In this continuation of Daniel Stern’s talk from September 18, I will discuss joint work with Karpukhin, Kusner, and Stern on the construction of new minimal surfaces in S^n and B^n. These surfaces are invariant under certain discrete groups and are constructed via an equivariant eigenvalue maximization procedure. While the surfaces produced by this method (when successful) are in general expected to merely be immersed and have high codimension—depending on the topology of the surface—certain symmetries permit the construction of embedded minimal surfaces in S^3 and in B^3 with prescribed topology.