Raymond Cheng, Department of Pure Mathematics, University of Waterloo
“Euler Characteristic of the Moduli Space”
Last time, we outlined a sort of combinatorial cell decomposition of the moduli space: we were able to decompose the moduli space into cells indexed by certain graphs. As we observed last time, this decomposition can be used to compute something which behaves as an Euler characteristic for the moduli space. But since the moduli space is not any old space but an orbifold, there is additional structure we need to account for when computing this invariant. Having seen one example of what this entails, we will proceed in this talk, following Harer–Zagier, to work out the general situation.