Alex Abreu, On the Torelli Theorem for graphs and stable curves

The classical Torelli theorem states that a smooth curve can be recovered from its polarized Jacobian. In this talk, we will discuss the extensions of this theorem to stable curves and their dual graphs, as well as its dependence on the concept of compactified Jacobians. First, we will recall Caporaso and Viviani’s theorem, which characterizes when two stable curves have the same Caporaso’s compactified Jacobian. Then we will discuss Torelli’s theorem via fine compactified Jacobians. This is based on an ongoing joint work with Marco Pacini and Nicola Pagani.