Descendent integrals and tautological rings of moduli spaces of curves

Abstract

The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications. We also present a conjectural relation between tautological rings and the mock theta function.

31 pages, to appear in proceedings of the conference "Geometric analysis: Present and Future" held at Harvard in August 27-Sept 1, 2008

References in corpus (7)

• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• Vertices from replica in a random matrix theory
• Crepant resolution conjecture in all genera for type A singularities
• Topological recursion relations and Gromov-Witten invariants in higher genus
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Computing top intersections in the tautological ring of $M_g$
• Localization and Conjectures from String Duality

Cited by in corpus (6)

• Solution of W-Constraints for R-Spin Intersection Numbers
• The intersection numbers of the p-spin curves from random matrix theory
• Computing top intersections in the tautological ring of $M_g$
• Formal pseudodifferential operators and Witten's r-spin numbers
• Simple Lie algebras and topological ODEs
• Random Matrix, Singularities and Open/Close Intersection Numbers