A topological quantum field theory of intersection numbers for moduli spaces of admissible covers

This dissertation studies the intersection theory of moduli spaces of admissible covers. Following a parallel work in Gromov-Witten theory by Jim Bryan and Rahul Pandharipande, we define a natural class of intersection numbers on moduli spaces of admissible covers. We show that they can be organized in the structure of a two-dimensional, two-level weighted Topological Quantum Field Theory. Using techniques of localization, we compute the theory in low degrees, and provide a conjecture for general degree d. We then study two interesting specializations of the theory, where we are able to produce closed formulas for our invariants. These formulas involve characters from the representation theory of the symmetric group Sn, thus opening an interesting perspective for further exploration of the connection between the two theories.