Summer 2009 Program
Conformal Geometry
During the summer of 2009 the lab conducted a series of lectures and workshops discussing the geometry of the complex projective line. Students participating were expected to give lectures, develop software and contribute to a conformal geometry handbook documenting our progress. At the end of the summer participating undergraduates each gave a presentation to the mathematics department.
Software
The software packages we have built using Mathematica provide tools for computing and drawing in conformal geometry. It contains tools for drawing various objects in the upper half plane and Poincare disk models of the hyperbolic plane as well. The notebook is called ConformalGeometry.nb, and contains many examples of its use. Simply download and execute the entire notebook to see examples.
One section relies upon the package FreeGroupAutos.nb by William Goldman.
An afternoon of Presentations
On Thursday July 30, 2009 each student gave a presentation on their work. Below are some of the supporting materials for each talk. Some of the Mathematica notebooks here are dependent upon the package ConformalGeometry.nb described above.
Greg Laun: The space of chains in CP1 is a 3-manifold homeomorphic to (S^2 * R)/Z_2
Jason Rauen: Pencils of chains and convexity properties of the space of chains
Ed Yasutake: Two generator Fuchsian Schottky systems: How quickly to circles shrink?
Joia Hertz: Actions of Isometry groups on the space of geodesics
Tevis Tsai: Circle packing and the Apollonian gasket
Pictures from the Presentations
And some pictures of the after party...
Return to EGL Homepage