5 problems

Let $S$ be a closed, oriented surface of genus at least $2$. An admissible weighted graph $(\Gamma,\theta)$ in $S$ is a graph embedded in $S$ that is the 1-skeleton of a cell decom…

Let $S_g$ be a closed surface of genus $g$, let $E$ be the edge set of a triangulation of $S_g$, and let $\Theta:E\to[0,\pi)$ be a Delaunay angle structure. Let $P(\Theta)$ be the…

Let $\Sigma$ be an orientable surface with finitely many punctures and no boundary, and let $\mathcal{P}(\Sigma)$ denote its deformation space of complex projective structures. Eac…

Let $S$ be an oriented closed surface of genus $g\geq 2$, let $\tau$ be a polygonal cell decomposition of $S$, and let $c$ be a complex structure on $S$. A complex projective struc…

Fix a marking of the projective structure $\Omega/\Gamma$ on $S$ with Schottky holonomy $\rho$. Let $\mathcal{P}_\rho$ be the collection of projective structures on $S$ with holono…