Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Uniformization of quasiconformal trees
Speaker: Daniel Meyer, University of Liverpool
Date: September 6, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Quasisymmetric maps are generalizations of conformal maps and may be viewed as a global versions of quasiconformal maps. Originally, they were introduced in the context of geometric function theory, but appear now in geometric group theory and analysis on metric spaces among others. The quasisymmetric uniformization problem asks when a given metric space is quasisymmetric to some model space. Here we consider this uniformization problem for certain trees. In particular, we consider the "continuum self-similar tree'' (CSST) and give necessary and sufficient conditions for another tree to be quasisymmetrically equivalent to the CSST. One motivation to study the CSST is that it is almost surely homeomorphic to the continuum random tree introduced by Aldous. This is joint work with Mario Bonk.
Title of Talk: Uniformization of quasiconformal trees
Speaker: Daniel Meyer, University of Liverpool
Date: September 6, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Quasisymmetric maps are generalizations of conformal maps and may be viewed as a global versions of quasiconformal maps. Originally, they were introduced in the context of geometric function theory, but appear now in geometric group theory and analysis on metric spaces among others. The quasisymmetric uniformization problem asks when a given metric space is quasisymmetric to some model space. Here we consider this uniformization problem for certain trees. In particular, we consider the "continuum self-similar tree'' (CSST) and give necessary and sufficient conditions for another tree to be quasisymmetrically equivalent to the CSST. One motivation to study the CSST is that it is almost surely homeomorphic to the continuum random tree introduced by Aldous. This is joint work with Mario Bonk.