| There is an expectation (arising in work of Bridgeland) that spaces of stability conditions should come with some additional geometric structure such as that of a Frobenius manifold. I will discuss some results in the toy model of finite length hearts with a well-defined Donaldson-Thomas theory. The upshot is that they come with natural formal families of infinite-dimensional Frobenius type and CV-structures in the sense of C. Hertling. A convergence result can be proved for the latter. Special collections of objects in the category reduce the structures to genuine, finite dimensional Frobenius manifolds. Joint work (partially in progress) with A. Barbieri and with T. Sutherland. |