# University of Toronto's Symplectic Geometry Seminar

January 29, 2007, 3:10pm

BA 2165

## Brad Safnuk

### Mcmaster University

## Localization on the moduli of curves

**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.