Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sphere packing problem in dimension 24   Building on Viazovska's recent solution of the sphere packing problem in
eight dimensions, we prove that the Leech lattice is the densest packing of
congruent spheres in twenty-four dimensions and that it is the unique optimal
periodic packing. In particular, we find an optimal auxiliary function for the
linear programming bounds, which is an analogue of Viazovska's function for the
eight-dimensional case.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph