Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
arXiv:1103.4674
Abstract
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil-Petersson form. Mirzakhani proved that Weil-Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers on moduli spaces of curves. In this survey article, we discuss these results as well as some consequences and applications.
arXiv comment37 pages - submitted to Handbook of Moduli (edited by G. Farkas and I. Morrison)
References in corpus (9)
- Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
- An algebro-geometric proof of Witten's conjecture
- Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
- On the large genus asymptotics of Weil-Petersson volumes
- A simple proof of Witten conjecture through localization
- Chimneys, leopard spots, and the identities of Basmajian and Bridgeman
- Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
- Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem
- The asymptotic Weil-Petersson form and intersection theory on M_{g,n}
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- Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
- Length statistics of random multicurves on closed hyperbolic surfaces
- Counting hyperbolic multi-geodesics with respect to the lengths of individual components