KP hierarchy for Hodge integrals

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's λg-conjecture, etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.