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.
Note: The Mathematica package ConformalGeometry.m will is included for legacy purposes only. The functions have been incorporated into Hyperbolic Toolbox, which will continue to be developed and supported.
The Space of Chains in CP1
Presentation and interactive demonstation of the space of chains in CP1, which is a 3-manifold homeomorphic to (S2 x R)/Z2.
Pencils of Chains and Convexity Properties of the Space of Chains
Interactive demonstration of pencils of chains.
Two Generator Fuchsian Schottky Systems: How Quickly do Circles Shrink?
Explores Schottky groups.
Actions of Isometry Groups on the Space of Geodesics
Demonstrates spherical, Euclidean, and hyperbolic transformations with graphics.
Circle Packing and the Apollonian Gasket
Investigates the Apollonian Gasket.