Huazhong Ke: Gamma conjecture II for quadrics

Abstract: Gamma conjecture II was proposed by Galkin, Golyshev and Iritani for quantum cohomology of Fano manifolds. The conjecture concerns the asymptotic behavior near irregular singularities of flat sections of Dubrovin connection of a Fano manifold X, and tries to describe the asymptotic behavior in terms of full exceptional collections of the bounded derived category of coherent sheaves of X, via the Gamma-integral structure of the quantum cohomology of X. Recently, we have obtained a sufficient condition for Gamma conjecture II, and used it to prove the conjecture for smooth quadric hypersurfaces. In this talk, we will give a brief introduction to Gamma conjecture II, and report our work. This is joint work with Xiaowen Hu.