Section: New Results

Energy of the Coulomb gas on the sphere at low temperature

In relation to the 7th Smale problem, which is about finding polynomial time algorithm to produce well spread configuration of points on the sphere in a quantified manner, C. Beltran and A. Hardy proved in [4] that the Coulomb gas on the sphere at a temperature proportional to the inverse number of points in a configuration reaches the numerical precision required by this problem. We however did not discuss yet the algorithmic procedure, which is currently in investigation by A. Hardy and M. Simon.