I am broadly interested in dynamical systems and information theory.

epsilon-machines

In my PhD, I studied causal representations of stochastic processes through use of information theory. We asked questions such as, How much memory does a stochastic process "require to run"? We also developed algorithms to compute these quantities-a nontrivial task due to the infinite range correlations present. A new length scale for stochastic processes, the crypticity emerged in this effort. It has since reappeared in the context of quantum compression.

burning invariant manifolds

As a postdoc with Kevin Mitchell at UC Merced, I studied reaction fronts propagating in fluid flows. Many reacting flow studies focus on high-dimensional PDEs. In contrast, we chose the simplest model possible and were thus able to proceed using many standard tools of dynamical systems theory. We demonstrated the existence and function of one-way barriers to front propagation in these systems. This basic idea was used to describe several system phenomena: pinning, mode-locking, turnstile-mediated front transport. We also defined finite-time versions of these structures.

quantum representations of structured processes

Currently I am working with quantum representations of classical stochastic processes. The goal is to understand in what ways quantum mechanics allows for a more efficient representation or simulation.