Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Symmetry breaking for ground states of biharmonic NLS via Fourier
  extension estimates
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin