10 problems

Extreme-point density conjecture. The extreme points of $\overline{\Omega_P}$ are dense in $\partial\Omega_P$ unless $W_P$ is affine of type $\widetilde{A}$.

Proximal limit set characterization.

Let $G$ be a noncompact linear real semisimple Lie group, let $\Gamma$ be an Anosov subgroup of $G$, and let $\langle\gamma\rangle$ be a maximal cyclic subgroup of $\Gamma$. Tholoz…

Triangular Finsler boundary conjecture. The quotient $\Delta Fins(S)/\mathbb{R}_+$ injects into $\mathbb{P}(\mathbb{R}^{\mathcal{L}(S)})$ and comprises an open dense subset of the…

Let $S$ be a closed real convex projective surface, and let $f\colon S\to S$ be a bijection mapping complete geodesics to complete geodesics as sets. Isometry conjecture. The map…

Gromov-Hausdorff convergence conjecture. The sequence $(\mathcal{O}_m)_m$ converges to $\mathcal{O}_\infty$ in the Gromov-Hausdorff topology.

Corner-invariant level-set conjecture. The map $\boldsymbol\alpha$ sends each orbit of the circle flow to a level set of the product $X$ of the corner invariants.

Lemmens–Walsh conjecture.

Let an end of a convex real projective orbifold be given, with lens-shaped ends, horospherical ends, and joins of ends understood as in the paper. Classification conjecture. Most e…

Let $(\Omega,d_{\Omega})$ be a Hilbert geometry, where $\Omega$ is a convex set of dimension $n$. If the volume entropy exists, define it by … Here $B(x,r)$ is a Hilbert-metric bal…