Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves   We derive two geometric approaches to categorification of quantum invariants
of links associated to an arbitrary compact simple Lie group $^L{G}$. In part
I, we describe the first approach, based on an equivariant derived category of
coherent sheaves on ${\cal X}$, the moduli space of singular $G$-monopoles,
where $G$ is related to $^LG$ by Langlands duality. In part II, we describe the
second approach, based on the derived category of a Fukaya-Seidel category of a
Calabi-Yau $Y$ with potential $W$. The two approaches are related by a version
of mirror symmetry, which plays a crucial role in the story. In part III, we
explain the string theory origin of these results, and the relation to an
approach due to Witten.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci