Explore a comprehensive lecture on vertex algebras associated with divisors on toric Calabi-Yau threefolds, presented by Dylan Butson from Oxford University. Delve into two conjecturally equivalent constructions of these vertex algebras and examine partial results towards proving their equivalence. Investigate the algebraic approach, involving the kernel of screening operators on lattice vertex algebras determined by the GKM graph and Jordan-Holder filtration of the divisor's structure sheaf. Analyze the geometric construction as a convolution algebra acting on the homology of moduli spaces of sheaves supported on the divisor, drawing from the AGT conjecture proof and its generalization to divisors in C^3. Discover the fascinating correspondence between the enumerative geometry of sheaves on Calabi-Yau threefolds and the representation theory of W-algebras and affine Yangian-type quantum groups in this advanced mathematical exploration.