Mark Hagen (Cambridge)

Title: Acylindrical hyperbolicity from cubical small-cancellation

Abstract: I will define cubical presentations and cubical small-cancellation groups, in the sense of Wise, and explain the increased flexibility this offers compared to classical small-cancellation theory. Then I'll talk about associating hyperbolic graphs to CAT(0) cube complexes, and how to use this to define a hyperbolic space on which a cubical small-cancellation group acts "nicely". From this, one can show that cubical small-cancellation groups are acylindrically hyperbolic, which has various consequences. This result generalizes the fact that strong classical small-cancellation implies hyperbolicity and is closely related to a recent result of Gruber-Sisto on acylindrical hyperbolicity of "graphical" small-cancellation groups. This talk is mainly about recent joint work with Goulnara Arzhantseva.