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