Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Weil-Petersson curvature of the moduli space of Riemann surfaces
  of large genus   Let $S_g$ be a closed surface of genus $g$ and $\mathbb{M}_g$ be the moduli
space of $S_g$ endowed with the Weil-Petersson metric. In this paper we
investigate the Weil-Petersson curvatures of $\mathbb{M}_g$ for large genus
$g$. First, we study the asymptotic behavior of the extremal Weil-Petersson
holomorphic sectional curvatures at certain thick surfaces in $\mathbb{M}_g$ as
$g \to \infty$. Then we prove two curvature properties on the whole space
$\mathbb{M}_g$ as $g\to \infty$ in a probabilistic way.

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The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga