| Summary: | The object under consideration in this article is the total volume Vg,n(x1, ..., xn) of the moduli space of hyperbolic surfaces of genus g with n boundary components of lengths x1, ..., xn, for the Weil-Petersson volume form. We prove the existence of an asymptotic expansion of the quantity Vg,n(x1, ..., xn) in terms of negative powers of the genus g, true for fixed n and any x1, ..., xn ≥ 0. The first term of this expansion appears in the work of Mirzakhani and Petri [Comment. Math. Helvetici 94, 869-889 (2019)], and we compute the second term explicitly. The main tool used in the proof is Mirzakhani's topological recursion formula, for which we provide a comprehensive introduction. © 2022 Author(s).
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