Towards large genus asymptotics of intersection numbers on moduli spaces of curves

By Maryam Mirzakhani, Peter Zograf. 2011

71 citations recorded by the source corpus.

We explicitly compute the diverging factor in the large genus asymptotics of the Weil–Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicative constant we prove the existence of a complete asymptotic expansion of the Weil–Petersson volumes in the inverse powers of the genus with coefficients that are polynomials in n. This is done by analyzing various recursions for the more general intersection numbers of tautological classes, whose large genus asymptotic behavior is also extensively studied.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/50185b93330301b48f1a404b068df0929ec29dcd

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In Geometry and Topology

1. Dawei Chen
2. Bram Petri
3. D. Stanford
4. Martin Moeller
5. E. Witten
6. Don Zagier
7. Phil Saad
8. S. Shenker

In Mathematical Physics

1. Dawei Chen
2. Martin Moeller
3. Don Zagier
4. E. Witten
5. D. Stanford
6. Bram Petri
7. S. Shenker
8. Phil Saad

Citations in the corpus

• JT gravity and the ensembles of random matrix theory (2019, background): “Zograf’s formulas were motivated by comparison to explicit low-genus computations, but aspects of his conjectures were later established rigorously [110, 111].”
• Quasimodularity and large genus limits of Siegel-Veech constants (2016, background): “ch volumes and Siegel-Veech constants. Large genus geometry of the moduli space has already attracted a lot of attention in the parallel world of Weil-Peterson volumes SIEGEL-VEECH CONSTANTS 9 ([28], [38]) and also in algebraic geometry in the form of the slope conjecture ([24], [21], see [9] for so”
• JT gravity as a matrix integral (2019, background): “11Parts of this conjecture have been established rigorously [31, 70, 45].”
• Lengths of closed geodesics on random surfaces of large genus (2017, methodology): “ng history. Estimates on Weil-Petersson volumes of moduli spaces of surfaces of large genus were derived by Penner [Pen92], Grushevsky [Gru01], Schumacher and Trappani [ST01] and Mirzkhani and Zograf [MZ15]. Closed geodesics on random surfaces have been studied in [Mir13a, Mir13b]. In [Mir13a], it w”