Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$

Abstract

We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formulæ of a new type for the generating series of intersection numbers of $\ddot{I}ˆ$-classes as well as of mixed $\ddot{I}ˆ$- and $\hat{I}º$-classes in full genera.

48 pages including 9 pages of tables; references added. V2: minor corrections in the proof of Theorem 1.2 (statement unaffected)