Many questions in analysis and geometry lead to problems of

quasiconformal geometry on non-smooth or fractal spaces. For example, there is a close relation of this

subject to the problem of characterizing fundamental groups of hyperbolic

3-orbifolds or to Thurston’s characterization of rational functions with

finite post-critical set.

In recent years, the classical theory of quasiconformal maps between Euclidean spaces has been successfully extended to more general settings and powerful tools have become available. Fractal 2-spheres or Sierpinski carpets are typical spaces for which this deeper understanding of their quasiconformal geometry is particularly relevant and interesting. In my talk I will report on some recent developments in this area.