Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adiabatic limits and noncommutative Weyl formula   We discuss asymptotic behavior of the eigenvalue distribution of the
differential form Laplacian on a Riemannian foliated manifold when the metric
on the ambient manifold is blown up in directions normal to the leaves (in the
adiabatic limit). Motivated by analogies with semiclassical spectral
asymptotics, we use ideas and notions of noncommutative geometry to suggest a
conjectural formula for the eigenvalue distribution in the adiabatic limit,
which we call noncommutative Weyl formula. We review known results and discuss
the correctness of the noncommutative Weyl formula in each case.

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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int