Stable commutator length (scl) is an invariant of groups that appears in many areas of mathematics, thanks to various different incarnations: algebraic, topological and analytic. It is generally hard to compute, and a central theme going back to a question of Gromov has been to understand what values scl can take on finitely presented groups: the "spectrum problem".

After introducing scl and the history of this spectrum problem, we will see that group actions on 1-manifolds can lead to very concrete and interesting examples. In particular, I will present joint work with Yash Lodha in which we show that scl can take algebraic irrational values in finitely presented groups, answering a question of Calegari.

This will be a hybrid seminar. The live talk in SR12 will be simulcast on Zoom.

Join Zoom meeting ID 978 1075 8446 or via the link below. Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)