Sophie Stevens

A survey on the sum-product problem

Given a finite set of numbers A, we can create a set by considering the sum of all pairs of elements in A. We can also create a different set made up of all pairwise products of elements of A. The sum-product conjecture is to show that one of these sets must be big. I’ll give a survey on why this conjecture exists, results, and the techniques used. In particular, I’ll talk about the role that geometry plays in this problem.