221122 – Arkadij Bojko

Virasoro constraints in Gromov-Witten theory were introduced by Witten and famously proved by Kontsevich, while their analogue for moduli of sheaves has been studied mostly on examples. Using the recent wall-crossing framework of D. Joyce phrased in terms of vertex algebras, I express them in joint work with M. Moreira and W. Lim universally in terms of primary states with respect to a fixed conformal vector. This new formulation is compatible with wall-crossing, which leads for example to proofs of the constraints by reduction on rank for vector bundles on curves and torsion-free sheaves on surfaces with (p,p) cohomology.