Jan 26 at 17:30 in 507

Title:  Enumerative invariants of divisors on Calabi-Yau threefolds and free field realizations of vertex algebras

Abstract: 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, following the proof of the AGT conjecture by Maulik-Okounkov and Schiffmann-Vasserot, and its generalization to divisors in C^3 by Rapcak-Soibelman-Yang-Zhao. The other 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. This provides a correspondence between the enumerative geometry of coherent sheaves on Calabi-Yau threefolds and the representation theory of W-algebras and affine Yangian-type quantum groups.