Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation

We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra, We also express the generating function of elliptic Gromov-Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.