Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near optimal spectral gaps for hyperbolic surfaces   We prove that if $X$ is a finite area non-compact hyperbolic surface, then
for any $\epsilon>0$, with probability tending to one as $n\to\infty$, a
uniformly random degree $n$ Riemannian cover of $X$ has no eigenvalues of the
Laplacian in $[0,\frac{1}{4}-\epsilon)$ other than those of $X$, and with the
same multiplicities.
  As a result, using a compactification procedure due to Buser, Burger, and
Dodziuk, we settle in the affirmative the question of whether there exist a
sequence of closed hyperbolic surfaces with genera tending to infinity and
first non-zero eigenvalue of the Laplacian tending to $\frac{1}{4}$.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex