Mathematical Conversations

Stable commutator length (or scl) of group elements is a well-known, simple-to-define invariant, related to bounded cohomology and quasimorphisms. Yet its simple definition is a trap: many of the exciting developments around scl required "better" definitions. Recently, better definitions led to the discovery of long-sought-after new relatives of scl. I will describe the evolution of the definition of scl, some works of Calegari and Wilton, and if time permits, why I'm interested in all of this.