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I will explain two conjecturally equivalent constructions of vertex algebras associated to divisors S on certain toric Calabi-Yau threefolds Y, and some partial results towards the proof of their equivalence. One construction is geometric, as a convolution algebra acting on the homology of certain moduli spaces of coherent sheaves supported on the divisor. The other is algebraic, as the kernel of screening operators on lattice vertex algebras determined by the geometry of Y and S. I will also explain the interpretation of these results as a generalization of the AGT conjecture to configurations of M5 branes in the Omega background, relating the equivariant geometry of moduli spaces of D-brane bound states to the algebraic structure of the corresponding CFTs.