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For an arbitrary semisimple Frobenius manifold we construct Hodge integrablehierarchy of Hamiltonian partial differential equations. In the particular caseof quantum cohomology the tau-function of a solution to the hierarchy generatesthe intersection numbers of the Gromov--Witten classes and their descendentsalong with the characteristic classes of Hodge bundles on the moduli spaces ofstable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy isa deformation of the Korteweg--de Vries hierarchy depending on an infinitenumber of parameters. Conjecturally this hierarchy is a universal object in theclass of scalar Hamiltonian integrable hierarchies possessing tau-functions.

Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs