Counter-examples to Gamma conjecture I

Moduli Spaces and Related Topics

Organizer：

Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：

Huazhong Ke (Zhongshan University)

Time：

Fri., 10:00 am, Nov. 22, 2024

Venue：

C654, Shuangqing Complex Building A

Title：

Counter-examples to Gamma conjecture I

Abstract：

For quantum cohomology of a Fano manifold X, Gamma conjectures try to describe the asymptotic behavior of Dubrovin connection in terms of derived category of coherent sheaves on X, via the Gamma-integral structure of the quantum cohomology. In particular, Gamma conjecture I expects that the structure sheaf corresponds to a flat section with the smallest asymptotics. Recently, we discovered that certain toric Fano manifolds do not satisfy this conjecture. In this talk, we will report our results on these counter-examples, and propose modifications for Gamma conjecture I. This talk is based on joint work with S. Galkin, J. Hu, H. Iritani, C. Li and Z. Su.