We will explain two conjecturally equivalent constructions of vertex algebras associated to divisors $S$ on certain toric Calabi-Yau threefolds $Y$. One construction is algebraic, as the kernel of screening operators on lattice vertex algebras determined by the GKM graph of $Y$ and a Jordan-Holder filtration of the structure sheaf of $S$. The other is geometric, as a convolution algebra acting on the homology of certain moduli spaces of sheaves supported on the divisor, following the proof of the AGT conjecture by Schiffmann-Vasserot. This provides a correspondence between the enumerative geometry of sheaves on Calabi-Yau threefolds and the representation theory of W-algebras and affine Yangian-type quantum groups.
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