Asymptotic coefficients of Weil-Petersson volumes in the large genus

Xuanyu Huang

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arXiv · 2501.06421

Asymptotic coefficients of Weil-Petersson volumes in the large genus

Xuanyu Huang

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Abstract

Mirzakhani-Zograf proved the large genus asymptotic expansions of Weil-Petersson volumes and showed that the asymptotic coefficients are polynomials in $\mathbb Q[\pi^{-2},\pi^2]$. They also conjectured that these are actually polynomials in $\mathbb Q[\pi^{-2}]$. In this paper, we prove Mirzakhani-Zograf's conjecture.

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Xuanyu Huang. 2025-01-11. Asymptotic coefficients of Weil-Petersson volumes in the large genus. https://arxiv.org/abs/2501.06421

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