Stable commutator length (scl) is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with non-positive curvature. We will present a geometric method to prove sharp lower bounds for scl, 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.
