10/02 at 17:30 in 507

Sam DeHority

Title: Vertex Algebras and the quantum connection

Abstract: Vertex algebras provide a powerful computational tool to construct and understand representations of the algebra generated by their Fourier modes. Using the interpretation of the cohomology of a Hilbert scheme of points on a smooth surface as a graded piece of a vertex algebra and the geometry of specific moduli spaces of sheaves on isotrivial elliptic surfaces we produce representations of lie algebras closely related to toroidal algebras and identify geometrically the action of Fourier modes. Using these representations we provide explicit formulas for enumerative invariants, specifically the Dubrovin connection, for curves in isotrivial Lagrangian fibrations.