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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(More)
Hamiltonian perturbations of the simplest hyperbolic equation u t + a(u)u x = 0 are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this(More)
Main mathematical applications of Frobenius manifolds are in the theory of Gromov-Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius man-ifolds establishes remarkable relationships between these,(More)