Masur-Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves

DOI10.1215/00127094-2021-0054zbMath1471.14066arXiv2011.05306OpenAlexW3114365336MaRDI QIDQ821492

Peter Zograf, Anton Zorich, Vincent Delecroix, Elise Goujard

Publication date: 20 September 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.05306

zbMATH Keywords

quadratic differentialhyperbolic surfacesTeichmüller theorymulticurvessimple closed curvessquare-tiled surfacesMasur-Veech volume

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) General geometric structures on low-dimensional manifolds (57M50) Families, moduli of curves (analytic) (14H15)

Related Items (14)

Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves ⋮ RECURSION FOR MASUR-VEECH VOLUMES OF MODULI SPACES OF QUADRATIC DIFFERENTIALS ⋮ Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes ⋮ Experimental Statistics for Mirzakhani’s Theorem ⋮ Large genus asymptotics for lengths of separating closed geodesics on random surfaces ⋮ Counting lattice points in moduli spaces of quadratic differentials ⋮ Topological recursion for Masur–Veech volumes ⋮ Contribution of \(n\)-cylinder square-tiled surfaces to Masur-Veech volume of \(\mathcal{H}(2g-2)\) ⋮ Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials. With an appendix by Gaëtan Borot, Alessandro Giacchetto and Danilo Lewanski ⋮ On the large genus asymptotics of psi-class intersection numbers ⋮ Enumerative geometry of surfaces. Abstracts from the workshop held June 13--19, 2021 (hybrid meeting) ⋮ ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES ⋮ On normalizations of Thurston measure on the space of measured laminations ⋮ Length statistics of random multicurves on closed hyperbolic surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Counting curves in hyperbolic surfaces
• The Kontsevich constants for the volume of the moduli of curves and topological recursion
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow
• Towards large genus asymptotics of intersection numbers on moduli spaces of curves
• Volumes of strata of moduli spaces of quadratic differentials: getting explicit values
• Square-tiled surfaces and rigid curves on moduli spaces
• Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
• Siegel-Veech constants for strata of moduli spaces of quadratic differentials
• Inequalities for the gamma function
• Earthquakes are analytic
• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and measured foliations
• Intersection theory on the moduli space of curves and the matrix Airy function
• Siegel measures
• Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants
• Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces
• Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
• Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics
• Hurwitz theory of elliptic orbifolds. I
• Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares
• Masur-Veech volumes of quadratic differentials and their asymptotics
• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials
• Counting lattice points in the moduli space of curves
• An explicit formula for Witten's 2-correlators
• On normalizations of Thurston measure on the space of measured laminations
• Large genus asymptotics for Siegel-Veech constants
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• Counting generalized Jenkins-Strebel differentials
• The theta characteristic of a branched covering
• Asymptotic formulas on flat surfaces
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP^1
• Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group
• Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes
• Weil-Petersson volumes and intersection theory on the moduli space of curves
• Ergodic Theory of the Earthquake Flow
• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Quasimodularity and large genus limits of Siegel-Veech constants
• The Teichmuller Flow is Hamiltonian
• A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces
• Large genus asymptotics for volumes of strata of abelian differentials
• ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES
• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
• Volumes of strata of abelian differentials and Siegel-Veech constants in large genera

This page was built for publication: Masur-Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves