Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex bodies with a point of curvature do not have Fourier bases   We prove that no smooth symmetric convex body $\Omega$ with at least one
point of non-vanishing Gaussian curvature can admit an orthogonal basis of
exponentials. (The non-symmetric case was proven by Kolountzakis). This is
further evidence of Fuglede's conjecture, which states that such a basis is
possible if and only if $\Omega$ can tile $R^d$ by translations.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga