I'll discuss joint work with Adrian Chu, relating Kapouleas's doubling construction for minimal surfaces to the variational theory for a Coulomb-type interaction energy for Schroedinger operators. For the Jacobi operator of a nondegenerate minimal surface, we show that suitable families of critical points of this energy give rise to high-genus minimal surfaces, provided a few key estimates are satisfied. By studying the ground states for this energy, we show that a generic minimal surface of index one admits such a doubling, and deduce as a corollary that generic 3-manifolds contain sequences of embedded minimal surfaces with bounded area and arbitrarily large genus. I'll also make some comparisons with the construction of minimal doublings via eigenvalue optimization.
