9 problems

Zograf's conjecture. Based on numerical data, Zograf conjectured that

Lipnowski–Wright conjecture. A transition occurs at order $\sqrt{g}$.

Let $V^{\text{Mirz}}_{g,n}(\underline{0})$ denote the Weil–Petersson volume of the moduli space of genus-$g$ hyperbolic surfaces with $n$ cusps. For fixed $n$, write its large-genu…

Let $F^{\text{ZZ}}_{(n_+,n_-)}(\hbar)$ denote the free-energy coefficient in the $(n_+,n_-)$ ZZ-instanton sector, let $W^{\text{ZZ}}_{(n_+,n_-)}(E)$ denote the corresponding non-pe…

Kimura's conjecture. For any given $n\geq 0$ and boundary lengths $\mathbf{L}=(L_1,\ldots,L_n)$, as $g\to\infty$,

Mirzakhani–Zograf's polynomiality conjecture. The asymptotic coefficients are polynomials in $\mathbb{Q}[\pi^{-2}]$.

Let the volumes defined in section be the Weil–Petersson volumes of moduli spaces with conical defects, and let the matrix-integral results of section be the corresponding volumes…

Let $V_{g,n}$ denote the Weil–Petersson volume of the moduli space of genus-$g$ hyperbolic surfaces with $n$ geodesic boundary components, and let $\alpha>0$ be the universal const…

Let $V_{g,n;d}$ denote the mixed intersection number associated with a fixed set $d=(d_1,\dots,d_n)$ of non-negative integers, and let $V_{g,n}$ denote the corresponding Weil–Peter…