Speaker: Renata Picciotto (University of Angers)

Title: Derived moduli spaces and cosection-localization

Abstract: Derived algebraic geometry provides a powerful tool for the study of virtual structures: a quasi-smooth 'derived enhancement' of a moduli space is a geometric object encoding the information of a perfect obstruction theory. Derived stacks are the natural setting for understanding virtual structure sheaves arising in the study of K-theoretic invariants. Many moduli spaces arising in enumerative geometry have clear derived enhancements. In a work in progress with Etienne Mann and David Kern, we propose a derived enhancement of the moduli of sections, which is a generalization of the usual Gromov-Witten moduli space of stable maps arising in the study of Landau-Ginzburg models. Our goal is to categorify the construction of the cosection-localized structure sheaf, a K-theoretic version of a refined Euler class.