## Abstract

We use the relation between the volumes of the strata of meromorphic quadratic differentials with at most simple poles on ℂP^{1} and counting functions of the number of (bands of) simple closed geodesics in associated flat metrics with singularities to prove a very explicit formula for the volume of each such stratum conjectured by M. Kontsevich a decade ago. Applying ergodic techniques to the Teichmüller geodesic flow we obtain quadratic asymptotics for the number of (bands of) closed trajectories and for the number of generalized diagonals in almost all right-angled billiards.

Original language | English |
---|---|

Pages (from-to) | 1311-1386 |

Number of pages | 76 |

Journal | Annales Scientifiques de l'Ecole Normale Superieure |

Volume | 49 |

Issue number | 6 |

Publication status | Published - 1 Nov 2016 |

Externally published | Yes |

## Fingerprint

Dive into the research topics of 'Right-angled billiards and volumes of moduli spaces of quadratic differentials on ℂP^{1}'. Together they form a unique fingerprint.