Department of Mathematics - Algebra and Geometry Seminar - Universal Virasoro constraints for quivers with relations

The recent reformulation of sheaf-theoretic Virasoro constraints opens many doors for future research. In particular, one may consider its analog for quivers. After phrasing a universal approach to Virasoro constraints for moduli of quiver-representations, I will sketch their proof for any finite quiver with relations, with frozen vertices, but without cycles. I will use partial flag varieties which are a special case of moduli of framed representations as a guiding example throughout. Using derived equivalences to quivers with relations, I give self-contained proofs of Virasoro constraints for all Gieseker semistable sheaves on $S = \mathbb{P}^2,\mathbb{P}^1 \times \mathbb{P}^1$, and $\mathrm{Bl}_\mathrm{pt}\mathbb{P}^2$. Combined with an existing universality argument for Virasoro constraints on Hilbert schemes of points of surface, this leads to a proof for any $S$ which is independent of the previous results in GW theory.