Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of unit-area triangles spanned by convex grids in the
  plane   A finite set of real numbers is called convex if the differences between
consecutive elements form a strictly increasing sequence. We show that, for any
pair of convex sets $A, B\subset\mathbb R$, each of size $n^{1/2}$, the convex
grid $A\times B$ spans at most $O(n^{37/17}\log^{2/17}n)$ unit-area triangles.
This improves the best known upper bound $O(n^{31/14})$ recently obtained in
\cite{RS}. Our analysis also applies to more general families of sets $A$, $B$,
known as sets of Szemer\'edi--Trotter type.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat