Joren Matthys (KU Leuven) -- Residual Finiteness Growth in Virtually Abelian Groups

A group is residually finite if for every non-trivial element there exists a homomorphism to a finite group such that the image of the chosen element is still non-trivial. Research has shown that most finitely generated groups arising in branches outside group theory have this desirable property. Starting in 2010, researchers have therefore started to quantify this property for these groups. More precisely, they have been studying the size of the finite group in terms of the word norm of the chosen group element. In this seminar, we introduce the topic, and we highlight some of the ideas and techniques used in this topic. We focus on the virtually abelian groups, where these techniques have led to positive research output.