Special Lecture: Finding Balance in Chaos: Approximating orthogonal polynomials on Julia sets

Equilibrium measures of compact sets in two dimensions are a generalization of equilibrium charge distributions on perfect conductors. Using equilibrium measures, we can compute the capacity of a compact set: the ability of the set to hold energy. We will compare two methods of approximating these equilibrium measures and thus the capacity of sets using finite collections of points, and then study the convergence behavior and properties of these approximations.