Speaker: Mr. Xiaowen Hu (Tsinghua University)

Time: Thursday Nov. 14, 9:30-11:30 am.

Venue: Room 29 at Quan Zhai, BICMR

Abstract: I will continue the talk on the on the computation of genus one local Gromov-Witten invariants. I will first briefly recall the virtual localization for genus one local Gromov-Witten invariants, and describe the virtual localzation on $\Mbar_{(m,J)}(Y,d)$. Then I recall the definition of refined decorated tree, and formally define the reduced genus one local Gromov-Witten invariants. We will see that the standard versus reduced formula holds for each decorated rooted tree. I will explain why this enables us to find a mirror formula for concave splitting 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.