Research

My research interests include areas of group theory, topology, and analysis that pertain to the study of dynamical systems as well as associated topics including geometric and combinatorial methods in group theory, measured group theory, actions on rooted trees, self-similar groups and automata theory, groupoids, iterated monodromy groups, tiling spaces, amenability, and ergodic theory.

Currently, I am studying the class of hyperbolic groupoids with totally disconnected unit spaces, their associated semigroups, and their applications to hyperbolic dynamical systems.