BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ryan Alweiss (Princeton University) DTSTART:20200930T140000Z DTEND:20200930T142500Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/1 DESCRIPTION:Title: Discrepancy Minimization via a Self-Balancing Walk\nby Ryan Alwei ss (Princeton University) as part of BIRS workshop: Combinatorial and Geom etric Discrepancy\n\n\nAbstract\nWe study discrepancy minimization for vec tors in $\\mathbb{R}^n$ under various settings. The main result is the an alysis of a new simple random process in multiple dimensions through a com parison argument. As corollaries\, we obtain bounds which are tight up to logarithmic factors for several problems in online vector balancing posed by Bansal\, Jiang\, Singla\, and Sinha (STOC 2020)\, as well as linear ti me algorithms of logarithmic bounds for the Komlós conjecture.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Samantha Fairchild (University of Washington) DTSTART:20200930T142500Z DTEND:20200930T145000Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/2 DESCRIPTION:Title: Families of well-approximable measures\nby Samantha Fairchild (Un iversity of Washington) as part of BIRS workshop: Combinatorial and Geomet ric Discrepancy\n\n\nAbstract\nIt is conjectured that the optimal order of approximation of the Lebesgue measure by a finite atomic measure is $N^{- 1} (\\log N)^{d-1}$. This result is known for dimensions 1 and 2. We will share recent work of Fairchild\, Goering\, Weiss which in dimension 1 conf irms Lebesgue measure is indeed the hardest to approximate. Moreover we im prove on recent work by Aistleitner\, Bilyk\, and Nikolov by constructing a family of discrete measures with star discrepancy bounded above by $N^{- 1} (\\log(N))$.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Neumayer (TU Berlin) DTSTART:20200930T145000Z DTEND:20200930T151500Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/3 DESCRIPTION:Title: Curve Based Approximation of Images on Manifolds\nby Sebastian Ne umayer (TU Berlin) as part of BIRS workshop: Combinatorial and Geometric D iscrepancy\n\n\nAbstract\nIn this talk\, we will discuss a way of approxim ating images living on a manifold with Lipschitz continuous curves. In ord er to quantify the approximation quality\, we employ discrepancies. This e nables us to provide approximation rates independent of the dimension. The proposed mathematical model is illustrated with some numerical examples.\ n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Tetiana Stepaniuk (Universität zu Lübeck) DTSTART:20200930T151500Z DTEND:20200930T154000Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/4 DESCRIPTION:Title: Hyperuniformity of point set sequences\nby Tetiana Stepaniuk (Uni versität zu Lübeck) as part of BIRS workshop: Combinatorial and Geometri c Discrepancy\n\n\nAbstract\nIn the talk we study hyperuniformity on 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 several examples of hyperuniform sequences of point sets.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Pasing (Ruhr West University of Applied Sciences) DTSTART:20200930T154000Z DTEND:20200930T160500Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/5 DESCRIPTION:Title: Improved Discrepancy Bounds and Estimates\nby Hendrik Pasing (Ruh r West University of Applied Sciences) as part of BIRS workshop: Combinato rial and Geometric Discrepancy\n\n\nAbstract\nError estimation in Monte-Ca rlo integration is related to the star discrepancy of random point sets. W e will present latest results for (probabilistic) upper bounds of the star discrepancy which are based on major improvements on bounds of bracketing numbers. Additionally we introduce upper bounds for the expected value of the star discrepancy. This is joint work with Michael Gnewuch and Christi an Weiß.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ujue Etayo (TU Graz) DTSTART:20201002T140000Z DTEND:20201002T142500Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/6 DESCRIPTION:Title: A deterministic set of spherical points with small discrepancy\nb y Ujue Etayo (TU Graz) as part of BIRS workshop: Combinatorial and Geometr ic Discrepancy\n\n\nAbstract\nIn this talk we present the problem of seeki ng for point configurations on the 2-dimensional sphere with small discrep ancies. In particular\, we prove that points coming from the Diamond ensem ble (a deterministic multiparametric model of points uniformly distributed on the sphere) for a concrete choice of parameters provides the best sphe rical cap discrepancy known until date for a deterministic family of point s.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathias Sonnleitner (JKU Linz) DTSTART:20201002T142500Z DTEND:20201002T145000Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/7 DESCRIPTION:Title: (Non-)optimal point sets for numerical integration\nby Mathias So nnleitner (JKU Linz) as part of BIRS workshop: Combinatorial and Geometric Discrepancy\n\n\nAbstract\nConnections between combinatorial/geometric di screpancy\, worst-case errors of algorithms and quantization of measures a re presented. The aim is to indicate possible answers to questions of the type: How to geometrically measure the quality of a point set for approxim ation problems?\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Reis (University of Washington) DTSTART:20201002T145000Z DTEND:20201002T151500Z DTSTAMP:20260422T185903Z UID:BIRS_20w5141/8 DESCRIPTION:Title: Vector Balancing in Lebesgue Spaces\nby Victor Reis (University o f Washington) as part of BIRS workshop: Combinatorial and Geometric Discre pancy\n\n\nAbstract\nThe Komlós conjecture in discrepancy theory asks for a ±1-coloring\, for any given unit vectors\, achieving constant discrepa ncy in the ell-infinity norm. We investigate what ell-q discrepancy bound to expect\, more generally\, for ±1-colorings of vectors in the unit ell- p ball for any p less than q\, and achieve optimal partial colorings. In p articular\, for p = q\, our result generalizes Spencer's "six standard dev iations" theorem.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Lily Li (University of Toronto) DTSTART:20201002T151500Z DTEND:20201002T154000Z DTSTAMP:20260422T185903Z 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 and Geome tric Discrepancy\n\n\nAbstract\nLinear discrepancy is a variant of discrep ancy that measures how well we can round vectors w in $[0\,1]^n$ to vector s x in ${0\,1}^n$\, with the error of the rounding measured with respect t o a matrix A\, i.e. as the ell-infinity norm of the difference Ax - Aw. Th is is a variant of classical combinatorial discrepancy\, which only consid ers the all-halves vector as w\, and also captures measure theoretic discr epancy. Our work initiates the study of the computational complexity of li near discrepancy. In particular\, we show that it is NP-Hard in general\, and is computable in polynomial time when A has a constant number of rows\ , and the magnitude of each entry in A has bounded bit complexity. When th ere is only one row\, we can compute the linear discrepancy in O(n log n) time.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5141/9/ END:VEVENT END:VCALENDAR