The research probems I work on involve algebraic geometry and dynamical systems. In particular, I am interested in the dynamics of rational self maps of P^1 and P^2. Below is a copy of my Ph.D. thesis as well as my other work. This includes published work, preprints, and papers in progess. Birational Maps of Surfaces with Invariant Curves, Ph.D. Thesis, University of Notre Dame, 2005. (with J. Diller and A. Sommese) Invariant Curves for Birational Surface Maps, To appear in Transactions of the American Mathematical Society. (with D. Gage) On Computer Generated Images for Quadratic Rational Maps with a Periodic Critical Point, Preprint (last updated 20 March 2008) Student Research Projects: Quadratic Rational Map Fractal Generator (JAVA applet by Dustin Gage) Dynamical Grapher for Quadratic Maps (JAVA applet by Adam Case and Hunter Basselet)