Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal maps and dispersionless integrable hierarchies   We show that conformal maps of simply connected domains with an analytic
boundary to a unit disk have an intimate relation to the dispersionless 2D Toda
integrable hierarchy. The maps are determined by a particular solution to the
hierarchy singled out by the conditions known as "string equations". The same
hierarchy locally solves the 2D inverse potential problem, i.e. reconstruction
of the domain out of a set of its harmonic moments. This is the same solution
which is known to describe 2D gravity coupled to c=1 matter. We also introduce
a concept of the $\tau$-function for analytic curves.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol