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

```@article{Dubrovin2014HodgeIA,
title={Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs},
author={B. Dubrovin and Si-Qi liu and Di Yang and You-jin Zhang},
year={2014},
volume={293},
pages={382-435}
}```
For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the intersection numbers of the Gromov–Witten classes and their descendents along with the characteristic classes of Hodge bundles on the moduli spaces of stable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy is a deformation of the… Expand
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