Geometry and Topology Seminar

The mapping class groups of infinite type surfaces aren't finitely generated or locally compact, so don't fall within the normal scope of geometric group theory. Nevertheless, there has been much recent work (starting with that of Calegari and J. Bavard) on essentially geometric questions about these groups: distortion of elements, hyperbolicity of associated curve graphs, etc. In new work with Kasra Rafi, we attack these kinds of questions by showing many large mapping class groups do have a well-defined large scale geometry, using Christian Rosendal's framework for geometric group theory of non-locally compact groups. In this talk I'll explain our classification theorem, some of the tools involved in its proof, and advertise some next steps.