Parker Evans

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20242026

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math.DG2026

Polynomial Maximal Surfaces in H^{2,2} and Spherical Polygons

Parker Evans, Alex Moriani

We study the moduli space of complete maximal surfaces in pseudo-hyperbolic space $H^{2, 2}$ with polygonal asymptotic boundary a lightlike $(n + 4)$ -gon in the Einstein univ…

math.DG2025

$G_{2}^{'}$ -Slodowy Slices I: Geometric Structures

Colin Davalo, Parker Evans

Let $S$ be a closed surface of genus $g \geq 2$ . We construct locally homogeneous geometric structures on closed 5-manifolds fibering over $S$ , modeled on the two partial flag mani…

math.DG2024

Geometric Structures for the $G_{2}^{'}$ -Hitchin Component

Parker Evans

We give an explicit geometric structures interpretation of the $G_{2}^{'}$ -Hitchin component $H i t (S, G_{2}^{'}) \subset χ (π_{1} S, G_{2}^{'})$ of a closed oriented surface $S$ of genus $g \geq 2$ . In…

Polynomial Maximal Surfaces in H^{2,2} and Spherical Polygons

G2′​-Slodowy Slices I: Geometric Structures

Geometric Structures for the G2′​-Hitchin Component

$G_{2}^{'}$ -Slodowy Slices I: Geometric Structures

Geometric Structures for the $G_{2}^{'}$ -Hitchin Component