David McKinnon, Department of Pure Mathematics, University of Waterloo
"Gaussian integers and gcds"
Say you’re having a cup of tea with your favourite Gaussian integer. The two of you get to discussing real and imaginary parts, you know, as you do. The subject of the gcd of those two quantities arises, and you start wondering how big that gcd can be. After you both realise how silly a question that is, you then figure out that there are nevertheless some interesting patterns in the answer that turn out to generalize to arbitrary number fields.