## Dynamics, Geometry, & Groups Seminar

### Thursday, January 21st, 2021

**Time:** 1:30 p.m** Place:**

**Speaker:** Macarena Arenas (University of Cambridge)

**Title:** Linear isoperimetric functions for surfaces in hyperbolic groups.

**Abstract:** One of the main characterisations of word-hyperbolic groups is that they are the groups with a linear isoperimetric function. That is, for a compact 2-complex X, the hyperbolicity of its fundamental group is equivalent to the existence of a linear isoperimetric function for disc diagrams D -->X.

It is likewise known that hyperbolic groups have a linear annular isoperimetric function and a linear homological isoperimetric function. I will talk about these isoperimetric functions, and about a (previously unexplored) generalisation to all homotopy types of surface diagrams. This is joint work with Dani Wise.