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BEGIN:VEVENT
SUMMARY:Ujué Etayo (TU Graz)
DTSTART:20200603T150000Z
DTEND:20200603T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/1
DESCRIPTION:Title: Astounding connections of the logarithmic e
nergy on the sphere\nby Ujué Etayo (TU Graz) as part of Point Distrib
utions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nD
uring this talk we will present different problems that are somehow relate
d to the following one: find the minimum value of the logarithmic energy o
f a set of N points on the sphere of dimension 2. This late problem has be
en studied for years\, a computational version of it can be found as Probl
em Number 7 of Steve Smale list "Mathematical Problems for the Next Centur
y". This computational version of the problem was proposed after Smale and
Shub found out a beautiful relation between minimizers of the logarithmic
energy and well conditioned polynomials. Working on this relation\, we ar
e able to relate these two concepts to yet a new one: a sharp Bombieri typ
e inequality for univariate polynomials. The problem can also be rewritten
as a facility location problem\, as proved by Beltrán\, since the logari
thmic energy is just a normalization of the Green function for the Laplaci
an on the sphere.\n\nThis talk will be recorded and posted on the webinar
homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josiah Park (Georgia Institute of Technology)
DTSTART:20200610T150000Z
DTEND:20200610T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/2
DESCRIPTION:Title: Optimal measures for three-point energies a
nd semidefinite programming\nby Josiah Park (Georgia Institute of Tech
nology) as part of Point Distributions Webinar\n\nLecture held in Zoom\, p
assword: 600Cell.\n\nAbstract\nGiven a potential function of three vector
arguments\, \, which is -invariant\, for all orthogonal\, we find that sur
face measure minimizes those interaction energies of the form over the sph
ere whenever the potential function satisfies a positive definiteness crit
eria. We use semidefinite programming bounds to determine optimizing proba
bility measures for other energies. This latter approach builds on previou
s use of such bounds in the discrete setting by Bachoc-Vallentin\, Cohn-Wo
o\, and Musin\, and is successful for kernels which can be shown to have e
xpansions in a particular basis\, for instance certain symmetric polynomia
ls in inner products \, \, and . For other symmetric kernels we pose conje
ctures on the behavior of optimizers\, partially inferred through numerica
l studies. This talk is based on joint work with Dmitriy Bilyk\, Damir Fer
izovic\, Alexey Glazyrin\, Ryan Matzke\, and Oleksandr Vlasiuk.\n\nThis ta
lk will be recorded and posted on the webinar homepage. Slides will be ava
ilable too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Dostert (EPFL)
DTSTART:20200617T150000Z
DTEND:20200617T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/3
DESCRIPTION:Title: Semidefinite programming bounds for the ave
rage kissing number\nby Maria Dostert (EPFL) as part of Point Distribu
tions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nTh
e average kissing number of $R^n$ is the supremum of the average degrees o
f contact graphs of packings of finitely many balls (of any radii) in $R^n
$.\nIn this talk I will provide an upper bound for the average kissing num
ber based on semidefinite programming that improves previous bounds in dim
ensions 3\, . . . \, 9.\nA very simple upper bound for the average kissing
number is twice the kissing number\; in dimensions 6\, . . . \, 9 our new
bound is the first to improve on this\nsimple upper bound. This is a join
ed work with Alexander Kolpakov and Fernando Mário de Oliveira Filho.\n\n
This talk will be recorded and posted on the webinar homepage. Slides will
be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillipe Moustrou (UiT - The Arctic University of Norway)
DTSTART:20200624T150000Z
DTEND:20200624T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/4
DESCRIPTION:Title: Exact semidefinite programming bounds for p
acking problems\nby Phillipe Moustrou (UiT - The Arctic University of
Norway) as part of Point Distributions Webinar\n\nLecture held in Zoom\, p
assword: 600Cell.\n\nAbstract\nIn the first part of the talk\, we present
how semidefinite programming methods can provide upper bounds for various
geometric packing problems\, such as kissing numbers\, spherical codes\, o
r packings of spheres into a larger sphere. When these bounds are sharp\,
they give additional information on optimal configurations\, that may lead
to prove the uniqueness of such packings. For example\, we show that the
lattice E8 is the unique solution for the kissing number problem on the he
misphere in dimension 8.\n\nHowever\, semidefinite programming solvers pro
vide approximate solutions\, and some additional work is required to turn
them into an exact solution\, giving a certificate that the bound is sharp
. In the second part of the talk\, we explain how\, via our rounding proce
dure\, we can obtain an exact rational solution of semidefinite program fr
om an approximate solution in floating point given by the solver.\n\nJoint
work with Maria Dostert and David de Laat.\n\nThis talk will be recorded
and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David de Laat (TU Delft)
DTSTART:20200701T150000Z
DTEND:20200701T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/5
DESCRIPTION:Title: High-dimensional sphere packing and the mod
ular bootstrap\nby David de Laat (TU Delft) as part of Point Distribut
ions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nRec
ently\, Hartman\, Mazáč\, and Rastelli discovered a connection between t
he Cohn-Elkies bound for sphere packing and problems in the modular bootst
rap. In this talk I will explain this connection and discuss our numerical
study into high dimensional sphere packing and the corresponding problems
in the modular bootstrap. The numerical results indicate an exponential i
mprovement over the Kabatianskii-Levenshtein bound. I will also discuss im
plied kissing numbers and how these relate to improvements over the Cohn-E
lkies bound.\n\nJoint work with Nima Afkhami-Jeddi\, Henry Cohn\, Thomas H
artman\, and Amirhossein Tajdini.\n\nThis talk will be recorded and posted
on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew de Courcy-Ireland (EPFL)
DTSTART:20200708T150000Z
DTEND:20200708T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/6
DESCRIPTION:Title: Lubotzky-Phillips-Sarnak points on a sphere
\nby Matthew de Courcy-Ireland (EPFL) as part of Point Distributions W
ebinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nWe will d
iscuss work of Lubotzky-Phillips-Sarnak on special configurations of point
s on the two-dimensional sphere: what these points achieve\, the sense in
which it is optimal\, and aspects of the construction that are specific to
the sphere.\n\nThis talk will be recorded and possibly posted on the webi
nar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateus Sousa (Ludwig Maximilian University of Munich)
DTSTART:20200717T150000Z
DTEND:20200717T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/7
DESCRIPTION:Title: Uncertainty principles\, interpolation form
ulas and packing problems\nby Mateus Sousa (Ludwig Maximilian Universi
ty of Munich) as part of Point Distributions Webinar\n\nLecture held in Zo
om\, password: 600Cell.\n\nAbstract\nIn this talk we will discuss how cert
ain uncertainty principles and interpolation formulas are connected to pac
king problems and talk about some recent developments on these fronts.\n\n
This talk will be recorded and posted on the webinar homepage. Slides will
be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Negro (U of Birmingham)
DTSTART:20200722T150000Z
DTEND:20200722T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/8
DESCRIPTION:Title: Sharp estimates for the wave equation via t
he Penrose transform\nby Giuseppe Negro (U of Birmingham) as part of P
oint Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\
nAbstract\nIn 2004\, Foschi found the best constant\, and the extremizing
functions\, for the Strichartz inequality for the wave equation with data
in the Sobolev space \n$\\dot{H}^{1/2}\\times\\dot{H}^{-1/2}(\\mathbb{R}^3
)$. He also formulated a conjecture\, concerning the extremizers to this S
trichartz inequality in all spatial dimensions $d\\geq 2$. We disprove suc
h conjecture for even $d$\, but we provide evidence to support it for odd
$d$. The proofs use the conformal compactification of the Minkowski space-
time given by the Penrose transform. \n\nPart of this talk is based on joi
nt work with Felipe Gonçalves (Univ. Bonn).\n\nThis talk will be recorded
and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tania Stepaniuk (U of Lübeck)
DTSTART:20200729T150000Z
DTEND:20200729T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/9
DESCRIPTION:Title: Estimates for the discrete energies on the
sphere\nby Tania Stepaniuk (U of Lübeck) as part of Point Distributio
ns Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nWe fi
nd upper and lower estimate for the discrete energies whose Legendre-Fouri
er coefficients decrease to zero approximately as power functions.\n\nThis
talk will be recorded and posted on the webinar homepage. Slides will be
available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathias Sonnleitner (JKU Linz)
DTSTART:20200731T150000Z
DTEND:20200731T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/10
DESCRIPTION:Title: Uniform distribution on the sphere and the
isotropic discrepancy of lattice point sets\nby Mathias Sonnleitner (
JKU Linz) as part of Point Distributions Webinar\n\nLecture held in Zoom\,
password: 600Cell.\n\nAbstract\nAistleitner\, Brauchart and Dick showed i
n 2012 how the spherical cap discrepancy of mapped point sets may be estim
ated in terms of their isotropic discrepancy. We provide a characterizatio
n of the isotropic discrepancy of lattice point sets in terms of the spect
ral test\, the inverse length of the shortest vector in the corresponding
dual lattice. This is used to give a lower bound on the discrepancy in que
stion. \n\nThe talk is based on joint work with F. Pillichshammer.\n\nThis
talk will be recorded and posted on the webinar homepage. Slides will be
available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Quesada (IMPA)
DTSTART:20200805T150000Z
DTEND:20200805T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/11
