4 problems

Unbounded-face conjecture. Every $\gamma=(g_1,g_2)$ where both $g_i$'s are hyperbolic admits a Dirichlet domain with more than two faces.

Cyclic loxodromic simplicity conjecture. The same conclusion holds for all cyclic loxodromic subgroups of $PO(n,1)$ with $n\geq 3$.

Generic simplicity conjecture. For generic $x\in\mathbb H^n$, the Dirichlet complex $\mathcal D_x(\Gamma)$ is simple.

Generic simplicity conjecture. For generic choice of $x$, the tiling $\mathcal D_x$ is simple, meaning that its dual cell-complex is a simplicial complex.