I am currently a PhD student in the Department of Mathematics at the University of California, San Diego. I am working with Professor Mike Holst, on discretisation techniques for constrained hyperbolic systems. I use semigroup techniques to prove well-posedness of such systems and am developing finite element methods for their discretization. I have spent two summers at Lawrence Livermore National Laboratory, working with Ulrike Yang on a nodal algebraic multigrid solver for systems derived from coupled partial differential equations. I spent my first year in the Department of Computer Science and Engineering working with Professor Scott Baden studying the scalability and latency tolerance of parallel FFTs.
In August 2002, I graduated from the Department of Computer Science at the University of Illinois at Urbana-Champaign with a Master of Science. While there, I had the privilege of working with Professor Paul Saylor conducting research focused on scalable linear solvers for large sparse systems. This work culminated in my thesis on the parallel scalability of the adaptive Chebyshev algorithm.
In May 2000, I graduated with First Class Honours from the University of Manitoba with a Bachelor of Computer Science. Starting in the summer after my second year, Professor William Kocay started me down the (sometimes dark) path of an academic when he offered me a research opportunity to work on Groups & Graphs. Over the next two years, I spent much time researching various topics including toroidal graph embeddings and the mysterious projective plane. This research went hand in hand with major additions to the Groups & Graphs code base. In my final semester, I worked on an undergraduate honours research project where Professor Kocay and I switched topics and delved into numerical analysis. The research focused on rudimentary solution methods for ordinary differential equations, applied to the following of light-like geodesics near Kerr-Newman black holes.
My statement of research interests, statement of teaching philosophy, and curriculum vitae are available.
Publications
- Kocay, W., Neilson, D., and Szypowski, R., "Drawing Graphs on the Torus", Ars Combinatoria, vol. 59, 259-277, 2001.
- Kocay, W. and Szypowski, R., "The Application of Determining Sets to Projective Configurations", Ars Combinatoria, vol. 53, 123-145, 1999.