Counting lattice points in the moduli space of algebraic curvesAlgebra & Discrete Mathematics
|Motohico Mulase, UC Davis
|Thu, Apr 28 2011, 4:10PM
The moduli space of smooth n-pointed algebraic curves admits n-parameter families of polytope realization. When the parameters are integers, the moduli space becomes a collection of rational orbi-polyopes, and hence counting its lattice points makes sense. Remarkably, the lattice point counting leads to yet another proof of the Witten conjecture and a recursive formula for the orbifold Euler characteristic of the moduli space. In this talk I will report recent developments on the subject inspired by Norbury and obtained in my collaboration with Chapman, Penkava and Safnuk.