3 problems

Let $S$ and $S'$ be hyperbolic surfaces, and let the multi-set of lengths of their simple closed geodesics be called their simple length spectrum. Simple length spectrum rigidity c…

Let $\Gamma_\mathfrak{D}$ be an arithmetic quaternion group. The complex length spectrum of $\mathbb{H}^3/\Gamma_\mathfrak{D}$ has gaps, and let $\mathcal{G}(x)$ denote the number…

Let $S$ be the surface and $\rho$ a representation in $Hit_n(S)$. A representation $\rho'$ is in the Fuchsian locus of $Hit_n(S)$ when it is a Fuchsian representation viewed in…