Recursion Formulae of Higher Weil–Petersson Volumes

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.