# Large genus asymptotics for volumes of strata of abelian differentials

@article{Aggarwal2020LargeGA, title={Large genus asymptotics for volumes of strata of abelian differentials}, author={Amol Aggarwal}, journal={Journal of the American Mathematical Society}, year={2020} }

<p>In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by Eskin-Okounkov to exactly evaluate these quantities, we show that the volume <inline-formula content-type="math/mathml">
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## 14 Citations

Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials

- MathematicsInventiones mathematicae
- 2021

In this paper we analyze the large genus asymptotics for intersection numbers between $\psi$-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a…

Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves

- Mathematics
- 2019

We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of…

Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes

- Mathematics
- 2019

We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting…

Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves

- MathematicsInventiones mathematicae
- 2022

We study the combinatorial geometry of a random closed multicurve on a surface of large genus and of a random square-tiled surface of large genus. We prove that primitive components of a random…

The Large Genus Asymptotic Expansion of Masur–Veech Volumes

- MathematicsInternational Mathematics Research Notices
- 2019

We study the asymptotic behavior of Masur–Veech volumes as the genus goes to infinity. We show the existence of a complete asymptotic expansion of these volumes that depends only on the genus and…

Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials

- Mathematics
- 2019

We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros. As applications,…

Uniform Lower Bound for Intersection Numbers of ψ-Classes

- Mathematics
- 2020

We approximate intersection numbers $\langle \psi_1^{d_1} \dots \psi_n^{d_n}\rangle_{g,n}$ on Deligne--Mumford's moduli space $\overline{\mathcal{M}}_{g,n}$ of genus $g$ stable complex curves with…

Conjectural Large Genus Asymptotics of Masur–Veech Volumes and of Area Siegel–Veech Constants of Strata of Quadratic Differentials

- Mathematics
- 2019

We state conjectures on the asymptotic behavior of the Masur–Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel–Veech…

Billiards in right triangles and orbit closures in genus zero strata

- Mathematics
- 2021

We classify GL(2,R) orbit closures of rank at least two in hyperelliptic components of strata of Abelian and quadratic differentials. As a consequence, the orbit closure of the unfolding of every…

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In the 80’s H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich…

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Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves

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We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of…

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We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting…

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