In this talk I will discuss some ideas in order to understand the relations between (certain) triangulated categories and semisimple Frobenius manifolds. In particular, I will discuss an example that (conjecturally) relates the Bondal quiver and its completion (Markov quiver) with the so-called Chazy Frobenius manifold. This case gives further evidence for a Dubrovin type conjecture for a wider class of semisimple Frobenius manifolds.