### Extremal problems for GCDs

Combinatorics Seminar

1st December 2021, 11:00 am – 12:00 pm

Fry Building, 2.04

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.

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