DESCRIPTION:Title: Developments on the Fourier sign uncertain
ty principle\nby Oscar Quesada (IMPA) as part of Point Distributions W
ebinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nCan we co
ntrol the signs of a function and its Fourier transform\, simultaneously\,
in an arbitrary way? \n\n\nAn uncertainty principle in Fourier analysis i
s the answer to this type of question. They lie at the heart of Fourier op
timization problems\, such as the Cohn-Elkies linear program for sphere pa
ckings. We will discuss some answers to this question from a new perspecti
ve\, and why it might be relevant for problems in diophantine geometry and
optimal configurations. (Joint work with Emanuel Carneiro).\n\nThis talk
will be recorded and posted on the webinar homepage. Slides will be availa
ble too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Brown (Yale)
DTSTART:20200812T150000Z
DTEND:20200812T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/12
DESCRIPTION:Title: Positive-definite Functions\, Exponential
Sums and the Greedy Algorithm: a Curious Phenomenon\nby Louis Brown (Y
ale) as part of Point Distributions Webinar\n\nLecture held in Zoom\, pass
word: 600Cell.\n\nAbstract\nWe describe a curious dynamical system that re
sults in sequences of real numbers in [0\,1] with seemingly remarkable pro
perties. Let the even function $f:\\mathbb{T} \\rightarrow \\mathbb{R}$ sa
tisfy $\\widehat{f}(k) \\geq c|k|^{-2}$ and define a sequence via\n\n$$x_n
= \\arg\\min_x \\sum_{k=1}^{n-1}{f(x-x_k)}.$$\n\nSuch greedy sequences se
em to be astonishingly regularly distributed in various ways. We explore
this\, and generalize the algorithm (and results on it) to higher-dimensio
nal manifolds\, where the setting is even nicer.\n\nThis talk will be reco
rded and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Hofstadler (JKU Linz)
DTSTART:20200814T150000Z
DTEND:20200814T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/13
DESCRIPTION:Title: On a subsequence of random points\nby
Julian Hofstadler (JKU Linz) as part of Point Distributions Webinar\n\nLec
ture held in Zoom\, password: 600Cell.\n\nAbstract\nWe want to study the i
deas of R. Dwivedi\, O. N. Feldheim\, O. Guri-Gurevich and A. Ramdas from
their paper 'Online thinning in reducing discrepancy'\, where they give a
criterion for choosing points of a random sequence. This technique\, calle
d thinning\, shall improve the distribution of random points\, and we also
want to discuss their attempt to create thinned samples with small discre
pancy.\n\nThis talk will be recorded and posted on the webinar homepage. S
lides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Gonçalves (U of Bonn)
DTSTART:20200819T150000Z
DTEND:20200819T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/14
DESCRIPTION:Title: Sign Uncertainty\nby Felipe Gonçalves
(U of Bonn) as part of Point Distributions Webinar\n\nLecture held in Zoo
m\, password: 600Cell.\n\nAbstract\nWe will talk about recent developments
of the sign uncertainty principle and its relation with sphere packing bo
unds and spherical designs. This is joint work with J. P. Ramos and D. Oli
veira e Silva.\n\nThis talk will be recorded and posted on the webinar hom
epage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Krieg (JKU Linz)
DTSTART:20200828T153000Z
DTEND:20200828T163000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/16
DESCRIPTION:Title: Order-optimal point configurations for fun
ction approximation\nby David Krieg (JKU Linz) as part of Point Distri
butions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\n
We show that independent and uniformly distributed sampling points are as
good as optimal sampling points for the approximation (and integration) of
functions from the Sobolev space $W_p^s(\\Omega)$ on domains $\\Omega\\su
bset \\mathbb{R}^d$ in the $L_q(\\Omega)$-norm whenever $q< p$\, where we
take $q=1$ if we only want to compute the integral. In the case $q\\ge p$
there is a loss of a logarithmic factor. More generally\, we characterize
the quality of arbitrary sampling points $P\\subset \\Omega$ via the $L_\\
gamma(\\Omega)$-norm of the distance function ${\\rm dist}(\\cdot\,P)$\, w
here $\\gamma=s(1/q-1/p)_+^{-1}$. This improves upon previous characteriza
tions based on the covering radius of $P$. \n\nThis is joint work with M.
Sonnleitner.\n\nThis talk will be recorded and posted on the webinar homep
age. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Bilyk (U of Minnesota)
DTSTART:20200916T140000Z
DTEND:20200916T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/17
DESCRIPTION:Title: Stolarsky principle: generalizations\, ext
ensions\, and applications\nby Dmitriy Bilyk (U of Minnesota) as part
of Point Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell
.\n\nAbstract\nIn 1973 Kenneth Stolarsky proved a remarkable identity\, wh
ich connected two classical quantities\, which measure the quality of poin
t distributions on the sphere: the $L^2$ spherical cap discrepancy and the
pairwise sum of Euclidean distances between points. This fact\, which cam
e to be known as the Stolarsky Invariance Principle\, established a certa
in duality between problems of discrepancy theory on one hand\, and distan
ce geometry or energy optimization on the other\, and allowed one to trans
fer methods and results of one field to the other. Since then numerous ve
rsions\, extensions\, and generalizations of this principle have been foun
d\, leading to connections between various notions of discrepancy and disc
rete energies in different settings and to a number of applications to var
ious problems of discrete geometry. In this talk we shall survey known w
ork on the Stolarsky principle\, as well as some related problems.\n\nThis
talk will be recorded and posted on the webinar homepage. Slides will be
available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (U of Washington)
DTSTART:20200930T170000Z
DTEND:20200930T180000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/18
DESCRIPTION:Title: Optimal Transport and Point Distributions
on the Torus\nby Stefan Steinerberger (U of Washington) as part of Poi
nt Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nA
bstract\nThere are lots of ways of measuring the regularity of a set\nof p
oints on the Torus. I'll introduce a fundamental notion from Optimal\nTra
nsport\, the Wasserstein distance\, as another such measure. It \ncorrespo
nds quite literally over what distance one has to spread the\npoints to be
evenly distributed\, it has a natural physical intuition\n(the notion its
elf was derived in Economics modeling transport) and is\nnaturally related
to other notions such as discrepancy or Zinterhof's\ndiaphony. Classical
Fourier Analysis allows us to bound this transport \ndistance via exponen
tial sums which are well studied\; this allows us to revisit\nmany classic
al constructions and get transport bounds basically for free. \nWe'll fini
sh by revisiting a classical problem from numerical integration \nfrom thi
s new angle. There will be many open problems throughout the talk.\n\nThi
s talk will be recorded and posted on the webinar homepage. Slides will be
available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (U of Washington)
DTSTART:20201002T170000Z
DTEND:20201002T180000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/19
DESCRIPTION:Title: Optimal Transport and Point Distributions
on Manifolds\nby Stefan Steinerberger (U of Washington) as part of Poi
nt Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nA
bstract\nWe'll go somewhat deeper into the connection between the\nWassers
tein distance and notions from potential theory: in particular\,\nhow the
classical Green function can be used to derive bounds on \nWasserstein tra
nsport on general manifolds. On the sphere\, our results\nsimplify and the
Riesz energy appears in a nice form. We conclude with\na fundamental new
idea: the Wasserstein Uncertainty Principle which\nsays that if it's terri
bly easy to buy milk wherever you are\, then there\nmust be many supermark
ets -- the precise form of this isoperimetric\nprinciple is not known and\
, despite being purely geometric\, it would \nhave immediate impact on som
e PDE problems.\n\nThis talk will be recorded and posted on the webinar ho
mepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michelle Mastrianni (U of Minnesota)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/20
DESCRIPTION:Title: Bounds for Star-Discrepancy with Dependenc
e on the Dimension\nby Michelle Mastrianni (U of Minnesota) as part of
Point Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\
n\nAbstract\nThe question of how the star-discrepancy (with respect to cor
ners) of an n-point set in the d-dimensional unit cube depends on the dime
nsion d was studied in 2001 by Heinrich\, Novak\, Wasilkowski and Wozniako
wski. They established an upper bound that depends only polynomially on d/
n. The proof makes use of the fact that the set of corners in the d-dimens
ional unit cube is a VC-class\, and employs a result by Talagrand (1994) t
hat uses a partitioning scheme to study the tails of the supremum of a Gau
ssian process under certain conditions that are always satisfied by VC-cla
sses. In 2011\, Aistleitner produced a simpler proof of this upper bound u
sing a direct dyadic partitioning argument. The best lower bound was achie
ved by Hinrichs (2003)\, who built upon the ideas of using VC-inequalities
to achieve a lower bound with polynomial behavior in d/n as well. In this
talk I will introduce the notion of VC dimension and discuss how it is em
ployed in the above proofs\, and outline how the direct partitioning argum
ent for the upper bound uses the same underlying ideas about where the bul
k of the contribution to the tails arises.\n\nThis talk will be recorded a
nd posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Reznikov (Florida State)
DTSTART:20200923T140000Z
DTEND:20200923T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/21
DESCRIPTION:Title: Minimal discrete energy on fractals\nb
y Alexander Reznikov (Florida State) as part of Point Distributions Webina
r\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstract\nWe will survey
some old and new results on the existence of\nasymptotic behavior of mini
mal discrete Riesz energy of many particles\nlocated in a fractal set. Unl
ike in the case of a rectifiable set\,\nwhen the asymptotic behavior alway
s exists\, we will show that on a\nlarge class of somewhat "balanced" frac
tals the energy (and\nbest-packing) does not have any asymptotic behavior.
