Abstract :
A long-standing problem in combinatorial number theory, posed by Erdős and Graham, asks for a classification of all integer subsets A and B for which d(A+B)=d(A)+d(B), where d(.) denotes the natural density in the integers. We will discuss the history and motivation of this problem, its connections to ergodic theory, as well as recent progress toward its resolution. This talk is based on joint work with Ethan Ackelsberg.