topological string seminar

Speaker: Constantin Teleman (UC Berkeley)
Title: The structure of 2D semi-simple field theories
Date (JST): Tue, Dec 14, 2010, 15:30 - 17:30
Place: Seminar Room A
Abstract: I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A: they are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point, confirming Givental's higher-genus reconstruction conjecture. This in turn implies the Virasoro conjecture for manifolds with semi-simple quantum cohomology. The proof uses the Mumford conjecture proved by Madsen-Weiss.