Fine Curve Graphs and Surface Homeomorphisms

In this talk, we will give an overview of a recent program that aims to study homeomorphism groups of surfaces using coarse geometric methods. More precisely, we will talk about the fine curve graph, which is a hyperbolic graph on which the homeomorphism group of a surface acts in an interesting way. No familiarity with curve graphs, fine or not, will be assumed. Most of the results are joint work with Jonathan Bowden and Richard Webb.