Title: W-constraints and genus zero Virasoro-like constraints for Frobenius manifolds

Speaker: Dr. Yang Di (Tsinghua University)

Time: 10:10-11:10 am, May 23 (Thursday)

Abstract: Frobenius manifolds were introduced by Dubrovin in 1990s to describe the genus zero parts of 2D topological field theories. In this talk, we construct from the spectrum data of a Frobenius manifold several families of constraints satisfied by the free energies associated to this Frobenius manifold, including W-constraints and genus zero Virasoro-like constraints. Here in the construction of W-constraints, the semi-simplicity condition as well as the non-degeneracy condition of the associated G-matrix are required. We note that our construction of W-constraints coincides with Bakalov and Milanov's when the Frobenius manifold comes from an ADE type singularity. And we prove that for these singularities, the W-constraints uniquely determine the corresponding Fan-Jarvis-Ruan-Witten invariants. We also prove for the P^1 topological sigma model, the genus zero Virasoro-like constraints together with Virasoro constraints uniquely dete rmine its Gromov-Witten invariants.