Fuchsian Groups and The Uniformization Theorem
|Date||Thursday, November 27, 2014|
The uniformization theorem is a deep generalization of the Riemann mapping theorem. It says that the universal cover of any Riemann surface is conformally equivalent to the disk, plane, or sphere. Aside from a handful of exceptions, the covering is the disk.
Fuchsian groups are the groups of complex analytic deck transformations of this covering. They also happen to be groups preserving hyperbolic distance, and thus can be seen to give tilings of the disk with respect to this non-Euclidean geometry.
In this talk I will give a friendly non-technical introduction to these concepts.