Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The algebraic meaning of genus-zero   The Conway--Norton conjectures unexpectedly related the Monster with certain
special modular functions (Hauptmoduls). Their proof by Borcherds et al was
remarkable for demonstrating the rich mathematics implicit there. Unfortunately
Moonshine remained almost as mysterious after the proof as before. In
particular, a computer check - as opposed to a general conceptual argument -
was used to verify the Monster functions equal the appropriate modular
functions. This, the so-called `conceptual gap', was eventually filled; we
review the solution here. We conclude by speculating on the shape of a new
proof of the Moonshine conjectures.

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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: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin