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BEGIN:VEVENT
SUMMARY:Ryan Alweiss (Princeton University)
DTSTART:20200930T140000Z
DTEND:20200930T142500Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/1
DESCRIPTION:Title: Discrepancy Minimization via a Self-Balancing Walk\nby Rya
n Alweiss (Princeton University) as part of BIRS workshop: Combinatorial a
nd Geometric Discrepancy\n\n\nAbstract\nWe study discrepancy minimization
for vectors in $\\mathbb{R}^n$ under various settings. The main result is
the analysis of a new simple random process in multiple dimensions throug
h a comparison argument. As corollaries\, we obtain bounds which are tigh
t up to logarithmic factors for several problems in online vector balancin
g posed by Bansal\, Jiang\, Singla\, and Sinha (STOC 2020)\, as well as li
near time algorithms of logarithmic bounds for the Komlós conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Fairchild (University of Washington)
DTSTART:20200930T142500Z
DTEND:20200930T145000Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/2
DESCRIPTION:Title: Families of well-approximable measures\nby Samantha Fairch
ild (University of Washington) as part of BIRS workshop: Combinatorial and
Geometric Discrepancy\n\n\nAbstract\nIt is conjectured that the optimal o
rder of approximation of the Lebesgue measure by a finite atomic measure i
s $N^{-1} (\\log N)^{d-1}$. This result is known for dimensions 1 and 2. W
e will share recent work of Fairchild\, Goering\, Weiss which in dimension
1 confirms Lebesgue measure is indeed the hardest to approximate. Moreove
r we improve on recent work by Aistleitner\, Bilyk\, and Nikolov by constr
ucting a family of discrete measures with star discrepancy bounded above b
y $N^{-1} (\\log(N))$.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Neumayer (TU Berlin)
DTSTART:20200930T145000Z
DTEND:20200930T151500Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/3
DESCRIPTION:Title: Curve Based Approximation of Images on Manifolds\nby Sebas
tian Neumayer (TU Berlin) as part of BIRS workshop: Combinatorial and Geom
etric Discrepancy\n\n\nAbstract\nIn this talk\, we will discuss a way of a
pproximating images living on a manifold with Lipschitz continuous curves.
In order to quantify the approximation quality\, we employ discrepancies.
This enables us to provide approximation rates independent of the dimensi
on. The proposed mathematical model is illustrated with some numerical exa
mples.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tetiana Stepaniuk (Universität zu Lübeck)
DTSTART:20200930T151500Z
DTEND:20200930T154000Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/4
DESCRIPTION:Title: Hyperuniformity of point set sequences\nby Tetiana Stepani
uk (Universität zu Lübeck) as part of BIRS workshop: Combinatorial and G
eometric Discrepancy\n\n\nAbstract\nIn the talk we study hyperuniformity o
n flat tori. Hyperuniform point sets on the unit sphere have been studied
by J. Brauchart\, P. Grabner\, W. Kusner and J. Ziefle. We will discuss s
everal examples of hyperuniform sequences of point sets.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Pasing (Ruhr West University of Applied Sciences)
DTSTART:20200930T154000Z
DTEND:20200930T160500Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/5
DESCRIPTION:Title: Improved Discrepancy Bounds and Estimates\nby Hendrik Pasi
ng (Ruhr West University of Applied Sciences) as part of BIRS workshop: Co
mbinatorial and Geometric Discrepancy\n\n\nAbstract\nError estimation in M
onte-Carlo integration is related to the star discrepancy of random point
sets. We will present latest results for (probabilistic) upper bounds of t
he star discrepancy which are based on major improvements on bounds of bra
cketing numbers. Additionally we introduce upper bounds for the expected v
alue of the star discrepancy. This is joint work with Michael Gnewuch and
Christian Weiß.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ujue Etayo (TU Graz)
DTSTART:20201002T140000Z
DTEND:20201002T142500Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/6
DESCRIPTION:Title: A deterministic set of spherical points with small discrepancy
\nby Ujue Etayo (TU Graz) as part of BIRS workshop: Combinatorial and
Geometric Discrepancy\n\n\nAbstract\nIn this talk we present the problem o
f seeking for point configurations on the 2-dimensional sphere with small
discrepancies. In particular\, we prove that points coming from the Diamon
d ensemble (a deterministic multiparametric model of points uniformly dist
ributed on the sphere) for a concrete choice of parameters provides the be
st spherical cap discrepancy known until date for a deterministic family o
f points.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathias Sonnleitner (JKU Linz)
DTSTART:20201002T142500Z
DTEND:20201002T145000Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/7
DESCRIPTION:Title: (Non-)optimal point sets for numerical integration\nby Mat
hias Sonnleitner (JKU Linz) as part of BIRS workshop: Combinatorial and Ge
ometric Discrepancy\n\n\nAbstract\nConnections between combinatorial/geome
tric discrepancy\, worst-case errors of algorithms and quantization of mea
sures are presented. The aim is to indicate possible answers to questions
of the type: How to geometrically measure the quality of a point set for a
pproximation problems?\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Reis (University of Washington)
DTSTART:20201002T145000Z
DTEND:20201002T151500Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/8
DESCRIPTION:Title: Vector Balancing in Lebesgue Spaces\nby Victor Reis (Unive
rsity of Washington) as part of BIRS workshop: Combinatorial and Geometric
Discrepancy\n\n\nAbstract\nThe Komlós conjecture in discrepancy theory a
sks for a ±1-coloring\, for any given unit vectors\, achieving constant d
iscrepancy in the ell-infinity norm. We investigate what ell-q discrepancy
bound to expect\, more generally\, for ±1-colorings of vectors in the un
it ell-p ball for any p less than q\, and achieve optimal partial coloring
s. In particular\, for p = q\, our result generalizes Spencer's "six stand
ard deviations" theorem.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lily Li (University of Toronto)
DTSTART:20201002T151500Z
DTEND:20201002T154000Z
DTSTAMP:20260404T042404Z
UID:BIRS_20w5141/9
DESCRIPTION:Title: On the Computational Complexity of Linear Discrepancy\nby
Lily Li (University of Toronto) as part of BIRS workshop: Combinatorial an
d Geometric Discrepancy\n\n\nAbstract\nLinear discrepancy is a variant of
discrepancy that measures how well we can round vectors w in $[0\,1]^n$ to
vectors x in ${0\,1}^n$\, with the error of the rounding measured with re
spect to a matrix A\, i.e. as the ell-infinity norm of the difference Ax -
Aw. This is a variant of classical combinatorial discrepancy\, which only
considers the all-halves vector as w\, and also captures measure theoreti
c discrepancy. Our work initiates the study of the computational complexit
y of linear discrepancy. In particular\, we show that it is NP-Hard in gen
eral\, and is computable in polynomial time when A has a constant number o
f rows\, and the magnitude of each entry in A has bounded bit complexity.
When there is only one row\, we can compute the linear discrepancy in O(n
log n) time.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5141/9/
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