Optimal polarization and covering on sets of low smoothness

Oleksandr Vlasiuk (Vanderbilt U, Nashville)

Jan 20. 2022, 15:45 — 16:25

We discuss the asymptotic properties of point configurations that achieve optimal covering on rectifiable sets as well as on fractals. Our results include the existence of asymptotics of best covering and maximal polarization for $ (\h_d,d) $-rectifiable sets and maximal polarization on self-similar fractals. This extends the classical results of Kolmogorov and Tikhomirov on metric entropy of compact sets in the Euclidean space.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Optimal Point Configurations on Manifolds (Workshop)
Christine Bachoc (U Bordeaux)
Henry Cohn (Microsoft, Redmond)
Peter Grabner (TU Graz)
Douglas Hardin (Vanderbilt U, Nashville)
Edward Saff (Vanderbilt U, Nashville)
Achill Schürmann (U of Rostock)
Robert Womersley (UNSW, Sydney)