My research interests fall under the broad areas of Combinatorics, Discrete Mathematics, and Number Theory. I am especially interested in combinatorics on words, from algebraic and geometric points of view, and its applications in Number Theory.
Much of my research to date has focussed on repetitions (including abelian repetitions) and periodicity (including quasiperiodicity) in finite and infinite words (particularly Sturmian and episturmian words, including the well-known Fibonacci word, and also the Thue-Morse sequence), as well as other combinatorial regularities and patterns occurring in words, such as recurring factors, Lyndon words, palindromes, and related notions of word complexity, lexicographic ordering, and distribution of real numbers modulo 1 from a combinatorial perspective. Some of these topics have applications to a wide variety of other scientific fields, ranging from theoretical computer science (digital imagery, pattern recognition) to theoretical physics (quasicrystal modelling) and molecular biology (DNA sequences).
I am happy to supervise Honours and PhD projects in any of the areas mentioned above. Feel free to e-mail me, or if you’re in Perth, drop by my office to discuss possible topics. To get an idea of the sorts of things I work on, see my publications or talks.