KP hierarchy for Hodge integrals

Understand

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 lambda_g conjecture etc.
• Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.