Interactions between algebra and formal language theory
Geometric and combinatorial group theory
I am currently a research fellow at the University of St Andrews.
I am working on various aspects of the interactions between semigroup theory and automata theory.
My two main projects at the moment are:
an investigation of semigroups with rational word problem, particularly focussing on Green's relations
on these semigroups; and some work on automaton semigroup constructions.
I have also started working on some questions on languages in group theory.
I completed my PhD on word problems of groups at the University of Warwick in early 2011, supervised by Derek Holt.
From October 2010 I spent a year as a research and teaching assistant at Kiel University in Germany, working with Richard Weidmann in geometric group theory.
Finitely generated soluble groups and their subgroups, with Derek Holt
Communications in Algebra, 41:5, 1790-1799 (2013)
Groups with poly-context-free word problem
Groups Complexity Cryptology, Volume 6, Issue 1, 9-29 (2014)
Automaton semigroup constructions, with Alan Cain
To appear in Semigroup Forum
Permutation closures of context-free and indexed languages, with Laura Ciobanu and Murray Elder
Multiplication tables, intersections of context-free languages, and free products,
GAGTA (Geometric and Asymptotic Group Theory with Applications), Newcastle, Australia, July 2014. Commutative rational semigroups, Algebra and Combinatorics Seminar,
University of Auckland, June 2014. Commutative rational semigroups, Algebra and Combinatorics Seminar,
University of St Andrews, April 2014. Solvable poly-context-free groups, International Group Theory Webinar, December 2013. (Slides and recording available
here.) Poly-context-free groups and semilinear sets, Group Theory Seminar, Algebraic Cryptography Center, Stevens Institute of Technology, November 2013. Group word problems related to the context-free languages, Algebra Kinderseminar, University of Oxford, October 2013. Anisimov's Theorem for inverse semigroups, Groups St Andrews, St Andrews, August 2013.