On the large genus asymptotics of Weil-Petersson volumes

By Peter Zograf. 2008

47 citations recorded by the source corpus.

A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the Weil-Petersson volumes is computed. Asymptotic formulas for the intersection numbers involving $\psi$-classes are conjectured as well. The precision of the formulas is high enough to believe that they are exact.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/731ac60dc60ec155bff010ed473910181094d5cc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Maryam Mirzakhani
2. D. Stanford
3. E. Witten
4. Phil Saad
5. S. Shenker

In Geometry and Topology

1. D. Stanford
2. E. Witten
3. Maryam Mirzakhani
4. Peter Zograf
5. Phil Saad
6. S. Shenker
7. Bram Petri
8. D. Gaiotto

In Mathematical Physics

1. D. Stanford
2. E. Witten
3. Maryam Mirzakhani
4. Peter Zograf
5. S. Shenker
6. Phil Saad
7. Sergei Gukov
8. D. Gaiotto

Citations in the corpus

• Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus (2010, methodology): “ Vg,n+1 = 1+O(1/g), as g→ ∞. • b): Vg,n+1 2gVg,n = 4π2 +O(1/g), • c): Vg,n Vg−1,n+2 = 1+O(1/g). Remark. • These estimates are consistent with the conjectures on the growth of WeilPetersson volumes in [Z2]; we remark that the statements had been predicted by Peter Zograf. • Following the ideas used i”
• JT gravity and the ensembles of random matrix theory (2019, methodology): “good large genus approximate formulas, based on Zograf’s [109] conjectures for the asymptotics of intersection numbers.”
• JT gravity as a matrix integral (2019, methodology): “For Vg,0 and for Vg,1(b) with b g, this prediction agrees with the Zograf conjecture [69].”
• Towards large genus asymptotics of intersection numbers on moduli spaces of curves (2011, background): “ces Mg,n of n-pointed complex algebraic curves of genus gas g→ ∞.Here V g,n= 1 (3g−3+n)! Z Mg,n ω3g−3+n, where ωg,n is the Weil-Petersson symplectic form on Mg,n. The following conjecture was made in [Z] on the basis of numerical data: Conjecture 1.1. For any fixed n≥ 0 Vg,n = (2g−3+n)!(4π2)2g−3+n 1 ”