Logarithmic Energy of Points on S^2

I will discuss a very old problem that has an elementary formulation: how do you place n points on the standard sphere embedded in three dimensions in such a way that the product of all pairwise distances is as large as possible -- and how large does that product have to be? The idea is that this forces the points to be regularly spread out -- there are many known constructions but few rigorous results. The problem also arises in a different framework in mathematical physics (where it is related to the `crystallization conjecture').  I will give an introduction to all these things and discuss a recent new perspective that improves the known results on the size of the product -- the heat kernel on S^2 plays an important role.