7 problems

Let $n$ be an odd integer with $n\geqslant 5$. Let $a_n$ and $b_n$ denote the cardinalities of the two discrete orbits of primitive $n$-square-tiled surfaces in ${\mathcal{H}}(2)$,…

Let $n$ be prime, and consider the elliptic points associated with primitive $n$-square-tiled surfaces in ${\mathcal{H}}(2)$. Elliptic-point count conjecture. For prime $n$, the nu…

Let $n$ be an odd integer, and consider the two orbits of primitive $n$-square-tiled surfaces in ${\mathcal{H}}(2)$, denoted orbit A and orbit B. For a prime $p$, write…

Let $(\mu,k)$ be a spherical profile, meaning profile data for square-tiled surfaces on the sphere. Let $\operatorname{ST}(\mu,k)$ denote the corresponding set of square-tiled surf…

Abelian-stratum mod-Poisson conjecture. For every $x>0$, uniformly for $k\in\{0,1,\ldots,\lfloor x\log(g)\rfloor\}$,

Let $\mathcal{C}$ be a non-hyperelliptic connected component of a stratum of holomorphic quadratic differentials, and let $p_{\mathcal{C}}(k)$ be the probability that a random quad…

Abelian mod-Poisson conjecture. For every $x>0$, uniformly for $k\in\{0,1,\ldots,\lfloor x\log(g)\rfloor\}$, as $g\to\infty$,