8 problems

Let $g$ be the genus and let $m_1,\dots,m_r$ be positive integers satisfying … Consider the even and odd connected components $\mathcal H^{\mathrm{even}}(2m_1,\dots,2m_r)$ and…

Let $M\in{\mathbb Z}_+$ be fixed. For every $0\leq p\leq M$ and every odd positive partition ${\underline{k}}$ of $4g-4+p$, write its parts as $\kappa_1,\dots,\kappa_n$. Adapted vo…

Fix a stratum of Abelian or quadratic differentials and let $k$ be a fixed number of cylinders. Consider the contribution of square-tiled surfaces having $k$ cylinders to the Masur…

Yang–Zagier–Zhang conjecture. The error term in this asymptotic admits an expansion in $g^{-1}$ whose leading term is $-\frac{\pi^2}{144}\frac{1}{g}$, with explicit coefficients fo…

For a fixed integer $n\geq 0$, let $\mathcal{Q}_{g,n}$ denote the principal stratum of quadratic differentials and let ${\rm Vol}\,\mathcal{Q}_{g,n}$ be its Masur–Veech volume. Def…

Let $\boldsymbol{d}=(d_1,\dots,d_n)$ be an unordered partition of $4g-4$ with parts $d_i\in\{-1,0,1,2,\dots\}$, and let $\hat\Pi_{4g-4}$ consist of those partitions having at most…

Let $MV_{g,n}$ denote the Masur–Veech volume, and set … For each $g\geq 0$, consider polynomials $p_g,q_g\in\mathbb{Q}[n]$. Polynomial structure conjecture. For any $g\geq 0$, ther…

Let $H_n[d]$ be the fixed-degree coefficients considered in the generating series, and for each $d$ define … For each $d\geq 0$, there exists a polynomial $P_d$ of degree $d$ with…