MS Seminar (Mathematics - String Theory)

Speaker: Todor Milanov (IPMU)
Title: Gromov-Witten invariants and representations of infinite dimensional Lie algebras
Date: Tue, Oct 19, 2010, 13:15 - 14:45
Place: Seminar Room A
Abstract: Part I: I am planning to explain a formalism, due to Givental, that allows us to reconstruct the higher-genus GW invariants of an algebraic manifold from genus-0 ones, provided the quantum cohomology is semi- simple. In the language of string theory, this means that there is a formalism for recovering the higher genus amplitudes of the topological string, provided that the target has sufficiently many rational curves.

Part II: I am planning to discuss the mirror symmetry description of the above formalism. This leads naturally to Saito's theory of primitive forms and the representations of certain vertex algebras. In the case of simple singularities the above representations may be used to identify the generating function of GW invariants as a highest weight vector of the so called W-algebras as well as a tau-function of the so called Kac--Wakimoto hierarchies. I'll try to keep my exposition elementary, so no previous knowledge of vertex algebras or integrable hierarchies will be assumed.
Remarks: There will be a 5-minute break after the first 25 min.