Ralph Morrison: Tropical graphs in the plane

Abstract: In tropical geometry, a polynomial in two variables defines a curve in the plane, just like in classical geometry. Unlike a classical curve, however, a tropical curve is a piecewise-linear object that embeds into the plane in a balanced, polyhedral way. Living inside such a tropical curve is its skeleton, which is a trivalent graph with lengths associated to its edges. I'll tell you some answers to two big questions: what can the graph of a skeleton look like, and what edge lengths are achievable? This talk includes previous work done with Brodsky, Joswig, and Sturmfels, as well as ongoing work with Coles, Dutta, Jiang, and Scharf.