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SUMMARY:Omar Kidwai (University of Tokyo)
DTSTART:20210630T120000Z
DTEND:20210630T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/1
DESCRIPTION:Title: Topological recursion and uncoupled BPS structures for hypergeom
etric spectral curves\nby Omar Kidwai (University of Tokyo) as part of
Number theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbst
ract\nThe notion of BPS structure formalizes many of the structures appear
ing in the study of four-dimensional $\\mathcal N=2$ QFTs by Gaiotto-Moore
-Neitzke as well as Bridgeland's spaces of stability conditions and the ge
neralized Donaldson-Thomas (equivalently\, BPS) invariants. We outline a c
orrespondence which relates the BPS invariants\, central charges\, and sol
utions to certain Riemann-Hilbert problems with the topological recursion
free energies and Voros symbols of corresponding quantum curves\, which we
have shown for the special case of spectral curves of "hypergeometric typ
e". This is joint work with K. Iwaki\, arXiv:2010.05596 + ongoing.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioana Coman (University of Amsterdam)
DTSTART:20210728T120000Z
DTEND:20210728T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/2
DESCRIPTION:Title: Quantum modularity of 3-manifold invariants and higher depth ext
ensions\nby Ioana Coman (University of Amsterdam) as part of Number th
eory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstract\nA re
cently proposed class of topological 3-manifold invariants $\\hat{Z}[M_3]$
which admit series expansions with integer coefficients has been the foca
l point of intense research over the past few years. Their definition has
its origins in the computation of the BPS spectrum of the 3d $\\mathcal{N}
=2$ theory $T[M_3]$ which is associated to $M_3$ by the compactification o
n this 3-manifold of the 6d $\\mathcal{N}=(2\,0)$ SCFT living on a stack o
f $N$ M5 branes and\, under the 3d-3d correspondence\, the $\\hat{Z}$-inva
riants are therefore related to the WRT invariant of $M_3$. Subsequently\,
$\\hat{Z}[M_3]$ have also been shown to possess interesting number-theore
tic features\, proving themselves to be quantum modular forms in the case
where $T[M_3]$ has gauge group $SU(2)$. After reviewing these developments
\, here we explore certain extensions to higher rank cases and features of
the corresponding $\\hat{Z}$ invariants.\n\nZoom link available on resear
ch seminars. For queries\, please contact abhiram(dot)kidambi(at)ipmu(dot)
jp\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Beneish (McGill & Berkeley)
DTSTART:20210811T120000Z
DTEND:20210811T130000Z
DTSTAMP:20260422T225705Z
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 Alg
ebraic Geometry\, and Physics\n\n\nAbstract\nIn this talk\, I will describ
e three ways of repackaging the mock modular forms of $M_{24}$ moonshine i
nto forms of weight two. In the first case\, I will describe quasimodular
forms as trace functions whose integralities are seen to be equivalent to
divisibility conditions on the number of $\\mathbb{F}_p$ points on the Jac
obians of modular curves. In the second case\, for certain subgroups of $M
_{24}$\, I will describe vertex operator algebraic module constructions wh
ose 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 elem
ents of $M_{24}$ with connections to the Monster group.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Raum (Chalmers)
DTSTART:20210825T120000Z
DTEND:20210825T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/4
DESCRIPTION:Title: Divisibility questions on the partition function and their conne
ction to modular forms\nby Martin Raum (Chalmers) as part of Number th
eory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstract\nThe
partition function records the number of ways an integer can be written as
a sum of positive integers. Already studied by Euler\, it has turned out
to be a great source of inspiration in the theory of modular forms over th
e course of the past century. This development was ignited by Ramanujan. A
t at a time when it was a challenge to merely calculate values of the part
ition function\, he anticipated divisibility properties of astonishing reg
ularity. We will explain some of the ideas that emerged from Ramanujan's c
