From October 2011 to February 2015 I was a research fellow at the University of St Andrews.
I am currently an independent travelling researcher, looking for an academic position to start around September 2016.
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.
Research
My main research interests are:
Interactions between algebra and formal language theory
Geometric and combinatorial group theory
The main projects I am working on at the moment are:
Finding new ways to construct automaton semigroups, and to prove semigroups not to be automaton semigroups,
with Alan Cain (Universidade Nova de Lisboa);
Solving the membership problem for soluble subgroups of the group of piecewise-linear orientation-preserving homeomorphisms of the unit interval,
with Collin Bleak (St Andrews) and Susan Hermiller (Nebraska);
Investigating the class of groups with poly-context-free multiplication table.
Publications
Finitely generated soluble groups and their subgroups, with Derek Holt
Communications in Algebra, 41:5, 1790-1799 (2013)
(Earlier version)
Groups with poly-context-free word problem
Groups Complexity Cryptology, Volume 6, Issue 1, 9-29 (2014)
(Preprint)
Automaton semigroup constructions, with Alan Cain
Semigroup Forum, 90:3, 763-774 (2015)
(Preprint)
Permutations of context-free and indexed languages, with Laura Ciobanu and Murray Elder
Discrete Mathematics & Theoretical Computer Science (to appear)
(Preprint)
Determining solubility for finitely generated
groups of PL homeomorphisms, with Collin Bleak and Susan Hermiller Preprint
Graded Lie algebras of Cartan type in characteristic 2, with Bettina Eick Preprint
Solubility and geometry for finitely generated groups of piecewise-linear homeomorphisms,
GAGTA-9 (Geometric and Asymptotic Group Theory with Applications), CIRM Luminy, September 2015. Automaton semigroups: some new examples and non-examples,
21st NBSAN Meeting, University of Essex, July 2015. Automaton semigroup constructions,
Special session on `New trends in automata groups and semigroups', AMS-EMS-SPM Conference, Porto, June 2015. Deciding solubility in finitely-generated groups of piecewise-linear homeomorphisms,
Algebra and Logic Seminar, Universidade Nova de Lisboa, June 2015. Finitely generated non-soluble groups of homeomorphisms,
Algebra Seminar, University of Aberdeen, February 2015. Multiplication tables, intersections of context-free languages, and free products,
Algebra-Geometry Seminar, Newcastle University (UK), November 2014.
An older talk available online: Solvable poly-context-free groups, International Group Theory Webinar, December 2013. (Slides and recording available
here.)
MT2001 Mathematics (linear algebra and calculus):
tutorials, examples classes and computer lab sessions (Sem 2 2013/14).
MT5823 Semigroups:
4 lectures, 4 tutorials, and helping students with their projects (Sem 2 2013/14). MT5824 Topics in Groups:
3 lectures (Sem 1 2013/14). MT4003 Groups:
6 lectures and all tutorials (Sem 2 2011/12).
In the 2012/13 academic year I supervised an MMath student, Xiaobing Sheng, for her project on 'Word problems of groups, languages and automata'.