A copy of my thesis can be found here. This page contains some supporting documents and pictures. The slides used in my thesis defense can be found here
Mathematica Notebooks
Calculations and notes accompanying my thesis are contained in Sp(4,R) Triangle Groups.nb. This notebook uses routines from 2 other Mathematica packages:
A construction of a triangle group representation where there are potentially deformations. The construction is given in the last section of my thesis. Here is a summary in 2 formats:
This shows a 3D subspace containing the above flat. The 2D subspace transverse to the flat is a copy of the upper half plane. The geodesics in the standard flat are shown and their images under a 1 parameter group of rotations fixing a singular geodesic in the standard flat.
Similar to the above, this is another 3D subspace fixing a different geodesic in the standard flat. The result is another copy of the upper half plane transverse to the standard flat.
This shows a 1 parameter family of rotations fixing yet another of the singular geodesics. The resulting 3D space is the cone of positive definite symmetric matrices. This is the cone for this Siegel Domain. This cone naturally contains an embedded copy of the hyperboloid model of the hyperbolic plane.
