My research interests span many areas of mathematics, including (geometric) group theory, fractal geometry, topology, and semigroup theory. Finite state automata are a major theme in my research, in relation to groups acting on Cantor space and characterizing fractal quotients of Cantor space. Prominent groups in my research are Thompson's group V and self-similar automorphism groups of trees. I am interested in generalizing notions in fractal geometry to `non-traditional' metric and topological spaces, such as Cantor space and profinite groups. Lastly, semigroups are of growing interest to me, with an emphasis on subsemigroup structure.
- PhD, University of St. Andrews