Speaker: Mr. Xiaowen Hu (Tsinghua University)

Time: Thursday Nov. 7, 9:30-11:30 am.

Venue: Room 29 at Quan Zhai, BICMR

Abstract: I will talk about my recent work on the computation of genus one local Gromov-Witten invariants. I will first recall A.Zinger's approach to compute genus one Gromov-Witten invariants of Calabi-Yau hypersurfaces，and discuss the formulation of Zinger's genus one mirror formula. For local Calabi-Yau manifolds, we find that there is a reasonable way to formally define the reduced genus one Gromov-Witten invariants, and we will see that the standard versus reduced formula holds for each graph. This enables us to find a mirror formula for concave splittinga vector bundles over projective spaces. As a byproduct, we will see that after a suitable modification, the genus one Gromov-Witten invariants of hypersurfaces in projective spaces can be computed by virtual localization.