\n\nThis talk will be recorded and posted on the webinar homepage.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Grabner (TU Graz)
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/22
DESCRIPTION:Title: Fourier-Eigenfunctions and Modular Forms\nby Peter Grabner (TU Graz) as part of Point Distributions Webinar\n\nL
ecture held in Zoom\, password: 600Cell.\n\nAbstract\nEigenfunctions of th
e Fourier-transform play a major role in Viazovska's\nproof of the best pa
cking of the $E_8$ lattice in dimension 8 and the\nsubsequent determinatio
n of the Leech lattice as best packing\nconfiguration dimension 24 by Cohn
\, Kumar\, Miller\, Radchenko\, and\nViazovska. In joint work with A. Feig
enbaum and D. Hardin we have shown\nthat the constructions as used for th
ese results are unique\; we could\nshed more light on the underlying modul
ar and quasimodular forms and\ndetermine linear recurrence relations and d
ifferential equations\ncharacterising these forms.\n\nThis talk will be re
corded and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Beltran (U of Cantabria)
DTSTART:20201028T140000Z
DTEND:20201028T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/23
DESCRIPTION:Title: Smale’s motivation in describing the 7th
problem of his list\nby Carlos Beltran (U of Cantabria) as part of Po
int Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\n
Abstract\nIn 1993\, Mike Shub and Steve Smale posed a question that would
be later included in Smale’s list as 7th problem. Although this last pro
blem has became so famous\, the exact reason for its form and the conseque
nces that its solution would have for the initial goal are not so well kno
wn in the mathematician community. In this seminar\, I will describe the t
hrilling story of these origins: where the problem came from\, would it st
ill be useful for that task\, and what is left to do. I will probably talk
a lot and show very few formulas\, and I will also present some open prob
lems.\n\nThis talk will be recorded and posted on the webinar homepage. Sl
ides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Ebert (RICAM)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/24
DESCRIPTION:Title: Construction of (polynomial) lattice rules
by smoothness-independent component-by-component digit-by-digit construct
ions\nby Adrian Ebert (RICAM) as part of Point Distributions Webinar\n
\nLecture held in Zoom.\n\nAbstract\nIn this talk\, we introduce component
-by-component digit-by-digit algorithms (CBC-DBD)\nfor the construction of
(polynomial) lattice rules in weighted Korobov/Walsh spaces with\nprescri
bed decay of the involved series coefficients and associated smoothness α
> 1. The\npresented methods are extensions of a construction algorithm es
tablished by Korobov\nin [1] to the modern quasi-Monte Carlo (QMC) setting
. We show that the introduced\nCBC-DBD algorithms construct QMC rules with
N = 2 n points which achieve the almost\noptimal worst-case error converg
ence rates in the studied function spaces. Due to the used\nquality functi
ons\, the algorithms can construct good (polynomial) lattice rules indepen
-\ndent of the smoothness α of the respective function class. Furthermore
\, we derive suitable\nconditions on the weights under which the mentioned
error bounds are independent of the\ndimension. The presented algorithms
can be implemented in a fast manner such that the\nconstruction only requi
res O(sN ln N ) operations\, where N = 2 n is the number of lattice\npoint
s and s denotes the dimension. We stress that these fast constructions ach
ieve this\ncomplexity without the use of fast Fourier transformations (FFT
s)\, as in\, e.g.\, [2]. We\npresent extensive numerical results which con
firm our theoretical findings.\n\n[1] N.M. Korobov. On the computation of
optimal coefficients. Dokl. Akad. Nauk SSSR\,\n26:590–593. 1982.\n\n[2]
D. Nuyens\, R. Cools. Fast component-by-component construction of rank-1 l
attice\nrules with a non-prime number of points. J. Complexity 22(1)\, 4
–28. 2006.\n\nJoint work with: Peter Kritzer (RICAM Linz)\,\nDirk Nuyens
(NUMA KU Leuven)\, \nOnyekachi Osisiogu (Ricam Linz) and \nTetiana Stepan
iuk (U. of Lübeck)\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Glazyrin (U of Texas Rio Grande Valley)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/25
DESCRIPTION:Title: Mapping to the space of spherical harmonic
s\nby Alexey Glazyrin (U of Texas Rio Grande Valley) as part of Point
Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbst
ract\nFor a variety of problems for point configurations in spheres\, the
space of spherical harmonics plays an important role. In this talk\, we wi
ll discuss maps from point configurations to the space of spherical harmon
ics. Such maps can be used for finding bounds on packings\, energy bounds\
, and constructing new configurations. We will explain classical results f
rom this perspective and prove several new bounds. Also we will show a new
short proof for the kissing number problem in dimension 3.\n\nThis talk w
ill be recorded and posted on the webinar homepage. Slides will be availab
le too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Vlasiuk (Florida State)
DTSTART:20201007T140000Z
DTEND:20201007T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/27
DESCRIPTION:Title: Asymptotic properties of short-range inter
action functionals\nby Alex Vlasiuk (Florida State) as part of Point D
istributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nAbstr
act\nShort-range interactions\, such as the hypersingular Riesz energies\,
are known to be amenable to asymptotic analysis\, which allows to obtain
for them the distribution of minimizers and asymptotics of the minima. We
extract the properties making such analysis possible into a standalone fra
mework. This allows us to give a unified treatment of hypersingular Riesz
energies and optimal quantizers. We further obtain new results about the s
cale-invariant nearest neighbor interactions\, such as the k-nearest neigh
bor truncated Riesz energy. The suggested approach has applications to com
mon methods for generating distributions with prescribed density: Riesz en
ergies\, centroidal Voronoi tessellations\, and popular meshing algorithms
due to Persson-Strang and Shimada-Gossard. It naturally generalizes from
2-body to k-body interactions.\n\nBased on joint work with Douglas Hardin
and Ed Saff.\n\nThis talk will be recorded and posted on the webinar homep
age. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Leopardi (NCI Australia)
DTSTART:20201209T210000Z
DTEND:20201209T220000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/29
DESCRIPTION:Title: Diameter bounded equal measure partitions
of Ahlfors regular metric measure spaces\nby Paul Leopardi (NCI Austra
lia) as part of Point Distributions Webinar\n\nLecture held in Zoom\, pass
word: 600Cell.\n\nAbstract\nThe algorithm devised by Feige and Schechtman
for partitioning higher dimensional spheres into regions of equal measure
and small diameter is combined with David and Christ's construction of dya
dic cubes to yield a partition algorithm suitable to any connected Ahlfors
regular metric measure space of finite measure. \n\nThis is joint work wi
th Giacomo Gigante of the University of Bergamo.\n\nThis talk will be reco
rded and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bétermin (U of Vienna)
DTSTART:20201216T150000Z
DTEND:20201216T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/30
DESCRIPTION:Title: Theta functions\, ionic crystal energies a
nd optimal lattices\nby Laurent Bétermin (U of Vienna) as part of Poi
nt Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\nA
bstract\nThe determination of minimizing structures for pairwise interacti
on energies is a very challenging crystallization problem. The goal of thi
s talk is to present recent optimality results among charges and lattice s
tructures obtained with Markus Faulhuber (University of Vienna) and Hans K
nüpfer (University of Heidelberg). The central object of these works is t
he heat kernel associated to a lattice\, also called lattice theta functio
n. Several connections will be showed between interaction energies and the
ta functions in order to study the following problems:\n- Born’s Conject
ure: how to distribute charges on a fixed lattice in order to minimize the
associated Coulombian energy? In the simple cubic case\, Max Born conject
ured that the alternation of charges +1 and -1 (i.e. the rock-salt structu
re of NaCl) is optimal. The proof of this conjecture obtained with Hans Kn
üpfer will be briefly discussed as well as its generalization to other la
ttices and energies.\n- stability of the rock-salt structure: what could b
e conditions on interaction potentials such that the minimal energies amon
g charges and lattices has a rock-salt structure? Many results\, both theo
retical and numerical and obtained with Markus Faulhuber and Hans Knüpfer
\, will be presented.\n- maximality of the triangular lattices among latti
ces with alternation of charges: we will present this new universal optima
lity among lattices obtained with Markus Faulhuber.\n\nThis talk will be r
ecorded and posted on the webinar homepage. Slides will be available too.\
n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Barg (University of Maryland)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/31
DESCRIPTION:Title: Stolarsky's invariance principle for the H
amming space\nby Alexander Barg (University of Maryland) as part of Po
int Distributions Webinar\n\nLecture held in Zoom\, password: 600Cell.\n\n
Abstract\nStolarsky's invariance principle has enjoyed considerable\natten
tion in the literature in the last decade. In this talk we study an\nanalo
g of Stolarsky's identity in finite metric spaces with an emphasis on\nthe
Hamming space. We prove several bounds on the spherical discrepancy of\nb
inary codes and identify some discrepancy minimizing configurations. We\na
lso comment on the connection between the problem of minimizing the\ndiscr
epancy and the general question of locating minimum-energy\nconfigurations
in the space. The talk is based on arXiv:2005.12995 and\narXiv:2007.09721
(joint with Maxim Skriganov).\n\nThis talk will be recorded and posted on
the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David García-Zelada (Aix-Marseille University)
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/32
DESCRIPTION:Title: A large deviation principle for empirical
measures\nby David García-Zelada (Aix-Marseille University) as part o
f Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nThe ma
in object of this talk will be a model of n interacting particles at equil
ibrium.\nI will describe its macroscopic behavior as n grows to in\nnity b
y showing a Laplace prin-\nciple or\, equivalently\, a large deviation pri
nciple. This implies\, in some cases\, an almost\nsure convergence to a de
terministic probability measure. Among the main motivating\nexamples we ma
y \nnd Coulomb gases on Riemannian manifolds\, the eigenvalue distri-\nbut
ion of Gaussian random matrices and the roots of Gaussian random polynomia
ls.\nThis talk is based on arXiv:1703.02680.\n\nThis talk will be recorded
and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arno Kuijlaars (Katholieke Universiteit Leuven)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/33
DESCRIPTION:Title: The spherical ensemble with external sourc
es\nby Arno Kuijlaars (Katholieke Universiteit Leuven) as part of Poin
t Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe study a m
odel of a large number of points on the unit sphere under \nthe influence
of a finite number of fixed repelling charges. \nIn the large n limit the
points fill a region that is known as \nthe droplet. For small external ch
arges the droplet is \nthe complement of the union of a number of spherica
l caps\, one around \neach of the external charges. When the external char
ges grow\,\nthe spherical caps will start to overlap and the droplet onder
goes a non-trivial\ndeformation.\n\nWe explicitly describe the transition
for the case of equal external\ncharges that are symmetrically located aro
und the north pole. In our\napproach we first identify a motherbody that\,
due to the symmetry in the problem\,\nwill be located on a number of meri
dians connecting the north and south poles.\nAfter projecting onto the com
plex plane\, and undoing the symmetry\, we\ncharacterize the motherbody by
means of the solution of a vector equilibrium\nproblem from logarithmic p
otential theory.\n\nThis talk will be recorded and posted on the webinar h
omepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/34
DESCRIPTION:Title: Finite point configurations and frame theo
ry\nby Alex Iosevich (University of Rochester) as part of Point Distri
butions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe are going to disc
uss some recent and not so recent applications of analytic and combinatori
al results on finite point configurations to problems of existence of expo
nential and Gabor frames and bases.\n\nThis talk will be recorded and post
ed on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasso Okoudjou (Tufts University)
DTSTART:20210224T160000Z
DTEND:20210224T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/35
DESCRIPTION:Title: Completeness of Weyl-Heisenberg POVMs\
nby Kasso Okoudjou (Tufts University) as part of Point Distributions Webin
ar\n\nLecture held in Zoom.\n\nAbstract\nThe finite Gabor (or Weyl-Heisenb
erg) system generated by a unit-norm vector $g\\in \\mathbb{C}^d$ is the
set of vectors $$\\big\\{g_{k\,\\ell}=e^{2\\pi i k\\cdot}g(\\cdot - \\ell
)\\big\\}_{k\, \\ell =0}^{d-1}.$$ It is know that every such system forms
a finite unit norm tight frame (FUNTF) for $\\C^d$\, i.e.\, $$d^3 \\|x\\|
^2=\\sum_{k\, \\ell=0}^{d-1}|\\langle x\, g_{k\,\\ell}\\rangle |^2\\quad \
\forall \\\, x\\in \\mathbb{C}^d.$$ Furthermore\, the Zauner conjecture as
serts that for each $d\\geq 2$\, there exist unit-norm vectors $g \\in \\
mathbb{C}^d$ such that this FUNTF is equiangular\, that is\, $|\\langle g\
, g_{k\, \\ell}\\rangle |^2= \\tfrac{1}{d+1}.$ \nAssuming the existence of
a unit-vector $g$ that positively answers Zauner's conjecture\, one can s
how that the set of rank-one matrices $$\\big\\{\\pi_{k\,\\ell}=\\langle \
\cdot\, g_{k\,\\ell}\\rangle g_{k\, \\ell}\\big\\}_{k \\ell=0}^{d-1}$$ is
complete in the space of $d\\times d$ matrices. Consequently\, $\\big\\{\\
pi_{k\,\\ell}\\big\\}_{k \\ell=0}^{d-1}$ forms a symmetric informationally
complete positive operator-valued measure (SIC-POVM). \n\nIn fact\, it is
known that given a unit-norm vector $g\\in \\mathbb{C}^d$\, the POVM $\\
big\\{\\pi_{k\,\\ell}\\big\\}_{k \\ell=0}^{d-1}$ is informationally comple
te (IC) if and only if $\\langle g\, g_{k\, \\ell} \\rangle \\neq 0$ for
all $(k \,\\ell)\\neq (0\,0)$. \nIn this talk\, we give a different proof
of the characterization of the IC-POVMs. We then focus on investigating n
on-informationally complete POVMs. We will present some preliminary result
s pertaining to the dimensions of the linear spaces spanned by these rank-
one matrices. (This talk is based on on-going joint work with S.~Kang and
A.~Goldberger.)\n\nThis talk will be recorded and posted on the webinar ho
mepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mircea Petrache (PUC Chile)
DTSTART:20210303T160000Z
DTEND:20210303T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/36
DESCRIPTION:Title: Sharp isoperimetric inequality\, discrete
PDEs and Semidiscrete optimal transport\nby Mircea Petrache (PUC Chile
) as part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstr
act\nConsider the following basic model of finite crystal cluster\nformati
on: in a periodic graph G with vertices in R^d (representing\npossible mol
ecular bonds) a subset (of atoms) must be chosen\, so that\nthe total numb
er of bonds between a point in X and one outside X is\nminimized. These bo
nds form the edge-perimeter of X\, denoted \\partial\nX.\nIf the graph is
periodic and locally finite\, any X satisfies an\ninequality of the form |
X|^{d-1} \\leq C |partial X|^d\, where the\noptimal C depends on the graph
. How can we determine the structure of\nsets X realizing equality in the
above\, based on the geometry and of\nG?\nIf we take the continuum limit o
f G\, then the classical Wulff shape\ntheory describes optimal limit shape
s\, and at least two proofs of\nisoperimetric inequality apply\, one based
on PDE and calibration\nideas\, and the other based on Optimal Transport
ideas. We focus on\nusing the heuristic coming from the continuum analogue
\, to answer the\nabove question in some cases\, in the discrete case. Thi
s approach\nhighlights the tight connection between discrete PDEs and semi
discrete\nOptimal Transport\, and a link to the Minkowski theorem for conv
ex\npolyhedra.\n\nThis talk will be recorded and posted on the webinar hom
epage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yeli Niu (U of Alberta)
DTSTART:20210310T153000Z
DTEND:20210310T163000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/37
DESCRIPTION:Title: Discretization of integrals on compact
metric measure spaces\nby Yeli Niu (U of Alberta) as part of Point Dis
tributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nLet $\\mu$ be a
Borel probability measure on a compact path-connected metric space $(X
\, \\rho)$ for which there exist constants $c\,\\be\\ge 1$ such that $\\m
u(B) \\ge c r^{\\be}$ \n for every open ball $B\\subset X$ of radius $r>0$
. For a class\n of Lipschitz functions $\\Phi:[0\,\\infty)\\to\\RR
$ that are\n piecewise within a finite-dimensional subspace of\
n continuous functions\, we prove under certain mild conditions\n
on the metric $\\rho$ and the measure $\\mu$ that for each\n
positive integer $N\\ge 2$\, and each $g\\in L^\\infty(X\,\n
d\\mu)$ with $\\|g\\|_\\infty=1$\, there exist points $y_1\,\n
\\ldots\, y_{ N}\\in X$ and real \n numbers $\\lambda_1\, \\ldot
s\, \\lambda_{ N}$ such that for any $x\\in X$\, \n \\begin{align*}\n &
\\left| \\int_X \\Phi (\\rho (x\, y)) g(y) \\\,\\dd \\mu (y) - \\sum_{j
=\n 1}^{ N} \\lambda_j \\Phi (\\rho (x\, y_j)) \\right| \\leqslant C
N^{- \\frac{1}{2} - \\frac{3}{2\\be}} \\sqrt{\\log N}\,\n \\end{align
*}\n where the constant $C>0$ is independent of $N$ and $g$. In the c
ase when $X$ is the unit sphere $\\sph$ of $\\RR^{d+1}$ with the ususal ge
odesic distance\, we also prove that the constant $C$ here is independent
of the dimension $d$. Our estimates are better than those obtained f
rom the standard Monte Carlo methods\, which typically yield a weaker
upper bound $N^{-\\f12}\\sqrt{\\log N}$.\n\nThis talk will be recorded a
nd posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuemei Chen (UNC Wilmington)
DTSTART:20210317T160000Z
DTEND:20210317T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/38
DESCRIPTION:Title: Frame Design Using Projective Riesz Energy
\nby Xuemei Chen (UNC Wilmington) as part of Point Distributions Webin
ar\n\nLecture held in Zoom.\n\nAbstract\nTight and well-separated frames a
re desirable in many signal \nprocessing applications. We introduce a proj
ective Riesz kernel for the \nunit sphere and investigate properties of N-
point energy minimizing \nconfigurations for such a kernel. We show that t
hese minimizing \nconfigurations\, for N sufficiently large\, form frames
that are \nwell-separated (have low coherence) and are nearly tight. We wi
ll also \nshow some numerical experiments. This is joint work with Doug Ha
rdin and \nEd Saff.\n\nThis talk will be recorded and posted on the webina
r homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruiwen Shu (U of Maryland)
DTSTART:20210324T150000Z
DTEND:20210324T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/39
DESCRIPTION:Title: Dynamics of Particles on a Curve with Pair
wise Hyper-singular Repulsion\nby Ruiwen Shu (U of Maryland) as part o
f Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe inv
estigate the large time behavior of $N$ particles restricted to a smooth c
losed curve in $\\mathbb{R}^d$ and subject to a gradient flow with respect
to Euclidean hyper-singular repulsive Riesz $s$-energy with $s>1$. We sho
w that regardless of their initial positions\, for all $N$ and time $t$ la
rge\, their normalized Riesz $s$-energy will be close to the $N$-point min
imal possible energy. Furthermore\, the distribution of such particles wil
l be close to uniform with respect to arclength measure along the curve.\n
\nThis talk will be recorded and posted on the webinar homepage. Slides wi
ll be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Musin (U of Texas Rio Grande Valley)
DTSTART:20210331T150000Z
DTEND:20210331T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/40
DESCRIPTION:Title: Majorization\, discrete energy on spheres
and f-designs\nby Oleg Musin (U of Texas Rio Grande Valley) as part of
Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe cons
ider the majorization (Karamata) inequality and minimums of the majorizati
on (M-sets) for f-energy potentials of m-point configurations in a sphere.
