In the Labourie-Loftin parametrization of the Hitchin component of surface group
representations into SL (3, R), we prove an asymptotic formula for holonomy along rays in …

We generalize arc coordinates for maximal representations from a hyperbolic surface with
boundary into $\text {PSp}(4,\mathbb {R}) $, focusing on the case where the surface is a pair …

We show that, in the character variety of surface group representations into the Lie group
$\mathrm {PSL}(2,\mathbb {R})\times\mathrm {PSL}(2,\mathbb {R}) $, the compactification of …

Riemann surfaces are of fundamental importance in many areas of mathematics and
theoretical physics. The study of the moduli space of Riemann surfaces of a fixed topological …

We develop a Lie-theoretic perspective on Hitchin's equations for cyclic $ G $-Higgs
bundles, which we use to study analytic and geometric properties of harmonic maps. Among …

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Let S be a closed surface of genus g≥ 2 and ρ a maximal PSL⁡(2, ℝ)× PSL⁡(2, ℝ) surface
group representation. By a result of Schoen, there is a unique ρ–equivariant minimal surface …

We show that, in the character variety of surface group representations into the Lie group
PSL⁡(2, ℝ)× PSL⁡(2, ℝ), the compactification of the maximal component introduced by the …

This thesis studies the degeneration of a particular class of minimal surfaces in the bidisc,
describing both the limiting metric structure and geometry. Minimal surfaces inside …