Combinatorial Algebraic Geometry: Pseudo-Divisors and Polyhedral Connections

Divisors on graphs foster a rich connection between algebraic geometry and combinatorics, especially connections between the moduli theory of algebraic curves to graph theory and polyhedral geometry. In this talk we will walk through results presented in A universal tropical Jacobian over M_g^trop by Abreu, Andria, Pacini, and Taboada: we'll start with defining relevant divisors on tropical curves and graphs, introduce some stability conditions and special polytopes, and conclude with a construction of a universal tropical Jacobian.