We discuss the optimality of regular simplexes\, describe M-sets with a s
mall number of points\, define spherical f-designs and study their propert
ies. Then we consider relations between the notions of f-designs and M-set
s\, \n$\\tau$\n-designs\, and two-distance sets\n\nThis talk will be recor
ded and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Woden Kusner (U of Georgia)
DTSTART:20210407T150000Z
DTEND:20210407T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/41
DESCRIPTION:Title: Measuring chirality with the wind\nby
Woden Kusner (U of Georgia) as part of Point Distributions Webinar\n\nLect
ure held in Zoom.\n\nAbstract\nThe question of measuring "handedness" is o
f some significance in both mathematics and in the real world. Propellors
and screws\, proteins and DNA\, in fact *almost everything* is chiral. Can
we quantify chirality? Or can we perhaps answer the question:\n"Are your
shoes more left-or-right handed than a potato?"\nWe can begin with the hyd
rodynamic principle that chiral objects rotate when placed in a collimated
flow (or wind). This intuition naturally leads to a trace-free tensorial
chirality measure for space curves and surfaces\, with a clear physical in
terpretation measuring twist. As a consequence\, the "average handedness"
of an object with respect to this measure will always be 0. This also stro
ngly suggests that a posited construction of Lord Kelvin--the isotropic he
licoid--can not exist.\njoint with Giovanni Dietler\, Rob Kusner\, Eric Ra
wdon and Piotr Szymczak\n\nThis talk will be recorded and posted on the we
binar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dragnev (Purdue Fort Wayne)
DTSTART:20210414T150000Z
DTEND:20210414T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/42
DESCRIPTION:Title: Bounds for Spherical Codes: The Levenshtei
n Framework Lifted\nby Peter Dragnev (Purdue Fort Wayne) as part of Po
int Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nBased on t
he Delsarte-Yudin linear programming approach\, we extend Levenshtein’s
framework to obtain lower bounds for the minimum henergy of spherical code
s of prescribed dimension and cardinality\, and upper bounds on the maxima
l cardinality of spherical codes of prescribed dimension and minimum separ
ation. These bounds are universal in the sense that they hold for a large
class of potentials h and in the sense of Levenshtein. Moreover\, codes at
taining the bounds are universally optimal in the sense of Cohn-Kumar. Ref
erring to Levenshtein bounds and the energy bounds of the authors as “fi
rst level”\, our results can be considered as “next level” universal
bounds as they have the same general nature and imply necessary and suffi
cient conditions for their local and global optimality. For this purpose\,
we introduce the notion of Universal Lower Bound space (ULB-space)\, a sp
ace that satisfies certain quadrature and interpolation properties. While
there are numerous cases for which our method applies\, we will emphasize
the model examples of 24 points (24-cell) and 120 points (600-cell) on \nS
\n3\n. In particular\, we provide a new proof that the 600-cell is univers
ally optimal\, and in so doing\, we derive optimality of the 600-cell on a
class larger than the absolutely monotone potentials considered by Cohn-K
umar.\n\nThis talk will be recorded and posted on the webinar homepage. Sl
ides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doug Hardin (Vanderbilt U)
DTSTART:20210421T150000Z
DTEND:20210421T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/43
DESCRIPTION:Title: Asymptotics of periodic minimal discrete e
nergy problems\nby Doug Hardin (Vanderbilt U) as part of Point Distrib
utions Webinar\n\nLecture held in Zoom.\n\nAbstract\nFor $s>0$ and a latti
ce $L$ in $R^d$\, we consider the\nasymptotics of $N$-point configuration
s minimizing the $L$-periodic Riesz\n$s$-energy as the number of points $
N$ goes to infinity. In particular\, we\nfocus on the case $0On the rank of non-informationally complet
e Gabor POVMs\nby Shujie Kang (UT Arlington) as part of Point Distribu
tions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe investigate Positiv
e Operator Valued Measures (POVMs) generated by Gabor frames in $\\mathbb{
C}^d$. A complete (Gabor) POVM is one that spans the space $\\mathbb{C}^{d
^{2}}$ of $d\\times d$ matrices. It turns out that being a complete Gabor
POVM is a generic property. As a result\, the focus of this talk will be o
n non-complete Gabor POVMs. We will describe the possible ranks of these G
abor POVMs\, and derive various consequences for the underlying Gabor fram
es. In particular\, we will give details in dimensions $4$ and $5$.\n\nTh
is talk will be recorded and posted on the webinar homepage. Slides will b
e available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Ullrich (JKU Linz)
DTSTART:20210505T141500Z
DTEND:20210505T150000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/45
DESCRIPTION:Title: Random matrices and approximation using fu
nction values\nby Mario Ullrich (JKU Linz) as part of Point Distributi
ons Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe consider $L_2$-approx
imation of functions using linear algorithms and want to compare the power
of function values with the power of arbitrary linear information. Under
mild assumptions on the class of functions\, we show that the minimal wors
t-case errors based on function values decay at almost the same rate as th
ose with arbitrary info\, if the latter decay fast enough. Our results are
to some extent best possible and\, in special cases\, improve upon well-s
tudied point constructions\, like sparse grids\, which were previously ass
umed to be optimal. The proof is based on deep results on large random mat
rices\, including the recent solution of the Kadison-Singer problem\, and
reveals that (classical) least-squares methods might be surprisingly power
ful in a general setting.\n\nThis talk will be recorded and posted on the
webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johann Brauchart (TU Graz)
DTSTART:20210519T150000Z
DTEND:20210519T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/46
DESCRIPTION:Title: Weighted $L^2$ -Norms of Gegenbauer Polyn
omials — and more!\nby Johann Brauchart (TU Graz) as part of Point D
istributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nAbstract: \nI d
iscuss integrals of the form\n\\begin{equation*}\n\\int_{-1}^1(C_n^{(\\lam
bda)}(x))^2(1-x)^\\alpha (1+x)^\\beta\\dd x\,\n\\end{equation*}\nwhere $C_
n^{(\\lambda)}$ denotes the Gegenbauer-polynomial of index $\\lambda>0$ an
d $\\alpha\,\\beta>-1$. Such integrals for orthogonal polynomials involvin
g\, in particular\, a ``wrong'' weight function appear in physics applicat
ions and point distribution problems. \n\nI present exact formulas for the
integrals and their generating functions\, and give asymptotic formulas a
s $n\\to\\infty$. \n\nThis is joint work with Peter Grabner also from TU
Graz.\n\nThis talk will be recorded and posted on the webinar homepage. Sl
ides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Chen (Macquarie U)
DTSTART:20210512T150000Z
DTEND:20210512T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/47
DESCRIPTION:Title: The Veech 2-circle problem and non-integra
ble flat dynamical systems\nby William Chen (Macquarie U) as part of P
oint Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe are mo
tivated by an interesting problem studied more than 50 years ago by Veech
and which can be considered a parity\, or mod 2\, version of the classical
equidistribution problem concerning the irrational rotation sequence. The
Veech discrete 2-circle problem can also be visualized as a continuous fl
at dynamical system\, in the form of 1-direction geodesic flow on a surfac
e obtained by modifying the surface comprising two side-by-side unit squar
es by the inclusion of barriers and gates on the vertical edges\, with app
ropriate modification of the edge identifications. A famous result of Gutk
in and Veech says that 1-direction geodesic flow on any flat finite polysq
uare translation surface exhibits optimal behavior\, in the form of an ele
gant uniform-periodic dichotomy. Here the modified surface in question is
no longer such a surface\, and there are vastly different outcomes dependi
ng on the values of certain parameters.\n\nThis talk will be recorded and
posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Austin Anderson and Alex White (Florida State)
DTSTART:20210602T153000Z
DTEND:20210602T163000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/48
DESCRIPTION:Title: Asymptotics of Best Packing and Best Cover
ing\nby Austin Anderson and Alex White (Florida State) as part of Poin
t Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe discuss r
ecent progress on asymptotics for the dual problems of best packing and be
st covering in Euclidean space. For future investigations\, we highlight t
heir relation to large parameter limits of minimal Riesz s-energy and Ries
z s-polarization\, respectively. Next\, we address a weak-separation argum
ent for coverings and its flexibility as compared to similar arguments for
polarization and packing. Finally\, we examine how a recent non-existence
proof for the asymptotics of best packing on dependent fractals is adapte
d to both constrained and unconstrained covering- the second case owing la
rgely to weak separation of coverings. This is joint work with Oleksandr V
lasiuk and Alexander Reznikov of Florida State University.\n\nThis talk wi
ll be recorded and posted on the webinar homepage. Slides will be availabl
e too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Legg (Purdue U Fort Wayne)
DTSTART:20210609T150000Z
DTEND:20210609T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/49
DESCRIPTION:Title: Logarithmic Equilibrium on the Sphere in t
he Presence of Multiple Point Charges\nby Alan Legg (Purdue U Fort Way
ne) as part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbs
tract\n(Joint work with Peter Dragnev) We consider the problem of finding
the equilibrium measure on the unit sphere in R^3 using logarithmic potent
ials\, in the presence of external fields made up of a finite number of po
int charges on the sphere. For any such external field\, the complement of
the equilibrium measure turns out to be the stereographic preimage from t
he plane of a union of classical quadrature domains.\n\nThis talk will be
recorded and posted on the webinar homepage. Slides will be available too.
