ELSV formula

In mathematics, the ELSV formula, named after its four authors Torsten Ekedahl [sv], Sergei Lando [ru], Michael Shapiro, Alek Vainshtein, is an equality between a Hurwitz number (counting ramified coverings of the sphere) and an integral over the moduli space of stable curves.

Several fundamental results in the intersection theory of moduli spaces of curves can be deduced from the ELSV formula, including the Witten conjecture, the Virasoro constraints, and the ${\displaystyle \lambda _{g}}$-conjecture.

It is generalized by the Gopakumar–Mariño–Vafa formula.