My research interests are in the field of dynamical systems and ergodic theory. In dynamical systems, we study how systems evolve under repeated iteration of a single function. Past work of mine includes the study of convergence for specialized ergodic averages.

Publications:

Convergence of Polynomial Ergodic Averages of Several Variables for Some Commuting Transformations, Illinois Journal of Mathematics, Volume 53, Number 3 (2009), 865-882.

Powers of Sequences and Convergence of Ergodic Averages (joint with N. Frantzikinaks, E. Lesigne, and M. Wierdl), Ergodic Theory & Dynamical Systems, Volume 30, Number 5 (2010), 1431-1456.

My recent research has been in the area of cellular automata. A priority of mine is to incorporate students in various research projects. Last summer, I worked with Sarah McRoberts to investigate a model used to describe the competition for rock space between two intertidal species. 

Sarah McRoberts presenting a poster titled, "Using Stochastic Cellular Automata to Model the Growth and Competition Between Two Stationary Species" at the Midstates Undergraduate Research Symposium.

This summer I will be working with a couple of Luther students to investigate a model to understand the frequency of various sized avalanches in a sandpile.