\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Assaf Goldberger (Tel Aviv U)
DTSTART:20210616T150000Z
DTEND:20210616T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/50
DESCRIPTION:Title: Configurations\, Automorphisms and Cohomol
ogy\nby Assaf Goldberger (Tel Aviv U) as part of Point Distributions W
ebinar\n\nLecture held in Zoom.\n\nAbstract\nPoint configurations on finit
e dimensional real or complex spaces\, typically on the unit sphere\, are
important in Physics\, Coding Theory\, Classical and Quantum Information T
heory\, Geometry\, Number Theory and more. The Automorphism group a of poi
nt configuration is a tool to study it\, and to generate new ones. In this
talk we will show how to generate automorphism groups from group-theoreti
c considerations\, and how to construct configurations that satisfy the gr
oup. The main tool in use is Group Cohomology. We show that there is a spe
ctral sequence which captures all possible solutions and all obstructions
to the construction of a solution. In addition this sequence captures the
Galois structure of algebraic configurations. Galois structures were disco
vered recently in the case of Zauner SIC-POVMs. This point of view can be
generalized to a much broader framework\, e.g. higher tensors as replaceme
nts of the Gramian matrix\, perfect squares are seen to be dual to configu
ration Gramians when one uses homology instead of cohomology\, and there a
re some connections to Number Theory\, such as the theory of Brauer Groups
. Other applications are the generation of Hadamard and Weighing matrices.
We will discuss these extensions as time permits. This is joint work with
Giora Dula.\n\nThis talk will be recorded and posted on the webinar homep
age. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McCann (University of Toronto)
DTSTART:20210630T150000Z
DTEND:20210630T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/51
DESCRIPTION:Title: Maximizing the sum of angles between pairs
of lines in Euclidean space\nby Robert McCann (University of Toronto)
as part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstra
ct\nChoose $N$ unoriented lines through the origin of $\\R^{d+1}$. \n Sup
pose each pair of lines repel each other with a force {whose strength is}
\n independent of the (acute) angle\nbetween them\, so that they prefer t
o be orthogonal to each other. However\, unless $N \\le d+1$\,\nit is im
possible for all pairs of lines to be orthogonal. What then are their sta
ble configurations?\nAn unsolved conjecture of Fejes T\\' oth (1959) asser
ts that the lines should be equidistributed as evenly as possible over a s
tandard\nbasis in $\\R^{d+1}$. By modifying the force to make it increase
as a power of the distance\, we show the analogous\nclaim to be true for
all positive powers if we are only interested in local stability\, and f
or sufficiently large powers if we require global stability.\n\nThese resu
lts represent joint work with Tongseok Lim (of Purdue's Krannert School of
Management).\n\nThis talk will be recorded and posted on the webinar home
page. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Negro (University of Birmingham)
DTSTART:20210707T150000Z
DTEND:20210707T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/52
DESCRIPTION:Title: Intermittent symmetry breaking for the max
imizers to the Agmon-Hörmander estimate on the sphere\nby Giuseppe Ne
gro (University of Birmingham) as part of Point Distributions Webinar\n\nL
ecture held in Zoom.\n\nAbstract\nThe $L^2$ norm of a function on Euclidea
n space equals the $L^2$ norm of its Fourier transform\; this is the theo
rem of Plancherel. This is true for functions\, but it fails for measures\
, such as densities on a sphere. In 1976\, Agmon and Hörmander observed t
hat it is possible to recover a kind of Plancherel theorem in this case\,
by localizing on balls\; this turns out to be the most basic example of a
"Fourier restriction estimate"\, relevant both to analysis and to PDE. In
this talk\, we will explicitly determine the densities that maximize such
estimate\, discovering that they break the rotational symmetry depending o
n the radius of the localizing ball. This is joint work with Diogo Oliveir
a e Silva.\n\nThis talk will be recorded and posted on the webinar homepag
e. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander McDonald (University of Rochester)
DTSTART:20210714T150000Z
DTEND:20210714T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/53
DESCRIPTION:Title: Volumes spanned by k-point configurations
in $\\mathbb{R}^d$\nby Alexander McDonald (University of Rochester) as
part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\
nWe consider a Falconer type problem concerning volumes determined by poin
t configurations in \n$\\mathbb{R}^d$\, and prove that a set with sufficie
ntly large Hausdorff dimension determines a positive measure worth of volu
mes. The strategy for proving the result is to study the group action of t
he special linear group on the space of configurations.\n\nThis talk will
be recorded and posted on the webinar homepage. Slides will be available t
oo.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Passant (U of Rochester)
DTSTART:20210721T150000Z
DTEND:20210721T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/54
DESCRIPTION:Title: Configurations and Erdős style distance p
roblems\nby Jonathan Passant (U of Rochester) as part of Point Distrib
utions Webinar\n\nLecture held in Zoom.\n\nAbstract\nI will discuss point
large configurations in real space and how incidence geometry results of G
uth-Katz and Rudnev can help generalise the results of Solymosi-Tardos and
Rudnev on the number of congruent and similar triangles.\n\nThis talk wil
l be recorded and posted on the webinar homepage. Slides will be available
too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damir Ferizović (TU Graz)
DTSTART:20210818T150000Z
DTEND:20210818T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/55
DESCRIPTION:Title: The spherical cap discrepancy of HEALPix p
oints\nby Damir Ferizović (TU Graz) as part of Point Distributions We
binar\n\nLecture held in Zoom.\n\nAbstract\nIn this talk I will present an
algorithm well known in the Astrophysics and\nCosmology community: HEALP
ix\, short for "Hierarchical\, Equal Area and\niso-Latitude Pixelation\,"
which divides the two dimensional sphere\n$\\mathbb{S}^2$ into 12 rectan
gular shapes (base pixel) of equal area\, and\nallows for further subdivi
sion of each pixel into four smaller\, equal area\nsubpixel mimicking the
simplicity of the unit square in many ways. This\nalgorithm\, introduced
by Górski et al.\, also comes with a projection to the\nplane that up t
o a constant preserves area.\n\nHEALPix also distributes $N$-many points
on $\\mathbb{S}^2$ by placing them\nat centers of pixel of the current le
vel of subdivision\, i.e. first $N=12$\,\nthen $N=12\\cdot 4$\, $N=12\\cd
ot 4^2\, \\ldots\, N=12\\cdot 4^k$\, etc. The\nspherical cap discrepancy
of these points will be proven to be of order\n$N^{-1/2}$\, via recycling
methods introduced by Aistleitner\, Brauchart and\nDick.\\\\\n\n\nThis i
s a joint work with Julian Hofstadler and Michelle Mastrianni.\n\nThis tal
k will be recorded and posted on the webinar homepage. Slides will be avai
lable too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aicke Hinrichs (JKU Linz)
DTSTART:20210825T150000Z
DTEND:20210825T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/56
DESCRIPTION:Title: Dispersion - a survey of recent results an
d applications\nby Aicke Hinrichs (JKU Linz) as part of Point Distribu
tions Webinar\n\nLecture held in Zoom.\n\nAbstract\nThe dispersion of a po
int set\, which is the volume of the largest axis-parallel box in the unit
cube that does not intersect the point set\, is an alternative to the dis
crepancy as a measure for certain (uniform) distribution properties. The c
omputation of the dispersion\, or even the best possible dispersion\, in d
imension two has a long history in computational geometry and computationa
l complexity theory. Given the prominence of the problem\, it is quite sur
prising that\, until recently\, very little was known about the size of th
e largest empty box in higher dimensions. This changed in the last five ye
ars. In this survey talk we focus on recent developments and new applicati
ons of dispersion outside the area of computational geometry.\n\nThis talk
will be recorded and posted on the webinar homepage.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedrich Pillichshammer (JKU Linz)
DTSTART:20210901T150000Z
DTEND:20210901T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/57
DESCRIPTION:Title: $L_{2}$--star\, extreme and periodic discr
epancy\nby Friedrich Pillichshammer (JKU Linz) as part of Point Distri
butions Webinar\n\nLecture held in Zoom.\n\nAbstract\nThis talk is devoted
to three notions of discrepancies with respect to the $L_{2}$ norm and a
variety of test sets. The $L_{2}$ -star discrepancy uses as test sets the
class of axis-parallel boxes anchored in the origin\, the $L_{2}$ extreme
discrepancy uses arbitrary axis-parallel boxes and the \n$L_{2}$ periodi
c discrepancy uses so-called periodic intervals which range over the whole
torus. All three geometrical notions of $L_{2}$ -discrepancy can be inter
preted as worst-case error for quasi-Monte Carlo integration in correspond
ing function spaces. We compare these notions of discrepancy\, discuss som
e relationships and present results for typical QMC point sets such as lat
tice point sets and digital nets. We turn our attention also to the depend
ence on the dimension $d$ and examine whether these $L_{2}$ discrepancies
satisfy some tractability properties or suffer from the curse of dimensio
nality.\n\nThis talk will be recorded and posted on the webinar homepage.
Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Vybíral (Czech Technical University)
DTSTART:20210908T150000Z
DTEND:20210908T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/58
DESCRIPTION:Title: Dispersion of point sets in high dimension
s\nby Jan Vybíral (Czech Technical University) as part of Point Distr
ibutions Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe will discuss the
dispersion of a point set\, which is simply the volume of the largest box
not intersecting the given point set. We shall present several recent res
ult about this notion\, including estimates of its high-dimensional asympt
otic and deterministic constructions. If time permits\, we sketch the most
important parts of the proofs.\n\nThis talk will be recorded and posted o
n the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fátima Lizarte (U of Cantabria)
DTSTART:20210728T150000Z
DTEND:20210728T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/59
DESCRIPTION:Title: A sequence of well conditioned polynomials
\nby Fátima Lizarte (U of Cantabria) as part of Point Distributions W
ebinar\n\nLecture held in Zoom.\n\nAbstract\nIn 1993\, Shub and Smale pose
d the problem of finding a sequence of\nunivariate polynomials $P_N$ of de
gree $N$ with condition number bounded\nabove by $N$. In this talk\, we s
how the origin of this problem\, previous\nknowledge until this work\, its
relation to other interesting mathematical\nproblems such as Smale's 7th
problem\, and our main result obtained: a simple\nand direct answer to the
Shub and Smale problem for $N=4M^2$\, with $M$ a\npositive integer\, as w
ell as comments on its proof.\\\\\n\nThis is a joint work with Carlos Belt
r\\'an.\n\nThis talk will be recorded and posted on the webinar homepage.
Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordi Marzo (U of Cantabria)
DTSTART:20210804T150000Z
DTEND:20210804T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/60
DESCRIPTION:Title: Quadrature rules\, Riesz energies\, discre
pancies and elliptic polynomials\nby Jordi Marzo (U of Cantabria) as p
art of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nI
will talk about the relation between optimal quadratures\, Riesz (or loga
rithmic) energies and minimal discrepancy configurations. In particular I
will discuss the use of the zeros of elliptic (or Kostlan-Shub-Smale) poly
nomials\, among other configurations\, as quadrature nodes for Sobolev spa
ces on the sphere. There will be many open problems throughout the talk.\n
\nThis talk will be recorded and posted on the webinar homepage. Slides wi
ll be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Rudolf (University of Göttingen)
DTSTART:20210922T150000Z
DTEND:20210922T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/61
DESCRIPTION:Title: On the spherical dispersion\nby Daniel
Rudolf (University of Göttingen) as part of Point Distributions Webinar\
n\nLecture held in Zoom.\n\nAbstract\nIn the seminar we provide upper and
lower bounds on the minimal spherical dispersion. In particular\, we see t
hat the inverse of the minimal spherical dispersion behaves linearly in th
e dimension. We also talk about upper and lower bounds of the expected dis
persion for points chosen independently and uniformly at random from the E
uclidean unit sphere. \n\nThe content of the talk is partially based on ht
tps://arxiv.org/abs/2103.11701.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kateryna Pozharska (Institute of Mathematics\, NAS of Ukraine)
DTSTART:20210929T150000Z
DTEND:20210929T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/62
DESCRIPTION:Title: Sampling recovery of functions from reprod
ucing kernel Hilbert spaces in the uniform norm\nby Kateryna Pozharska
(Institute of Mathematics\, NAS of Ukraine) as part of Point Distribution
s Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe study the recovery of m
ultivariate functions from reproducing kernel Hilbert spaces in the unifor
m norm. Surprisingly\, a certain weighted least squares recovery operator
which uses random samples from a distribution\, depending on the spectral
properties of the corresponding embedding\, leads to near optimal results
in several relevant situations. As an application we obtain new recovery g
uarantees for Sobolev type spaces related to Jacobi type differential oper
ators on the one hand and classical multivariate periodic Sobolev type spa
ces with general smoothness weight on the other hand. By applying a recent
ly introduced sub-sampling technique related to Weaver's conjecture\, we f
urther reduce the sampling budget and improve on bounds for the correspond
ing sampling numbers.\nThis is a joint work with Tino Ullrich.\n\nThis tal
k will be recorded and posted on the webinar homepage. Slides will be avai
lable too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nihar Gargava (EPFL)
DTSTART:20210915T150000Z
DTEND:20210915T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/63
DESCRIPTION:Title: Lattice packings through division algebras
\nby Nihar Gargava (EPFL) as part of Point Distributions Webinar\n\nLe
cture held in Zoom.\n\nAbstract\nWe will show the existence of lattice pac
kings in a sparse family of dimensions. This construction will be a genera
lization of Venkatesh's lattice packing result of 2013. In our constructio
n\, we replace the appearance of the cyclotomic number field with a divisi
on algebra over the rationals. This improves the best known lower bounds o
n lattice packing problem in many dimensions. The talk will cover previous
ly known bounds\, an overview of the new bounds and a live numerical simul
ation of Siegel's mean value theorem.\n\nThis talk will be recorded and po
sted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Travaglini (Università di Milano-Bicocca)
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/64
DESCRIPTION:Title: Irregularities of distribution and convex
planar sets\nby Giancarlo Travaglini (Università di Milano-Bicocca) a
s part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract
\nThe term \\textit{Irregularities of Distribution} (often replaced with
Geometric Discrepancy) has been introduced by Klaus Roth in 1954 and refer
s to the question of how to choose a set of $N$ sampling points which can
be used to approximate all the sets in a given reasonably large family in
side the unit square.\nIn this talk\nwe consider a planar convex body $C$
and we prove several analogs of Roth's\ntheorem. When $\\partial C$ is $\\
mathcal{C}%\n^{2}$ regardless of curvature\, we prove that for every set $
\\mathcal{P}_{N}$\nof $N$ points in $\\mathbb{T}^{2}$ we have the sharp bo
und%\n\\[\n\\left\\{\\int_{0}^{1}\\int_{\\mathbb{T}^{2}}\\left\\vert \\mat
hrm{card}\\left(\n\\mathcal{P}_{N}\\mathcal{\\cap}\\left( \\lambda C+t\\r
ight) \\right) -\\lambda\n^{2}N\\left\\vert C\\right\\vert \\right\\vert
^{2}~dtd\\lambda\\right\\}^{1/2}\\geqslant cN^{1/4}\\\;.\n\\]\nWhen $\\pa
rtial C$ is only piecewise $\\mathcal{C}^{2}$ and is not a polygon we\npro
ve the sharp bound%\n\\[\n\\left\\{\\int_{0}^{1}\\int_{\\mathbb{T}^{2}}\\l
eft\\vert \\mathrm{card}\\left(\n\\mathcal{P}_{N}\\mathcal{\\cap}\\left(
\\lambda C+t\\right) \\right) -\\lambda\n^{2}N\\left\\vert C\\right\\ver
t \\right\\vert ^{2}~dtd\\lambda\\right\\}^{1/2}\\geqslant cN^{1/5}.\n\\]\
nWe also give a whole range of intermediate sharp results between $N^{1/5}
$ and\n$N^{1/4}$. Our proofs depend on a lemma of Cassels-Montgomery\, on
ad hoc\nconstructions of finite point sets\, and on a geometric type estim
ate for the\naverage decay of the Fourier transform of the characteristic
function of $C$.\n\nThis talk will be recorded and posted on the webinar h
omepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Beltrán (University of Cantabria)
DTSTART:20220209T160000Z
DTEND:20220209T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/65
DESCRIPTION:Title: Distributing many points in the complex Gr
assmannian an its application in communications\nby Carlos Beltrán (U
niversity of Cantabria) as part of Point Distributions Webinar\n\nLecture
held in Zoom.\n\nAbstract\nI will discuss on a fundamental model for wirel
ess communications (called Noncoherent Communications) that has a very sim
ple mathematical explanation and modelling. It turns out that in order to
achieve optimal communication rate one must choose a finite collection of
points in the complex Grassmannian. In this talk I will present the proble
m from scratch\, explaining the setting\, the model\, the road to the math
ematical problem of point distribution… and a new approach to this last
mathematical problem\, based on Riemannian optimization\, which outperform
s all known methods to the date for choosing well distributed codes in the
se classical spaces. This is joint work with a team of engineers\, credits
will be given during the talk.\n\nThis talk will be recorded and posted o
n the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galyna Livshyts (Georgia Tech)
DTSTART:20220216T160000Z
DTEND:20220216T170000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/66
DESCRIPTION:Title: An efficient net construction and applicat
ions to random matrix theory\, and to minimal dispersion estimation\nb
y Galyna Livshyts (Georgia Tech) as part of Point Distributions Webinar\n\
nLecture held in Zoom.\n\nAbstract\nWe explain a construction of an effici
ent net on the sphere in a high-dimensional space\, and draw some applicat
ions in random matrix theory (partly joint with Tikhomirov and Vershynin).
