| Abstract: |
Volume can be approximated by counting points in a fine lattice.
More generally integration uses a function defined over the lattice. In
topology, integration appears in the form of cohomology. I will describe
how to define and count lattice points in the moduli space of genus g curves
with n labeled points, and hence get deep topological/cohomological
information about the moduli space related to work of Kontsevich. I will
also describe other counting problems equivalent to counting lattice points.
In particular, the number of branched coverings of the two-sphere branched
over 3 points, and the number of triples of elements of the symmetric group
with product the identity related to the work of Okounkov.
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