Stable commutator length (scl) is a measure of homological complexity of group elements, with connections to many topics in group theory and geometric topology, including quasimorphisms, bounded cohomology, and circle actions. The first part of the talk will be a general introduction to scl and to some of these topics
In the second part, we will focus on spectral gaps and their relation with notions of negative curvature in group theory. We will present a geometric method to prove spectral gap results, giving a new proof of a theorem of Heuer on the spectral gap of scl in right-angled Artin groups. We will explain the idea of the method and show how it works in the special case of free groups

https://indico.math.cnrs.fr/event/16149/