Current Research Interests
- Monte Carlo Simulation & Random Number Generation
- I have had the opportunity at work over the past several
years to model some extremely complex systems using Monte
Carlo techniques in a large grid environment. Not only are
the results interesting, but so are the statistical and
mathematical problems associated with it - generating random
numbers, selecting good sub-sample populations from the
result sets, and insuring consistent random number sequences
network wide. Great fun.
- Numerical Linear Algebra
- I am interested in a wide array of numerical linear
algebra topics. Most recently, iterative and direct methods
for sparse systems have captured my imagination. For
example, I have spent a good deal of time exploring
multi-threaded approaches to GMRES recently. I have also
been playing around with a distributed multi-processing
approach for Gaussian elimination.
- Autonomous, Dynamical Systems
- I am most interested in distributed, dependent systems of
independent nodes. One such system in nature is coral - many
tiny organisms working to build a large, organized
structure. Some time ago, I expended considerable effort
implementing software to simulate systems capable of
generating tree-like structures. Check out some of the
results:
images.
More recently, I have been exploring truly distributed
software to implement similar systems in a massively
parallel grid environment.
- Computational Algebra
- The topic of my master's thesis was using ancient OOP
techniques to develop very a generic implementation of
B. Buchburger's
algorithm in such a way that the same code was capable of
working over various rings without modification. I have
continued to be interested in this topic; however, now I am
more focused on using modern template meta-programming
methods to do the same thing but with dramatically greater
performance.
- Computer visualization of mathematical objects
- I became interested in the visualization of sections of
3-manifolds and knot spaces in my undergraduate years. Back
then the visualization of these objects was completely
beyond the range existing OpenGL hardware, and so very
specialized software implementations were the only
possibility. Even today such problems push what one can buy
at the local Fry's.
Consulting
I occasionally engage in consulting activity; however, I tend
to be quite selective regarding the contracts I elect to
accept. Of paramount importance in the decision making
process is if the contract sounds interesting to me. If your
problem involves one of the topics listed above, then you have
a much better chance of securing my services. In particular,
if your problem involves large scale system modeling with
simulation or numerical linear algebra, you may have a very
good chance.
My bill rate is variable depending upon how interesting the
problem is, but $2400/day plus expenses with travel time
billed at 25% is typical. That said, I have agreed to the
much lower NSF rate of around $600/day for a couple of more
interesting problems.
