One of the main contributions I made to the field of Computational Topology is the construction of complicated test examples which identified limitations to existing heuristic topological software.
Triangulations of the Akbulut-Kirby Spheres
These examples have been used to test and improve some heuristic algorithms including, Random_Discrete_Morse, bistellar_simplification, and Perseus.
I mostly program in C++, Mathematica, R and also have experience using C, Perl, Python, bash.
- Topological Software
- Mathematical Visualization: Animation in “real” 3D