Personal profile
Research interests
My main interest, and the subject of my current FCT grant project, is automata and languages in algebra, particularly in group and semigroup theory. I study languages arising in algebra, such as word problems, cross-sections (normal forms) and multiplication tables. I also do research on automaton semigroups, primarily from a semigroup constructions perspective.
Other interests: geometric and combinatorial group theory; modular Lie algebras; computational algebra.
Education/Academic qualification
Mathematics, Doctorate, Groups with poly-context-free word problem, University of Warwick
Award Date: 18 Apr 2011
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Collaborations and top research areas from the last five years
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Preserving self-similarity in free products of semigroups
Brough, T. M., Wächter, J. P. & Welker, J., 1 Dec 2025, In: International Journal Of Algebra And Computation. 35, 8, p. 1091-1121 31 p.Research output: Contribution to journal › Article › peer-review
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Determining solubility for finitely generated groups of pl homeomorphisms
Bleak, C., Brough, T. & Hermiller, S., Oct 2021, In: Transactions of the American Mathematical Society. 374, 10, p. 6815-6837 23 p.Research output: Contribution to journal › Article › peer-review
2 Link opens in a new tab Citations (Scopus) -
A language hierarchy of binary relations
Brough, T. & Cain, A. J., Dec 2020, In: Information and Computation. 275, 104607.Research output: Contribution to journal › Article › peer-review
1 Link opens in a new tab Citation (Scopus) -
Two applications of monoid actions to cross-sections
Brough, T., Cain, A. J. & Maltcev, V., 3 May 2020, In: Communications in Algebra. 48, 5, p. 1894-1903 10 p.Research output: Contribution to journal › Article › peer-review
1 Link opens in a new tab Citation (Scopus) -
Context-free word problem semigroups
Brough, T., Cain, A. J. & Pfeiffer, M., 2019, Developments in Language Theory - 23rd International Conference, DLT 2019, Proceedings. Hofman, P. & Skrzypczak, M. (eds.). Cham: Springer, p. 292-305 14 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 11647 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
Open AccessFile7 Link opens in a new tab Citations (Scopus)118 Downloads (Pure)