* A question of Erdős on whether the set of perfect squares can be close to a sumset, and a multiplicative analogue by Hajdu and Sárközy.

* A conjecture of Van Lint and MacWilliams on the characterization of maximum subsets of a finite field of square order such that pairwise differences are all squares (also known as the Erdős-Ko-Rado theorem for Paley graphs), and its generalization.

* Inverse sieve problems (that have been studied by Green–Harper, Helfgott–Venkatesh, Shao, and Walsh), motivated by the inverse Goldbach problem.

Joint work with Ernie Croot and Junzhe Mao.