Generating functions for Hurwitz–Hodge integrals

We describe explicit generating functions for a large class of Hurwitz–Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz schemes.Admissible covers and their tautological classes are interesting mathematical objects on their own, but recently they have proved to be a useful tool for the study of the tautological ring of the moduli space of curves, and the orbifold Gromov–Witten theory of DM stacks.