Group Seminar: Multivariate Algorithms and Quasi-Monte Carlo Methods (QMC)

Jan Vybiral/Czech Technical University, Prague. Title: Dispersion of a point set: lower and upper bounds

January 16, 2025 10:00, SP2 416-2

ABSTRACT:

The dispersion of a set of points in the unit cube is defined as the volume of the largest axis-parallel box, which does not intersect this point set. Intuitively, the smaller is the dispersion of a set, the better are the point distributed across the unit cube. We are therefore interest in point sets, which have both small cardinality as well as small dispersion. We present some recent results about the minimal dispersion, which a set of $n$ points in the unit cube $[0,1]^d$ can achieve. In particular, we report on some work in progress, where we employ recent results from extreme combinatorics to obtain surprising lower bounds for minimal dispersion.