University of Toronto's Symplectic Geometry Seminar

Abstract: A useful principle in symplectic geometry is that in the presence of a hamiltonian torus action the cohomology of the manifold localizes to the fixed points of the action. Although the moduli of stable curves does not seem to admit any group actions, nevertheless there are many cohomology calculations on this space, most notably the Witten-Kontsevich Theorem, that look like they should originate from a localization technique. In this talk I will explain how such formulas naturally arise by considering group actions on an infinite cover of moduli space. If time permits I will also mention potential applications to the moduli space of flat SU(2) bundles and the moduli space of maps of a symplectic manifold.