Tara Brough

Former Research Fellow in Algebra

Contact: tara[at]mcs.st-andrews.ac.uk

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.


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)

    Automaton semigroup constructions, with Alan Cain
    Semigroup Forum, 90:3, 763-774 (2015)

    Permutations of context-free and indexed languages, with Laura Ciobanu and Murray Elder
    Discrete Mathematics & Theoretical Computer Science (to appear)

    Determining solubility for finitely generated groups of PL homeomorphisms, with Collin Bleak and Susan Hermiller

    Graded Lie algebras of Cartan type in characteristic 2, with Bettina Eick

    A note

    Inverse semigroups with rational word problem are finite

    (This material will be included in a forthcoming paper with Markus Pfeiffer)

    PhD thesis and MSc project

    PhD thesis: Groups with poly-context-free word problem, November 2010
    MSc research project: Alternating and Symmetric Quotients of $G^{3,11,42}$, June 2006

    Recent talks

    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.)

    Complete list of talks


    I was involved in teaching the following courses during my time in St Andrews:

    MT1002 Mathematics: 11 lectures, plus two tutorials per week (Sem 1 2014/15).
    MT3600 Fundamentals of Pure Mathematics: 12 lectures, 5 tutorials (Sem 1 2014/15).
    MT2501 Linear Mathematics: assisted with examples classes (Sem 1 2014/15).

    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'.


    Michael Brough is my husband. He makes video-games.
    NBSAN (North British Semigroups and Applications Network)

    Tara Brough
    Last modified 02.11.2015