Marco Linton (ICMAT)

Title: Characterising local quasi-convexity

Abstract: A hyperbolic group is locally quasi-convex if all of its finitely generated subgroups are quasi-convex. Local quasi-convexity is a very restrictive condition which implies several strong subgroup properties such as local hyperbolicity and decidability of the membership problem. In this talk I will sketch a proof of the fact that cubulated locally quasi-convex hyperbolic groups are in fact all virtually free-by-cyclic. I will spend some time explaining the main ingredients of the proof which mostly come from recent developments in the theory of $L^2$-invariants and free-by-cyclic groups. (based on my appendix to an article of Fisher--Sanchez-Peralta).

We will gather in the lounge for teatime after the talk, and then we will go for dinner with Marco.