Energy Minimizing Spherical Codes and Designs

01/27/2009 - 12:15pm
01/27/2009 - 1:10pm
Achill Schurmann (University of Magdeburg)

In this talk we consider the problem of distributing points on the n-dimensional unit sphere so that they minimize some potential energy. We are in particular interested in "universally optimal" configurations, which minimize the energy for all completely monotonic potential functions, and in "balanced configurations", which are in equilibrium under all possible force laws. Both properties can be proven to be valid for high enough spherical designs. Using massive computer experiments we obtain new (potential) universal optima and other beautiful spherical codes. Analyzing them reveals a lot of interesting structure and there is hope that this may lead to new insights. One of the very surprising discoveries is the existence of balanced configurations without symmetries.

ML 211