Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphic Spectra and the Conformal Bootstrap   We point out that the spectral geometry of hyperbolic manifolds provides a
remarkably precise model of the modern conformal bootstrap. As an application,
we use conformal bootstrap techniques to derive rigorous computer-assisted
upper bounds on the lowest positive eigenvalue $\lambda_1(X)$ of the
Laplace-Beltrami operator on closed hyperbolic surfaces and 2-orbifolds $X$. In
a number of notable cases, our bounds are nearly saturated by known surfaces
and orbifolds. For instance, our bound on all genus-2 surfaces $X$ is
$\lambda_1(X)\leq 3.8388976481$, while the Bolza surface has
$\lambda_1(X)\approx 3.838887258$. Our methods can be generalized to
higher-dimensional hyperbolic manifolds and to yield stronger bounds in the
two-dimensional case.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat