Integer distance sets

A set in the Euclidean plane is called an integer distance set if the distance between any pair of its points is an integer.  All so-far-known integer distance sets have all but up to four of their points on a single line or circle; and it had long been suspected, going back to Erdős, that any integer distance set must be of this special form. In a recent work, joint with Marina Iliopoulou and Sarah Peluse, we developed a new approach to the problem, which enabled us to make the first progress towards confirming this suspicion.  In the talk, I will discuss the study of integer distance sets, its connections with other problems, and our new developments.