Jacobians of tropical curves and finite graphs (Carrie Frizzell, Scripps)

A Jacobian variety is a principally polarized abelian variety (PPAV) associated with a smooth complex algebraic curve. For dimensions less than or equal to 3, every PPAV is either a Jacobian or a product of Jacobians. The Schottky problem concerns dimensions 4 and greater: which PPAVs are Jacobians? The Schottky problem can also be posed in the tropical setting, in which the Jacobian of a tropical curve is a real torus. We will spend most of the talk discussing tropical Jacobians and their discrete counterparts, but we will also survey a few results related to the aforementioned Schottky problem.