Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in
  sets of positive density in finite field geometries   We prove that if the cardinality of a subset of the 2-dimensional vector
space over a finite field with $q$ elements is $\ge \rho q^2$, with
$\frac{1}{\sqrt{q}}<<\rho \leq 1$, then it contains an isometric copy of $\ge
c\rho q^3$ triangles.

7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas