If n negatively charged particles are free to move about a compact subset of the complex plane, then the pairwise repulsion among the particles will cause them to spread out as much as possible. In the limit of large n, the particles approach an equilibrium distribution supported on the boundary of the set, and the limiting measure can be studied using potential theory. I’ll describe a variation in which complex plane is replaced by the complex projective line (a.k.a. the Riemann sphere) and the potential kernels arise naturally from questions in number theory (in which the "negatively charged particles” are actually algebraic numbers with height as small as possible.) This is joint work with Paul Fili.