One of the steps in our construction is also relevant for estimating mini
mal dispersion in the cube (joint with Litvak).\n\nThis talk will be recor
ded and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Sloan (U of New South Wales)
DTSTART:20220309T210000Z
DTEND:20220309T220000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/67
DESCRIPTION:Title: Pros and cons of lattice points for high-d
imensional approximation\nby Ian Sloan (U of New South Wales) as part
of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nIn th
is talk\, based on recent joint work with Vesa Kaarnioja\, Yoshihito Kazas
hi\, Frances Kuo and Fabio Nobile\, I describe a fast method for high-dime
nsional approximation on the torus. A typical approximation scheme for a g
iven function $f(\\bt)$ involves choosing a set of points $\\bt_1\, \\ldot
s\, \\bt_n$ at which function values are to be given as inputs\, and a met
hodology for constructing a more or less smooth approximation $f_n(\\bt)$.
We shall see that lattice points have advantages\, but also limitations\
, as sample points. The method to be described is based on so-called kern
els and lattice points. It appears to offer considerable promise for prac
tical high-dimensional approximation.\n\nThis talk will be recorded and po
sted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Fukshansky (Claremont McKenna College)
DTSTART:20220323T150000Z
DTEND:20220323T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/68
DESCRIPTION:Title: Lattices from group frames and vertex tran
sitive graphs\nby Lenny Fukshansky (Claremont McKenna College) as part
of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nTigh
t frames in Euclidean spaces are widely used convenient generalizations of
orthonormal bases. A particularly nice class of such frames is generated
as orbits under irreducible actions of finite groups of orthogonal matrice
s: these are called irreducible group frames. Integer spans of rational ir
reducible group frames form Euclidean lattices with some very nice geometr
ic properties\, called strongly eutactic lattices. We discuss this constru
ction\, focusing on an especially interesting infinite family in arbitrari
ly large dimensions\, which comes from vertex transitive graphs. We demons
trate several examples of such lattices from graphs that exhibit some rath
er fascinating properties. This is joint work with Deanna Needell\, Josiah
Park and Yuxin Xin.\n\nThis talk will be recorded and posted on the webin
ar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bence Borda (TU Graz)
DTSTART:20220406T150000Z
DTEND:20220406T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/69
DESCRIPTION:Title: A smoothing inequality for the Wasserstein
metric on compact manifolds\nby Bence Borda (TU Graz) as part of Poin
t Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nImproving a
result of Brown and Steinerberger\, we present a Berry-Esseen type smoothi
ng inequality for the quadratic Wasserstein metric on compact Riemannian m
anifolds\, which estimates the distance between two probability measures i
n terms of their Fourier transforms. The inequality is sharp\, and has a w
ide range of applications in probability theory and number theory. We disc
uss sharp convergence rates of the empirical measure of an i.i.d. or stati
onary weakly dependent sample\, complementing recent results of Bobkov and
Ledoux on the unit cube\, and Ambrosio\, Stra and Trevisan on compact man
ifolds. We also estimate the convergence rate of random walks on compact g
roups to the Haar measure\, and establish the functional CLT and the funct
ional LIL for additive functionals. On compact semisimple Lie groups these
hold even without a spectral gap assumption. As an application to finite
point sets arising in number theory\, we show that a classical constructio
n of Lubotzky\, Phillips and Sarnak on SU(2) and SO(3) achieves optimal ra
te in the quadratic Wasserstein metric.\n\nThis talk will be recorded and
posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bétermin (Université Claude Bernard Lyon 1)
DTSTART:20220420T150000Z
DTEND:20220420T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/70
DESCRIPTION:Title: Minimality results for the Embedded Atom M
odel\nby Laurent Bétermin (Université Claude Bernard Lyon 1) as part
of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\nThe
Embedded-Atom Model (EAM) provides a phenomenological description of atomi
c arrangements in metallic systems. It consists of a configurational energ
y depending on atomic positions and featuring the interplay of two-body at
omic interactions and nonlocal effects due to the corresponding electronic
clouds. In this talk\, I will present minimality results for this system
among lattices in dimensions 2 and 3 as well as other aspects of the probl
em. This is a joint work with Manuel Friedrich (University of Erlangen) an
d Ulisse Stefanelli (University of Vienna).\n\nThis talk will be recorded
and posted on the webinar homepage. Slides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Codina Cotar (University College London)
DTSTART:20220511T150000Z
DTEND:20220511T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/71
DESCRIPTION:Title: Equality of the Jellium and Uniform Electr
on Gas next-order asymptotic terms for Coulomb and Riesz potentials\nb
y Codina Cotar (University College London) as part of Point Distributions
Webinar\n\nLecture held in Zoom.\n\nAbstract\nWe consider the sharp next-o
rder asymptotics problems for: (1) the minimum energy for optimal N-point
configurations\; (2) the N-Marginal Optimal Transport\; and (3) the Jelliu
m problem for N-point configurations\, in all three cases with Riesz costs
with inverse power-law long-range interactions. The first problem describ
es the ground state of a Coulomb or Riesz gas\, the second appears as a se
miclassical limit of DFT energy\, modelling a quantum version of the same
system (and is called Uniform Electron Gas in the physics literature)\, an
d the third describes charges in a uniform negative background\, a rough m
odel for electrons in a metal. Recently the second-order terms in the larg
e-N asymptotic expansions for power s in dimension d were shown for: (1) f
or \\max(0\,d-2)\\le sGeneralized Erdős-Turán inequalities and
stability of energy minimizers\nby Ruiwen Shu (University of Oxford)
as part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstrac
t\nThe classical Erdős-Turán inequality on the distribution of roots for
complex polynomials can be equivalently stated in a potential theoretic f
ormulation\, that is\, if the logarithmic potential generated by a probabi
lity measure on the unit circle is close to 0\, then this probability meas
ure is close to the uniform distribution. We generalize this classical ine
quality from $d=1$ to higher dimensions $d>1$ with the class of Riesz pote
ntials which includes the logarithmic potential as a special case. In orde
r to quantify how close a probability measure is to the uniform distributi
on in a general space\, we use Wasserstein-infinity distance as a canonica
l extension of the concept of discrepancy. Then we give a compact descript
ion of this distance. Then for every dimension $d$\, we prove inequalities
bounding the Wasserstein-infinity distance between a probability measure
$\\rho$ and the uniform distribution by the $L^p$-norm of the Riesz potent
ials generated by $\\rho$. Our inequalities are proven to be sharp up to t
he constants for singular Riesz potentials. Our results indicate that the
phenomenon discovered by Erdős and Turán about polynomials is much more
universal than it seems. Finally we apply these inequalities to prove stab
ility theorems for energy minimizers\, which provides a complementary pers
pective on the recent construction of energy minimizers with clustering be
havior\n\nThis talk will be recorded and posted on the webinar homepage. S
lides will be available too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damir Ferizović (KU Leuven)
DTSTART:20220519T150000Z
DTEND:20220519T160000Z
DTSTAMP:20260404T095208Z
UID:PointDistributionsPotentialThry/73
DESCRIPTION:Title: Spherical cap discrepancy of perturbed lat
tices under the Lambert projection\nby Damir Ferizović (KU Leuven) as
part of Point Distributions Webinar\n\nLecture held in Zoom.\n\nAbstract\
nGiven any full rank lattice and a natural number N \, we regard the point
set given by the scaled lattice intersected with the unit square under th
e Lambert map to the unit sphere\, and show that its spherical cap discrep
ancy is at most of order N \, with leading coefficient given explicitly an
d depending on the lattice only. The proof is established using a lemma th
at bounds the amount of intersections of certain curves with fundamental d
omains that tile R^2 \, and even allows for local perturbations of the lat
tice without affecting the bound\, proving to be stable for numerical appl
ications. A special case yields the smallest constant for the leading term
of the cap discrepancy for deterministic algorithms up to date.\n\nThis t
alk will be recorded and posted on the webinar homepage. Slides will be av
ailable too.\n
LOCATION:https://stable.researchseminars.org/talk/PointDistributionsPotent
ialThry/73/
END:VEVENT
END:VCALENDAR