My research interests

I work in the field of complex dynamics, a subfield of dynamical systems. My interests lie in Julia sets and measure and dimension in specific. Also I am interested in teaching chaos and fractals to undergraduates.

I completed my dissertation under the direction of Greg Swiatek. My thesis, entitled ``Geometry of the Julia set for some maps with invariant circles'' shows the porosity of the immediate basin of infinity of the Julia set for Herman's Blaschke product for all irrational rotation numbers. Here is the Full text of my thesis ``Geometry of the Julia set for some maps with invariant circles''

"Non-uniform Porosity for a Subset of Some Julia Sets". is a version of the thesis result which will be published in the refereed proceedings of Complex Dynamics: 25 years after the first appearance of the Mandelbrot Set. This conference was a a Joint AMS, SIAM, and IMS Summer Research Conference that was held in Snowbird, UT in the summer of 2004. The proceedings will be published in the AMS Contemporary Math series.

I have written an expository paper about fractals as well. It is called "Julia Sets that are Full of Holes". I have submitted this article to the Mathematical Intellegencer.

Along with my mathematics articles, I wrote an article about teaching courses that stretched my teaching abilities, both by teaching new skills in math courses and teaching courses outside my discipline. Entitled "Teaching outside my comfort zone", it was published in the in-house refereed Wheeling Jesuit journal Cardinal Perspectives. The article is available here.