GSAS: A Calderón's problem for harmonic maps

The anisotropic Calderón's problem asks to what extent the Dirichlet-to-Neumann (DN) map of the Dirichlet problem for the Laplace-Beltrami equation determines the metric on a Riemannian manifold. I will review some classic results, in addition to some recent results for the analogous problem for minimal surfaces. Finally, I will present recent progress on the analogous problem for harmonic maps between Riemannian manifolds: the DN map for the Dirichlet problem for harmonic maps determines the metrics of both, the domain and the codomain, in certain cases.