Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laplace equations, conformal superintegrability and B\^ocher
  contractions   Quantum superintegrable systems are solvable eigenvalue problems. Their
solvability is due to symmetry, but the symmetry is often "hidden". The
symmetry generators of 2nd order superintegrable systems in 2 dimensions close
under commutation to define quadratic algebras, a generalization of Lie
algebras. Distinct systems and their algebras are related by geometric limits,
induced by generalized In\"on\"u-Wigner Lie algebra contractions of the
symmetry algebras of the underlying spaces. These have physical/geometric
implications, such as the Askey scheme for hypergeometric orthogonal
polynomials. The systems can be best understood by transforming them to Laplace
conformally superintegrable systems and using ideas introduced in the 1894
thesis of B\^ocher to study separable solutions of the wave equation. The
contractions can be subsumed into contractions of the conformal algebra
$so(4,C)$ to itself. Here we announce main findings, with detailed
classifications in papers under preparation.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol