Tara Brough

Research Fellow in Algebra


Tel.: (+44) (0) 1334 463754
Office: Room 217
Email: t.brough[at]st-andrews.ac.uk

Postal address:

School of Mathematics and Statistics
Mathematical Institute
North Haugh
St Andrews, Fife KY16 9SS


My main research interests are:
  • 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)
    (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, online (2014)

    Permutations of context-free and indexed languages, with Laura Ciobanu and Murray Elder
    Submitted (Preprint)

    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

    Multiplication tables, intersections of context-free languages, and free products, Algebra-Geometry Seminar, Newcastle University (UK), November 2014.
    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.

    Complete list of talks


    This semester I taught half each of the following courses:

    MT1002 Mathematics
    MT3600 Fundamentals of Pure Mathematics

    I also assisted with examples classes for MT2501 Linear Mathematics.

    I have previously been involved in teaching the following courses at St Andrews:

    MT2001 Mathematics (linear algebra and calculus): tutorials, examples classes and computer lab sessions (2014).
    MT5823 Semigroups: 4 lectures, 4 tutorials, and helping students with their projects (2014).
    MT5824 Topics in Groups: 3 lectures (2013).
    MT4003 Groups: 6 lectures and all tutorials (2012).

    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 20.12.2014