What I do
I teach courses at all levels within the mathematics department, conduct mathematics research, and perform various service activities, both within DU and for mathematics in general.
mathematics, dynamical systems, ergodic theory
- Ph.D., Mathematics, The Ohio State University, 2007
- MS, Mathematics, The Ohio State University, 2003
- BS, Mathematics, The Ohio State University, 2000
My main research focus is to better understand the behavior of symbolically defined systems. Much of my work has defined natural hypotheses on multidimensional systems which guarantee behavior more similar to the better understood one-dimensional case. On the other hand, some of my work is in the opposite direction: giving quantifiable results about the full range of esoteric behavior achievable by symbolically defined systems. Almost all of my work, in one way or another, relates to a fundamental quantity called entropy, which is associated to any dynamical system. Entropy is both a useful concept in its own right, and by its relation to so-called measures of maximal entropy. These are measures which "best encapsulate" the behavior of a system, also called equilibrium states in statistical physics. Recently, the main topic in my research program has been to isolate reasonable hypotheses guaranteeing that a symbolically defined system (in either one or multiple dimensions) has a unique measure of maximal entropy, which can be thought of as a type of regularity of the system.
- Topics in Symbolic Dynamics
- 2014 Pingree Park Dynamical Systems Workshop
- 2017 Pingree Park Dynamical Systems School
- Pioneer Faculty Award, University of Denver
- Postdoctoral Teaching Award, University of British Columbia