Interactions between algebra and formal language theory
Geometric and combinatorial group theory
I am currently a research fellow at the University of St Andrews (Oct 2011 to Feb 2014), funded by the EPSRC grant "Automata, Languages, Decidability in Algebra".
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 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
To appear in Groups--Complexity--Cryptology
Automaton semigroup constructions, with Alan Cain
Inverse semigroups with rational word problem are finite
Solvable poly-context-free groups, International Group Theory Webinar, December 2013. (Slides and recording available
here at bottom of page.) 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. Poly-context-free groups, University of Neuchâtel, July 2013. Automaton semigroups, Algebra and Geometry Seminar, University of Bristol, June 2013. Automaton semigroup constructions, Novi Sad Algebraic Conference, Novi Sad, June 2013. Free products and wreath products of automaton semigroups, Questions, Algorithms and Computations in Abstract Group Theory,
Braunschweig, May 2013. Automaton semigroups, Algebra and Combinatorics Seminar, University of Auckland, January 2013. Automaton semigroup constructions, Mathematics Research Seminar, University of Newcastle (Australia), January 2013.
Since October 2012 I have been the organiser for the Algebra and Analysis Seminar in St Andrews, in which members of the algebra and analysis
research groups explore interactions between the two areas.
In the 2012/13 academic year I supervised an MMath student, Xiaobing Sheng, for her project on 'Word problems of groups, languages and automata'.
In early 2012 I taught six lectures (out of 25) and all tutorials for