Recently, I and Yu Qiu introduced the notion of a q-stability condition as a certain q-deformation of a Bridgeland stability condition. In this talk, we will see the spaces of q-stability conditions on CY-categories associated with ADE quivers.
I will give a conjecture (theorem for type A) that these spaces can be identified with the universal covering spaces of regular locus of Frobenius manifolds associated with ADE singularities. I will also explain that central charges of q-stability conditions can be identified with twisted periods of ADE singularities, which are given as horizontal sections of deformed second structure connections of Frobenius manifolds.