I received my PhD from Boston University in 2005 working under Robert L. Devaney. I work in an area of mathematics called Complex Dynamics. This area studies the behavior of iterated functions of the complex plane. Essentially, I try to discover the long-term behavior of points that are run through a feedback loop of sorts. This often involves studying the Julia set for a function, where the Julia set is a (usually very stunning) fractal picture that acts as a type of graph. In terms of teaching, my dream class is one where no student is afraid to ask questions and all students feel challenged, yet not overwhelmed, by the material. I do my best with each class I teach to create such an environment.
Current Research: I am currently working on a few research projects. In the field of Complex Dynamics I am looking at the dynamics of perturbed complex polynomials as well as a map derived from a form of multiple circle inversion in the complex plane. Outside of Complex Dynamics I have research involving text mining and stylometry (a mathematical/statistical study of linguistic style) as well as the use of mathematics in comic books and other pop culture media.