstract\nMathieu moonshine is a corresp
ondence between modular objects and conjugacy classes of the Mathieu group
M_24. The most famous one (due to Eguchi-Ooguri-Tachikawa) associates Jac
obi forms and mock Modular forms to every conjugacy class of M_24.\nA seco
nd-quantized version of Mathieu moonshine leads to a product formula for f
unctions that are potentially genus-two Siegel Modular Forms analogous to
the Igusa Cusp Form. The modularity of these functions do not follow in an
obvious manner. We express these product formulae for all conjugacy cla
sses of M_{24} in terms of products of standard modular forms. This provid
es a new proof of their modularity.\n\nZoom link now available.\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mussardo (SISSA)
DTSTART:20220525T120000Z
DTEND:20220525T130000Z
DTSTAMP:20260404T110743Z
UID:NAAPingClassGroup/14
DESCRIPTION:Title: Generalised Riemann Hypothesis and Brownian Motion\n
by Giuseppe Mussardo (SISSA) as part of Number theory\, Arithmetic and Alg
ebraic Geometry\, and Physics\n\n\nAbstract\nIf Number Theory is arguably
one of the most fascinating subjects in Mathematics\, Theoretical Physics
adds to it the standard of clarity\, beauty and deepness which have helped
us to shape our understanding of the laws of Nature: together\, these two
subjects present a fascinating story worth telling\, one of those vital\,
wonderful and superb narrative of enquires often found in science. From t
his point of view\, the seminar presents the main features of the Riemann
Hypothesis and discusses its generalisation to an infinite class of comple
x functions\, the so-called Dirichlet L-functions\, regarded as quantum pa
rtition functions on the prime numbers. The position of the infinite numbe
r of zeros of all the Dirichlet L-functions along the axis with real part
equal to $1/2$ finds a very natural explanation in terms of one of the mos
t basic phenomena in Statistical Physics\, alias the Brownian motion. We p
resent the probabilistic arguments which lead to this conclusion and we al
so discuss a battery of highly non-trivial tests which support with an ext
remely high confidence the validity of this result.\n
LOCATION:https://stable.researchseminars.org/talk/NAAPingClassGroup/14/
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