Vertex algebras and Gromov–Witten invariants

My talk will be based on my on-going project with B. Bakalov, whose goal is to use the methods of representation theory of vertex algebras to compute the Gromov–Witten invariants of a compact Kahler orbifold with a semi-simple quantum cohomology. Our construction can be formulated in more general framework using the language of semi-simple Frobenius manifolds. As an application, I will explain how our methods can be used to compute Givental's J-function of $\mathbb{P}^1$.