Miguel Moreira: Virasoro constraints for sheaves and quivers

Date: 2024-07-26

Time: 10:00 - 11:00

Miguel Moreira, MIT


The Virasoro constraints made their way into the story of enumerative geometry via Witten’s conjecture and have been a central problem in Gromov-Witten theory for the past 30 years. More recently, Virasoro constraints have been studied in the context of moduli spaces of sheaves or representations of quivers. It turns out that they are quite general: in appropriate conditions, it is possible to define a representation of half of the Virasoro Lie algebra in the cohomology of moduli spaces/stacks parametrizing objects in some abelian/triangulated category, and moreover this representation constraints the integrals of tautological classes. In this talk I will survey some of the developments in this story, based on results obtained in joint works with Oblomkov-Okounkov-Pandharipande, Bojko-Lim and Lim.