Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and
  Gromov - Witten invariants   We present a project of classification of a certain class of bihamiltonian
1+1 PDEs depending on a small parameter. Our aim is to embed the theory of
Gromov - Witten invariants of all genera into the theory of integrable systems.
The project is focused at describing normal forms of the PDEs and their local
bihamiltonian structures satisfying certain simple axioms. A Frobenius manifold
or its degeneration is associated to every bihamiltonian structure of our type.
The main result is a universal loop equation on the jet space of a semisimple
Frobenius manifold that can be used for perturbative reconstruction of the
integrable hierarchy. We show that first few terms of the perturbative
expansion correctly reproduce the universal identities between intersection
numbers of Gromov - Witten classes and their descendents.

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The categories of this paper are: atom-ph
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th