Abstract: 

I will talk about properties of a class of bihamiltonian integrable hierarchies associated to a semisimple Frobenius manifold. These integrable hierarchies are certain deformations of the so called Principal Hierarchy of the Frobenius manifold, which is a hierarchy of bihamiltonian integrable PDEs of hydrodynamic type. When the Frobenius manifold comes from a 2d TFT, a special solution of the Principal Hierarchy yields the genus zero free energy of the 2d TFT, and the full genera 2d TFT is controlled by a certain deformation, called the topological deformation, of the Principal Hierarchy. These bihamiltonian integrable hierarchies are shown to possess Virasoro symmetries when the central invariants of the bihamiltonian structures are constant. When the central invariants of the bihamiltonian structure are equal to 1/24, the Virasoro symmetries are proved to be linearizable, and the corresponding bihamiltonian integrable hierarchy is equivalent to the topological deformation of the Principal Hierarchy.