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Fractals and Quasiconformal Geometry
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 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.
Thursday, October 6, 2005, 245 Altgeld Hall, 4:00 p.m.
Mathematics Colloquia homepage