3 problems

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;…

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