Moduli spaces of Admissible Covers are smooth (as DM stacks) compactifications of the classical Hurwitz schemes, parametrizing ramified covers of Riemann Surfaces with specified numerical invariants and ramification data. Not surprisingly, the theory of Hurwitz numbers is strictly related with such spaces. What I intend to present is how this theory in fact extends to a TQFT (Frobenius Algebra) encoding more general intersection numbers on Admissible Cover spaces, and strictly related to Gromov-Witten Theory. The upshot is that Hurwitz numbers and Atiyah-Bott localization allow us to compute explicitly generating functions for this theory.

Lecture #12383

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