10 problems

Pu's relative 1-systole conjecture. For any such $S$ and $\hat\phi$,

Liechti–Strenner's conjecture. For all $k\geq 2$,

Odd-genus Penner dilatation limit conjecture. The limit is the largest real root of

Genus 9 and 11 minimal stretch factor conjecture. The minimal stretch factors and minimal polynomials are predicted to be

Closure-equality conjecture. The inclusions in Theorems and are equalities, except when $\lambda$ is the bounding geodesic of the genus-three closed surface.

Rational-density conjecture.

Simple-closed-geodesic growth conjecture. There exists a constant $c>0$ such that

Sullivan-type invariant-measure conjecture. There exists a unique, up to scaling, ergodic $\operatorname{Map}(S)$-invariant Radon measure supported on $\mathcal{ML}^+(S)$, and it i…

Limit-set conjecture. The limit set of $\operatorname{Map}(S)$ in $\mathcal{PML}(S)$ is $\mathcal{PML}^+(S)$.

The $b$-conjecture. The series $\Psi(\mathbf{x},\mathbf{y},\mathbf{z};t,1+b)$ has coefficients that are polynomials in $b$ with non-negative integer coefficients. The constant term…