Video library: O. R. Musin, Optimal Packings of Circles on Spheres and Flat Tori

VIDEO LIBRARY


Information Technologies and Systems 2013 September 4, 2013 15:30, Svetlogorsk (Kaliningrad Region, Russia)

Optimal Packings of Circles on Spheres and Flat Tori O. R. Musin^ab ^a University of Texas at Brownsville ^b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
Abstract: We consider packings of congruent $N$ circles on spheres (the Tammes problem) and flat square tori. Toroidal packings are interesting due to a practical reason – the problem of super resolution of images. We classified ed all locally optimal spherical arrangements up to $N=11$. For packings on tori we have found optimal arrangements for $N = 6, 7$ and $8$. Surprisingly, for the case $N=7$ there are three different optimal arrangements. Our proofs are based on computer enumerations of spherical and toroidal irreducible contact graphs. This is joint work with Alexey Tarasov (spheres) and Anton Nikitenko (tori).