Mitch Richling: Mathematics Research Interests

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.

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.

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.

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.

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.