Topology and Geometric Group Theory Seminar
Quasisymmetries are an important class of homeomorphisms between metric spaces that arise in quasiconformal geometry. In this talk, I will introduce quasisymmetries and describe some connections between geometric group theory and quasisymmetries of fractals. I will then discuss a new characterization of quasisymmetries for finitely ramified fractals and give some examples of infinite discrete groups such as Thompson's groups acting on finitely ramified Julia sets by quasisymmetries. This is joint work with Bradley Forrest.