Abstract: Using the notion of reflection vectors (which only depends on the second structure connection) I will show how to get explicitly the Stokes and central connection matrices for a semisimple Frobenius manifold. In the case of quantum cohomology, I will discuss some implications for the so-called Dubrovin conjecture which relates the quantum cohomology of a (Fano) manifold with its bounded derived category of coherent sheaves. This is a joint work in progress with Todor Milanov.