  In this paper we study effective recursion formulae for computing
intersection numbers of mixed $\psi$ and $\kappa$ classes on moduli spaces of
curves. By using the celebrated Witten-Kontsevich theorem, we generalize
Mulase-Safnuk form of Mirzakhani's recursion and prove a recursion formula of
higher Weil-Petersson volumes. We also present recursion formulae to compute
intersection pairings in the tautological rings of moduli spaces of curves.

Algebraic Geometry