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Counting lattice points in the moduli space of algebraic curves
Algebra & Discrete Mathematics| Speaker: | Motohico Mulase, UC Davis |
| Location: | 2112 MSB |
| Start time: | Thu, Apr 28 2011, 4:10PM |
Description
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.