Published Work and Preprints: 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) Research Tools Programmed by Former Students: Quadratic Rational Map Fractal Generator (JAVA applet by Dustin Gage, Class of 2007) Dynamical Grapher for Quadratic Maps (JAVA applet by Adam Case, Class of 2009 and Hunter Basselet, Class of 2008)