Amenable groups and Noetherian group rings

Abstract: In joint work with Karl Lorensen and Dawid Kielak, we study an old question of Reinhold Baer which dates back to around 1960. which are the groups such that the integral group ring is Noetherian. We shall see that as well satisfying the maximal condition on subgroups (which Baer knew), they also must be amenable. This then connects the question to some interesting Burnside groups constructed by Ivanov and Olshanskii. I love this topic because it touches on two important and apparently very different things in 20th century mathematics: the Banach-Tarski paradox and the roots of non-commutative algebraic geometry.

Mathematics

Audience: researchers in the topic

Royal Holloway CANTA-Launch