Collinear triples and quadruples for Cartesian products in   $\mathbb{F}_p^2$
  In this ote, which has been absorbed by arXiv1702.01003, we combine a recent point-line incidence bound of Stevens and de Zeeuw with an older lemma of Bourgain, Katz and Tao to bound the number of collinear triples and quadruples in a Cartesian product in $\mathbb{F}_p^2$. 
Giorgis Petridis
math.CO