David Conlon: Difference sets in higher dimensions

Let $d\ge 2$ be a natural number. We determine the minimum possible size of the difference set $A-A$ in terms of $|A|$ for any sufficiently large finite subset $A$ of $R^d$ that is not contained in a translate of a hyperplane. By a construction of Stanchescu, this is best possible and thus resolves an old question first raised by Uhrin. If time permits, we will also discuss some recent related results. Joint work with Jeck Lim.