Matt Szczesny (BU), Toroidal algebras via factorization algebras

The theory of factorization algebras developed by Kevin Costello and Owen Gwilliam describes the algebraic structure of observables in quantum field theories. When the space-time manifold has complex dimension 1, a certain class of factorization algebras corresponds to vertex algebras. I will give a sketch of this theory and describe a construction of factorization algebras on Riemann surfaces from holomorphic fibrations. When the fiber is a torus, the corresponding factorization algebra gives a vertex realization of a toroidal algebra. This is joint work with Jackson Walters.