|Date:||Tue, February 8, 2011|
|Place:||Research I Seminar Room|
Abstract: In this talk I describe how I ended up doing complex dynamics. Quasisymmetric (qs) maps are close relatives (more precisely global versions) of quasiconformal maps. Quasisymmetric uniformization asks whether a given metric space is qs-equivalent to some standard space. Of particular interest is the question when a metric sphere is qs-equivalent to the standard sphere. It turns out that certain fractal spheres can be quasisymmetrically parametrized via a rational map. Whether a topological rational map is equivalent to a rational map turns out to be equivalent to the question whether a certain metric sphere is qs-equivalent to the standard sphere.