In enumerative geometry, Virasoro constraints first appeared in the context of moduli of stable curves and maps. These constraints provide a rich set of conjectural relations among Gromov-Witten descendent invariants. Recently, the analogous constraints were formulated in several sheaf theoretic contexts; stable pairs on 3-folds, Hilbert scheme of points on surfaces, and higher rank sheaves on surfaces with only (p,p)-cohomology. In joint work with A. Bojko, M. Moreira, we extend and reinterpret Virasoro constraints in sheaf theory using Joyce's vertex algebra. This new interpretation yields a proof of Virasoro constraints for curves and surfaces with only (p,p) cohomology by means of wall-crossing formulas.

Pre-talk for graduate students 12:30 - 1:00pm.