6 problems

Consider arithmetic subgroups and their associated quotients in the setting of the paper, where a group is non-cocompact if the quotient is not compact. Non-cocompact minimality co…

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 $[0;2,3,7]$, $[0;2,4,5]$,…

A link orbifold is a hyperbolic $3$-orbifold whose singular locus is a disjoint union of closed curves. The volume of an orbifold is denoted by $\operatorname{vol}(\mathcal{O})$. M…