Ralf Morrison: Moduli of Tropical Plane Curves

Smooth curves in the tropical plane come from unimodular triangulations of lattice polygons. The skeleton of such a curve is a metric graph whose genus is the number of lattice points in the interior of the polygon. In this talk we report on work concerning the following realizability problem: Characterize all metric graphs that admit a planar representation as a smooth tropical curve. For instance, about 29.5 percent of metric graphs of genus 3 have this property. (Joint work with Sarah Brodsky, Michael Joswig, and Bernd Sturmfels.)