Title: Enumerating Triangulations
Speaker: Philip Engel (Harvard University)
Abstract: A triangulation of $S^2$ has non-negative curvature if every vertex has six or fewer triangles adjacent to it. Thurston showed that non-negative curvature triangulations correspond to lattice points in a moduli space of flat cone metrics on $S^2$. In joint work with Peter Smillie, we use an arithmetic technique of Siegel to count such lattice points. The appropriately weighted number of triangulations with $2n$ triangles is an explicit constant times the ninth divisor power sum of $n$. If time permits, I will discuss work in progress on the enumeration of triangulations with any set of specified non-zero curvatures.
Seminar URL: https://research.math.osu.edu/agseminar/
