9 problems

Volume–Dehn separation conjecture. In Euclidean, spherical, and hyperbolic geometries, do the volume and generalized Dehn invariant separate the scissors congruence classes of poly…

Let $\operatorname{\mathcal P}(\mathbb X)$ be the scissors congruence group of polytopes in a 3-dimensional geometry $\mathbb X$, and let … be the kernel of the Dehn invariant. Deh…

Let $M$ be a weakly-gentle cusped manifold, and let $H_N(M)$ be its quantum dilogarithmic invariant. Let $\mathfrak c_{\mathcal I_{fc}}(M)$ denote its ${\mathcal I}_{fc}$-scissors…

Let $\widetilde{\mathcal{P}}(S^{n-1})$ be the reduced spherical scissors congruence group, and let the direct sum … be equipped with the Sah algebra Hopf structure, whose coproduct…

Let $G$ be a finite group. The equivariant $SK^G$-groups, as $H$ varies over the subgroups of $G$, form a Mackey functor, and let $K_G(\underline{\mathbb{Z}})$ denote the genuine…

Let $E^n$ be the $n$-dimensional Euclidean space and let $P\subseteq E^n$ be a polytope. The abelianisation of a group is its quotient by its commutator subgroup. Zakharevich's con…

Let $P$ be a flexible polyhedron in one of the constant-curvature spaces $\mathbb{E}^n$, $\mathbb{S}^n$, or $\mathbbl{\Lambda}^n$. Two polyhedra are scissors congruent if they can…

Let $M$ be a hyperbolic manifold, and let its stable scissors congruence class mean its scissors congruence class after adjoining a common hyperbolic polyhedron. Let…

For an angle $\theta$, let $\operatorname{L}(\theta)$ denote the Lobachevsky function. Consider angles $\theta$ that are rational multiples of $\pi$, and rational coefficients…