Complete classification of the Dehn functions of Bestvina—Brady groups

Introduced by Bestvina and Brady in 1997, Bestvina—Brady groups form an important class of examples in geometric group theory and topology, known for exhibiting unusual finiteness properties. In this talk, I will focus on the Dehn functions of finitely presented Bestvina—Brady groups. Very roughly speaking, the Dehn function of a group measures how difficult it is to fill loops by discs in spaces associated to the group, and captures geometric information that is invariant under coarse equivalence. After reviewing known results, I will present a classification of the Dehn functions of Bestvina—Brady groups. This talk is based on joint work with Yu-Chan Chang and Matteo Migliorini.