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.