Vertex Algebras from Divisors on CY Threefolds and Perverse Coherent Extensions - Lecture 1

Explore a 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. Discover the algebraic approach involving screening operators on lattice vertex algebras, determined by the GKM graph and Jordan-Holder filtration of the divisor's structure sheaf. Investigate the geometric construction as a convolution algebra acting on the homology of moduli spaces of sheaves supported on the divisor. Learn about the connection between enumerative geometry of sheaves on Calabi-Yau threefolds and the representation theory of W-algebras and affine Yangian-type quantum groups. Gain insights into the generalization of the AGT conjecture proof to divisors in C^3 by Rapcak-Soibelman-Yang-Zhao.