My recent research has been in four main areas:
While in graduate school, I modeled a minicelling, filamenting mutant of the bacteria Bacillus Subtili. That is a picture I took of them up top! The ``normal'' cells are about 5-10 microns long, while the ``minicells'' are only about a micron long. I performed experiments in the laboratory of Dr. Neil Mendelson, and built models to help us understand the system with Dr. Joe Watkins .
We have a recent paper in the Journal of Theoretical Biology describing this work.
Along with Claudia Neuhauser and Yoh Iwasa, I've been studying the spatial distribution of individuals in gynodioecious plant populations (those are populations in which some individuals are female, and some are hermaphrodites.) We have built and analysed a model composed of a pair of differential-integral equations which describe the system. Our model, along with field observations, makes specific predictions about the dispersal of seed and pollen in these systems.
This work has been submitted to Journal of Mathematical Biology . Here are preprints in [PDF (1876K) or PostScript (10437K)].
I've also been working on a problem with members of the Business Modeling Group at the Ford Motor Company . We have been building and analyzing game theoretic models describing a durable goods monopoly. Ford is obviously very interested in asking questions about how to price a durable good!
I'm also interested in non-parametric statistical methods. For example, here is an IMA reprint on Implicit Assumptions in Gott's Formula. [PDF (94K) or PostScript (191K)].