Bestvina and Brady introduced a broad class of groups—now known as Bestvina--Brady groups—that have played a significant role in geometric group theory, particularly due to their exotic finiteness properties. In this talk, we will focus on the Dehn functions of finitely presented Bestvina--Brady groups. The Dehn function is a fundamental quasi-isometry invariant which can be thought as a quantitative version of a group's finite presentability.

I will present new results that generalise previous known work and give a complete description of Dehn functions of all finitely presented Bestvina–Brady groups.

This talk is based on joint work with Yu-Chan Chang and Matteo Migliorini.