Combinatorics of the tropical moduli space of curves and Outer space
Melody Chan, Harvard

A tropical curve is a metric graph marked with integer vertex weights obtained as a metrized dual graph of a semistable model of a curve over a valued field. We will review the construction of the tropical moduli space of genus g tropical curves with n marked points and report on joint work with M. Melo and F. Viviani studying Outer Space, as constructed by Culler and Vogtmann, as a Teichmuller analogue in tropical geometry.