14 problems

Let $K$ be a connected component of a stratum of translation surfaces, and let $N_{cyl}(M,L)$ and $N_{sc}(M,L)$ denote the cylinder and saddle-connection counting functions for a s…

For fixed $n\geq 0$, let $C_{\rm area}(\mathcal{Q}_{g,n})$ be the area Siegel–Veech constant associated with the principal stratum $\mathcal{Q}_{g,n}$, and set $M=-\pi^2/144$. Area…

Let $\hat\Pi_{4g-4}$ be the set of partitions of $4g-4$ with parts in $\{-1,0,1,2,\dots\}$ and at most $\log(g)$ entries equal to $-1$. For a stratum ${\mathcal Q}(d_1,\dots,d_n)$…

Let ${\mathcal H}(m)$ be a stratum of Abelian differentials and let $c_{\mathit{area}}({\mathcal H}(m))$ be its area Siegel–Veech constant. Configurations contributing to this cons…

Let ${\mathcal H}(m)$ be a stratum of Abelian differentials, and let $c_{\mathit{area}}({\mathcal H}(m))$ denote its area Siegel–Veech constant. The principal boundary strata arise…

Let $\boldsymbol{d}\in\hat\Pi_{4g-4}$, and let ${\mathcal Q}(\boldsymbol{d})$ be a non-hyperelliptic connected component of a stratum of meromorphic quadratic differentials with at…

Let ${\mathcal H}^{\mathrm{comp}}(m)$ be a nonhyperelliptic connected component of a stratum of Abelian differentials in genus $g$, and let…

Consider the Siegel–Veech constants obtained by counting saddle connections on strata of Abelian differentials, and distinguish saddle connections of multiplicity one from configur…

Let $m=(m_1,\dots,m_n)$ be an unordered partition of $2g-2$, and consider the Siegel–Veech constants associated with saddle connections on the stratum ${\mathcal H}(m_1,\dots,m_n)$…

Let $\mu$ index a stratum of Abelian differentials, let ${\rm dim}({\mathcal H}(\mu))$ denote its dimension, and let $\epsilon_1(\mu)$ and $\epsilon_2(\mu)$ be the error terms in t…

Let $\epsilon_1(\mu)$ and $\epsilon_2(\mu)$ be the error terms in the volume and area Siegel–Veech constant asymptotics for strata indexed by partitions $\mu\vdash 2g-2$. Eskin–Zor…

Let $g$ tend to infinity, let $\mu\vdash 2g-2$ be a partition indexing a stratum of Abelian differentials, and let $c_{\rm area}(\mu)$ denote its area Siegel–Veech constant. Define…

Consider square-tiled-surface $T,R$-orbits in the connected components of strata in genera $3$, $4$, and $5$ belonging to the authors' specified list. For an orbit, let its Siegel–…

Let ${\mathcal M}_1$ be a regular $\operatorname{SL}(2,\mathbb R)$-invariant suborbifold in a stratum of Abelian differentials, and let $c_{\operatorname{area}}({\mathcal M}_1)$ be…