An infinite-dimensional Frobenius manifold and the extended 2D Toda hierarchy

We consider the recent advances in the programme of extending the Frobenius manifolds techniques to integrable PDE's with two spatial variables. First, we review the construction of an infinite-dimensional Frobenius manifold structure $M$ on a 2-vector bundle on the space of simple analytic curves in the complex plane. Second, we show that it is possible to explicitly solve the operator-valued singular linear system on the complex plane associated with the deformed flat connection of the Frobenius manifold. This solution defines a principal hierarchy which extends the dispersionless 2D Toda hierarchy.