In this talk, we will discuss Gamma conjecture II for Fano manifolds in more details. We will give a criterion for Gamma conjecture II, which is based on Dubrovin's result of meromorphic continuation of semi-simple Frobenius manifolds. As an application, we use this criterion to verify Gamma conjecture II for smooth quadratic hypersurfaces. The talk is based on a joint work with Xiaowen Hu. This talk is the second one of the series of talks on Gamma conjectures, and the context of this talk will be self-contained.