Speaker
Nick McCleerey, Purdue University
Abstract
We show that the metric defined by the solution to the tropical Monge-Ampere equation on the boundary of the 3-simplex, as defined by Hultgren-Jonsson-Mazzon-M., has the same asymptotics as the Gross-Wilson metric on S^2 near each of its 6 singular points; this is done by reducing the equation to a planar optimal transport problem with a non-convex target, and then applying a partial Legendre transform. In addition, we show that the solution fails to be C^{1,1} at the singular points. Based on joint work with M. Jonsson, N. Patram, and B. Scott.