Optimal Packings of Circles on Spheres and Flat Tori

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).