From curve graphs to fine curve graphs

Fine curve graphs have been introduced by Bowden, Hensel and Webb to study homeomorphism groups of closed surfaces. A main tool in their work is the fact that fine curve graphs can be approximated by curve graphs of surfaces with punctures. I will talk about joint work with Sebastian Hensel, where we study to which extent the boundary of the fine curve graph can be approximated via curve graphs of surfaces with punctures. I will also discussion of fine curve graph techniques to the study of mapping classes of infinite-type surface.