Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is the total Betti number of a random real hypersurface?   We bound from above the expected total Betti number of a high degree random
real hypersurface in a smooth real projective manifold. This upper bound is
deduced from the equirepartition of critical points of a real Lefschetz pencil
restricted to the complex domain of such a random hypersurface, equirepartition
which we first establish. Our proofs involve H\"ormander's theory of peak
sections as well as the formula of Poincar\'e-Martinelli.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas