Chapter 1 presents joint work with Nikolaos Kapouleas and is concerned with constructions of new closed, embedded minimal surfaces in the round three sphere using …
We study the boundary of the moduli space of Higgs bundles using analytic methods such as harmonic maps and partial differential equations to give new …
We study existence and regularity of harmonic maps between 2-dimensional simplicial complexes. This work begins by defining metrics on these simplicial complexes and describing their …
We study the roles of domain and target curvatures in harmonic maps into metric spaces with upper curvature bounds. We begin computing the domain and …