9 problems

Let a closed hyperbolic surface be equipped with its hyperbolic structure, and let its length spectrum be the multiset of lengths of closed geodesics, counted with multiplicities.…

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…

Relative Poisson relation conjecture. One should have

Let $n\geq 3$, and let $\Omega_1$ and $\Omega_2$ be convex $n$-gons. A primitive closed geodesic is a closed geodesic that is not a nontrivial iterate of a shorter closed geodesic;…

Finiteness conjecture. This set should form a compact (or finite) set in the space of Riemannian metrics.

Lafont–McReynolds' conjecture. Having the stronger progression property characterizes the arithmeticity of $M$.

Modified Lee–Zhang conjecture.

Lee–Zhang conjecture. For any Hitchin representation $\rho:\Gamma\to\operatorname{PSL}(n,\mathbb{R})$, there is a Fuchsian representation $j$ such that

Nilmanifold spectral determination conjecture. The marked length spectrum determines the Laplacian spectrum for all nilmanifolds.