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 2022年亚洲世界杯预选赛 12:30 - 1:00pm.