onjectures and some of their modern manifestations. Many of these are conn
ected to modular forms and via these to Galois representations. They help
us to understand in an increasingly precise sense how frequently Ramanujan
's divisibility patterns and their generalizations occur.\n\nZoom link ava
ilable now\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenz Eberhardt (IAS)
DTSTART:20210922T113000Z
DTEND:20210922T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/5
DESCRIPTION:Title: Worldsheet correlators in AdS$_3$ and Hurwitz theory\nby Lor
enz Eberhardt (IAS) as part of Number theory\, Arithmetic and Algebraic Ge
ometry\, and Physics\n\n\nAbstract\nWe revisit the computation of string c
orrelation functions in AdS$_3$ with pure NS-NS flux from a worldsheet poi
nt of view. These correlators contain all the perturbative information abo
ut 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 c
orrelators. The winding correlators encode information about branched cove
ring maps from the worldsheet to the boundary of AdS$_3$. Consistency of t
his proposal leads to many new and non-trivial relations for branched cove
ring maps.\n\nZoom link available\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter/Dalhousie)
DTSTART:20201006T120000Z
DTEND:20201006T130000Z
DTSTAMP:20260422T225705Z
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://researchseminars.org/talk/NAAPingClassGroup/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter/Dalhousie)
DTSTART:20211006T120000Z
DTEND:20211006T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/7
DESCRIPTION:Title: A menagerie of N = 1 SVOAs\nby Theo Johnson-Freyd (Perimeter
/Dalhousie) as part of Number theory\, Arithmetic and Algebraic Geometry\,
and Physics\n\n\nAbstract\nThe Conway Moonshine module $V^{f\\natural}$ i
s specific "N=1" supersymmetric vertex operator algebra\; its name reflect
s that its automorphism group is the Conway sporadic group $\\mathrm{Co}_1
$. It is a supersymmetric analogue of the Monstrous Moonshine module\, and
a quantum analogue of the Leech lattice. I will tell you about some inter
esting subalgebras of $V^{f\\natural}$\, which seem to correspond to some
interesting subgroups of $\\mathrm{Co}_1$. Some of these subalgebras fit w
ithin a theorem about WZW algebras\, and others fit within a conjecture ab
out umbral moonshine. Along the way\, I will highlight some of the techniq
ues for building and analyzing SVOAs and superconformal field theories.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (LIMS/Oxford U.)
DTSTART:20211110T120000Z
DTEND:20211110T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/8
DESCRIPTION:Title: From String Theory to Machine-Learning Mathematical Structures\nby Yang-Hui He (LIMS/Oxford U.) as part of Number theory\, Arithmetic
and Algebraic Geometry\, and Physics\n\n\nAbstract\nWe report and summariz
e some of the recent experiments in machine-learning of various structures
from different fields of mathematics\, ranging from the string landscape\
, to geometry\, to representation theory\, to combinatorics\, to number th
eory. We speculate on a hierarchy of inherent difficulty and where string
theoretic problems tend to reside.\n\nZoom link available\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UC Irvine)
DTSTART:20220126T040000Z
DTEND:20220126T050000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/9
DESCRIPTION:Title: The Ratios Conjecture and negative moments of L-functions\nb
y Alexandra Florea (UC Irvine) as part of Number theory\, Arithmetic and A
lgebraic Geometry\, and Physics\n\n\nAbstract\nThe Ratios Conjecture is a
wide-reaching\, very general conjecture\, predicting asymptotic formulas f
or averages of ratios of L–functions in families. The Ratios Conjecture
has applications to many questions of interest in number theory\, such as
obtaining non-vanishing results for L-functions or computing the n-level c
orrelations of zeros of L-functions. In this talk\, I will describe some r
ecent results on the Ratios Conjecture for the family of quadratic L-funct
ions over function fields. I will also discuss the closely related problem
of obtaining upper bounds for negative moments of L-functions\, which all
ows us to prove partial results towards the Ratios Conjecture in the case
of one over one\, two over two and three over three L-functions. Part of t
