I have served on UW-L's Undergraduate Research Committee from 2006-2009. Visit the website to learn more about undergraduate research at UW-L.
I am currently a councilor on the Council on Undergraduate Research (CUR).
I am always interested in advising undergraduate research projects. I have a few project ideas in the areas of differential equations, mathematical biology, and fluid dynamics. Please see me if you are interested.
Spring 2009/Summer 2009. Katherine Ott worked on mathematical biology research project. She used systems of differential equations to model the spread of the West Nile virus through a mosquito population and multiple host bird populations. The goal of the project is to discover how bird composition in a given environment affects the severity of the spread of the disease. In epidemiological models, the spread of the disease is described by the basic reproduction number R0. The value of R0 is the number of new infections created by introducing a single infected individual to an entirely susceptible population. Katherine developed a model involving one mosquito and two bird populations. She showed that in three environments of Wisconsin (wetlands, agricultural, and urban) the value of R0>1. She was able to determine strategies that can be implemented to reduce the Ro to a value less than one. Katherine plans on presenting her work Spring semester 2010 on campus and at a state-wide meeting.
Fall-Spring 2007-2008. Trever Hallock worked on a research project looking at the motion of a vortex line in an averaged fluid domain. Trever showed that averaging removes the singularity at the line premiting an asymptotic model for the local effects of rotation define on the entire fluid domain. He presented his work at the 2008 UW-L Celebration of Research and Creativity Day. Trever is currently a student at UC Berkeley.
Summer 2005. Devin Bickner used partial differential equations to model the motion of a plucked guitar string. He proposed an equation that included the effects of dampening and proved that the total energy of this new model decreases as we expect from a real guitar string. Devin solved the general partial differential equation, applied it to the plucked string model, and used Mathematica to "pluck the string" and hear the solution. Devin presented his work at the Pi Mu Epsilon Conference at St. Norbert College in Fall 2005. Devin has decided to continue his study of mathematics in a Ph.D. program at Iowa State University.