January 11, 2023
TITLE: Virasoro constraints; history and moduli of sheaves

ABSTRACT: Virasoro constraints were first conjectured for the moduli of stable curves (the Witten conjecture) and stable maps. These conjectures provide a set of universal relations among descendent invariants described by a representation of half of the Virasoro algebra. Recently, the analogous constraints were conjectured in several sheaf theoretic contexts. In joint work with A. Bojko and M. Moreira, we provide a unifying viewpoint to Virasoro constraints for general moduli of sheaves and prove the conjecture for torsion-free sheaves on curves and surfaces.