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Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes

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arxiv 1103.4674 v1 pith:EQZA2QG2 submitted 2011-03-24 math.GT math.AGmath.SG

Norman Do This is my paper · ORCID
classification math.GTmath.AGmath.SG
keywords modulispacesweil-peterssonhyperbolicsurfacesvolumesapplicationsarticle
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Random punctured hyperbolic surfaces & the Brownian sphere

    math.PR 2025-08 conditional novelty 8.0 of 10

    Random Weil-Petersson punctured spheres converge, after fourth-root rescaling, to the Brownian sphere.

  2. A single geometry from an all-genus expansion in quantum gravity

    hep-th 2024-12 conditional novelty 7.0 of 10

    The all-genus JT gravity path integral at beta ~ e^{2S0/3} is reproduced at leading order by a disk path integral with a cubic, nonlocal dilaton interaction.

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