Large-genus asymptotics of Masur–Veech volumes of quadratic-differential strata

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 $\log(g)$ entries equal to $-1$. The Masur–Veech volume of the corresponding stratum is denoted by $\operatorname{Vol}{\mathcal Q}(d_1,\dots,d_n)$. Large-genus volume conjecture. For every $\boldsymbol{d}\in\hat\Pi_{4g-4}$,

$$\operatorname{Vol}{\mathcal Q}(d_1,\dots,d_n)=\frac{4}{\pi}\prod_{i=1}^n\frac{2^{d_i+2}}{d_i+2}\bigl(1+\varepsilon_1(\boldsymbol{d})\bigr),$$

where

$$\lim_{g\to\infty}\max_{\boldsymbol{d}\in\hat\Pi_{4g-4}}|\varepsilon_1(\boldsymbol{d})|=0.$$

This predicts a uniform large-genus asymptotic formula for volumes of strata of meromorphic quadratic differentials with at most logarithmically many simple poles; numerical computations and recursive formulas provide supporting evidence.