Maximal surfaces in the pseudo-hyperbolic space

Abstract

The pseudo-hyperbolic space $\mathbb{H}^{p,q}$ is a pseudo-Riemannian analogue of the classical hyperbolic space. In this talk, I will explain how equivariant maximal surfaces in $\mathbb{H}^{2,n}$ are related to harmonic maps into some non-compact symmetric space (so in particular to Higgs bundles). This link provides a powerful tool to study maximal representations in rank 2 Hermitian Lie groups. This is a joint work with Brian Collier and Nicolas Tholozan.Non UBCUnreviewedAuthor affiliation: USC DornsifeResearche