In this talk we will discuss how ideas from Koukoulopoulos and Maynard’s proof of an old conjecture in diophantine approximation led to some surprisingly subtle questions in combinatorial number theory. These questions ask for a bound on the maximal size of two finite sets of natural numbers A and B with the property that 1% of the pairs (a,b) have a large greatest common divisor. We will also describe our recent joint work with Ben Green, in which we proved close-to-optimal bounds on these problems.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
