5 problems

Let $n \in 2\mathbb{Z}_{\geq 1}$. Write $\Gamma^n_{\mathrm{eis}} \setminus \mathbb{R} H^n$ for the non-arithmetic hyperbolic orbifold $M({\mathscr{L}}_{\mathrm{eis}}^n,\alpha_0)$,…

Let $N(r)$ denote the order of the outer automorphism group of the principal arithmetic subgroup $\Lambda_0^n$, in the setting of the arithmetic quotients considered in the paper.…

For a cocompact lattice $\Gamma$ in $G=\operatorname{PSL}_2(\mathbf{R})$, let $\lambda_1(\Gamma\backslash\mathbf{H})$ be the first Laplace eigenvalue of the compact hyperbolic $2$-…

Let $\Delta(2,3,7)$ be the $(2,3,7)$-triangle group acting on the hyperbolic plane $\mathbb{H}$, and let $\ell_n$ denote the lengths of the relevant closed geodesics, subject to th…

Spectral classification conjecture. The set $E$ is bounded above by $44.8883537$. The only orbifolds with $\ell_1>\ell_1^{(0)}$ are isometric to $[0;2,3,7]$, $[0;2,4,5]$,…