2008 DG-MP-PDE Seminar - 02

Suppose $A$ is a subset of the integers of positive density. We prove a quantitative result on the existence of linearly independent polynomial configurations in the difference set of $A$. Our approach is based on first establishing a higher dimensional analogue of a theorem of S\'{a}rk\"{o}zy and Furstenberg, and then applying a simple lifting argument. This is joint work with Neil Lyall.