he work is joint with H. Bui and J. Keating.\n\nZoom link available\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/9/
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BEGIN:VEVENT
SUMMARY:Johanna Knapp (University of Melbourne)
DTSTART:20220302T080000Z
DTEND:20220302T100000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/10
DESCRIPTION:Title: Genus 1 fibered Calabi-Yau 3-folds with 5-sections - A GLSM per
spective\nby Johanna Knapp (University of Melbourne) as part of Number
theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstract\nE
lliptic and genus one fibered Calabi-Yau spaces play a prominent role in s
tring theory and mathematics. In this talk we will discuss examples and pr
operties 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) with non
-abelian gauge groups. This approach makes it possible to find connections
between different genus one fibrations with 5-sections that fit into the
framework of homological projective duality. Furthermore we briefly discus
s applications in topological string theory and M-/F-theory. This is joint
work with Emanuel Scheidegger and Thorsten Schimannek.\n\nZoom link avail
able\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Cesana (University of Cologne)
DTSTART:20220406T120000Z
DTEND:20220406T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/12
DESCRIPTION:Title: Asymptotic equidistribution for partition statistics and topolo
gical invariants\nby Giulia Cesana (University of Cologne) as part of
Number theory\, Arithmetic and Algebraic Geometry\, and Physics\n\n\nAbstr
act\nThroughout mathematics\, the equidistribution properties of certain o
bjects 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 equidistribution\,
convexity\, and log-concavity of coefficients of generating functions on a
rithmetic progressions.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/12/
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BEGIN:VEVENT
SUMMARY:Suresh Govindarajan (IIT Madras)
DTSTART:20220504T090000Z
DTEND:20220504T100000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/13
DESCRIPTION:Title: Siegel modular forms for Mathieu moonshine\nby Suresh Govin
darajan (IIT Madras) as part of Number theory\, Arithmetic and Algebraic G
eometry\, and Physics\n\n\nAbstract\nMathieu moonshine is a correspondence
between modular objects and conjugacy classes of the Mathieu group M_24.
The most famous one (due to Eguchi-Ooguri-Tachikawa) associates Jacobi for
ms and mock Modular forms to every conjugacy class of M_24.\nA second-quan
tized version of Mathieu moonshine leads to a product formula for function
s that are potentially genus-two Siegel Modular Forms analogous to the Igu
sa Cusp Form. The modularity of these functions do not follow in an obviou
s manner. We express these product formulae for all conjugacy classes of
M_{24} in terms of products of standard modular forms. This provides a ne
w proof of their modularity.\n\nZoom link now available.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mussardo (SISSA)
DTSTART:20220525T120000Z
DTEND:20220525T130000Z
DTSTAMP:20260422T225705Z
UID:NAAPingClassGroup/14
DESCRIPTION:Title: Generalised Riemann Hypothesis and Brownian Motion\nby Gius
eppe Mussardo (SISSA) as part of Number theory\, Arithmetic and Algebraic
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 subjec
ts present a fascinating story worth telling\, one of those vital\, wonder
ful and superb narrative of enquires often found in science. From this poi
nt of view\, the seminar presents the main features of the Riemann Hypothe
sis and discusses its generalisation to an infinite class of complex funct
ions\, the so-called Dirichlet L-functions\, regarded as quantum partition
functions on the prime numbers. The position of the infinite number of ze
ros of all the Dirichlet L-functions along the axis with real part equal t
o $1/2$ finds a very natural explanation in terms of one of the most basic
phenomena in Statistical Physics\, alias the Brownian motion. We present
the probabilistic arguments which lead to this conclusion and we also disc
uss a battery of highly non-trivial tests which support with an extremely
high confidence the validity of this result.\n
LOCATION:https://researchseminars.org/talk/NAAPingClassGroup/14/
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