Title: Stability conditions for the universal Jacobian
Abstract: There is a large body of work, beginning with a 1979 paper of Oda and Seshadri, on how to define a stability condition so that the moduli space of stable sheaves is a well-behaved compactification of the universal Jacobian. This work provides many tools for defining stability conditions, but the combinatorics of these stability conditions is only partially understood. In my talk, I will present results describing the combinatorics and then given applications, such as an analysis of the indeterminacy of the Abel section.