Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian
  evolutionary PDEs   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 Korteweg--de Vries hierarchy depending on an infinite
number of parameters. Conjecturally this hierarchy is a universal object in the
class of scalar Hamiltonian integrable hierarchies possessing tau-functions.

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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph