Biography

Studied mathematics at the University of St Andrews, obtaining a PhD in pure mathematics (combinatorial group and semigroup theory) in 2006, under the supervision of Prof Nik Ruškuc. Spent two years as a Research Fellow in the Logic Group at the University of Leeds working with Prof John Truss and Prof Dugald Macpherson on an EPSRC funded project in infinite combinatorics and model theory. Went on to win a personal EPSRC Postdoctoral Fellowship (Project reference: EP/E043194/1) held for two years at the University of St Andrews (2008—2010), where he was the principal investigator leading a project in combinatorial semigroup theory. In 2010 moved to work at the Centre of Algebra of the University of Lisbon where he held a personal five year FCT Ciência 2008 Research Fellowship. In 2013 he was appointed at the University of East Anglia as a Lecturer in Pure Mathematics. He is involved in research in several areas of algebra and combinatorics including topics in: geometric and combinatorial group and semigroup theory, algebraic graph theory, finite and infinite permutation groups, homogeneous structures in the model-theoretic sense, and interactions between these areas via the study of groups and semigroups acting on geometric, algebraic and combinatorial objects. He is currently lecturing the second year Ring Theory course, and the first year course Sets, Numbers and Probability. He is supervising three undergraduate projects, one MMath project, and is co-supervising (with Prof David Evans) a PhD student who is investigating endomorphisms and automorphisms of homogeneous structures.

Website: http://www-history.mcs.st-and.ac.uk/~robertg/

Follow this link for details of current PhD opportunities in Mathematics. But feel free to email me to discuss projects outside these areas and alternative sources of funding.

Career History

  • ·         2006–2008: Research Fellow, School of Mathematics, University of Leeds, UK. Member of the Leeds Logic Group working on the EPSRC funded project “Homogeneous structures, bipartite graphs, and partial orders”.
  • ·         2008–2010: EPSRC Postdoctoral Research Fellow, School of Mathematics and Statistics, University of St Andrews, UK.
  • ·         2010—2013: FCT Ciência 2008 Research Fellow, Centre of Algebra of the University of Lisbon, Portugal.
  • ·         2013—present: Lecturer in Pure Mathematics, University of East Anglia, UK

All Publications

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Gray, R., Kambites, M.

(2017)

Amenability and geometry of semigroups,

in Transactions of the American Mathematical Society

369

pp. 8087-8103

Full Text UEA Repository

(Article)

(Published)


East, J., Gray, R. D.

(2017)

Diagram monoids and Graham–Houghton graphs: Idempotents and generating sets of ideals,

in Journal of Combinatorial Theory, Series A

146

pp. 63–128

Full Text UEA Repository

(Article)

(Published)


Dolinka, I., East, J., Gray, R. D.

(2017)

Motzkin monoids and partial Brauer monoids,

in Journal of Algebra

471

pp. 251–298

Full Text UEA Repository

(Article)

(Published)


Dolinka, I., Gray, R. D., Ruškuc, N.

(2017)

On regularity and the word problem for free idempotent generated semigroups,

in Proceedings of the London Mathematical Society

114

(3)

pp. 401–432

Full Text UEA Repository

(Article)

(Published)


Cain, A. J., Gray, R. D., Malheiro, A.

(2017)

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids,

in Information and Computation

255

(1)

pp. 68-93

Full Text UEA Repository

(Article)

(Published)


Dolinka, I., Gray, R., McPhee, J., Mitchell, J., Quick, M.

(2016)

Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph,

in Mathematical Proceedings of the Cambridge Philosophical Society

160

(03)

pp. 437-462

Full Text UEA Repository

(Article)

(Published)


Craik, S., Gray, R., Kilibarda, V., Mitchell, J., Ruškuc, N.

(2016)

Ends of semigroups,

in Semigroup Forum

93

(2)

pp. 330-346

Full Text UEA Repository

(Article)

(Published)


Cain, A. J., Gray, R., Malheiro, A.

(2015)

Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids,

in Journal of Algebra

423

pp. 37–53

Full Text UEA Repository

(Article)

(Published)


Cain, A. J., Gray, R., Malheiro, A.

(2015)

Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids,

in International Journal of Algebra and Computation

25

(01n02)

article no. 51

Full Text UEA Repository

(Article)

(Published)


Gray, R., Maltcev, V., Mitchell, J., Ruskuc, N.

(2014)

Ideals and finiteness conditions for subsemigroups,

in Glasgow Mathematical Journal

56

(01)

pp. 65-86

Full Text UEA Repository

(Article)

(Published)


Gray, R.

(2014)

The minimal number of generators of a finite semigroup,

in Semigroup Forum

89

(1)

pp. 135-154

Full Text UEA Repository

(Article)

(Published)


Dolinka, I., Gray, R. D.

(2014)

Maximal subgroups of free idempotent generated semigroups over the full linear monoid,

in Transactions of the American Mathematical Society

366

pp. 419-455

Full Text UEA Repository

(Article)

(Published)


Gray, R., Malheiro, A.

(2014)

Homotopy bases and finite derivation type for subgroups of monoids,

in Journal of Algebra

410

pp. 53-84

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(Article)

(Published)


Gray, R., Ruškuc, N.

(2014)

On residual finiteness of monoids, their Schützenberger groups and associated actions,

in Journal of Algebra

407

pp. 21-45

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(Article)

(Published)


Gray, R., Truss, J. K.

(2014)

Countable locally 2-arc-transitive bipartite graphs,

in European Journal of Combinatorics

39

pp. 122-147

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(Article)

(Published)


Gray, R., Kambites, M.

(2014)

A strong geometric hyperbolicity property for directed graphs and monoids,

in Journal of Algebra

420

pp. 373–401

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(Article)

(Published)


Gray, R., Malheiro, A., Pride, S.

(2013)

Homotopy bases and finite derivation type for Schützenberger groups of monoids,

in Journal of Symbolic Computation

50

pp. 50-78

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(Article)

(Published)


Gray, R., Kambites, M.

(2013)

Groups acting on semimetric spaces and quasi-isometries of monoids,

in Transactions of the American Mathematical Society

365

(2)

pp. 555-578

Full Text UEA Repository

(Article)

(Published)


Gray, R., Kambites, M.

(2013)

Quasi-isometry and finite presentations for left cancellative monoids,

in International Journal of Algebra and Computation

23

(5)

pp. 1099

Full Text UEA Repository

(Article)

(Published)


Cain, A., Gray, R., Ruškuc, N.

(2012)

Green index in semigroups: generators, presentations, and automatic structures,

in Semigroup Forum

85

(3)

pp. 448-476

Full Text UEA Repository

(Article)

(Published)


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Key Research Interests

My research interests include: geometric and combinatorial group and semigroup theory, groups acting on graphs, finite and infinite permutation groups, homogeneous structures in the model-theoretic sense, and interactions between these areas via the study of groups and semigroups acting on geometric, algebraic and combinatorial objects.
Research keywords:

Group and semigroup theory

Geometric and combinatorial group theory

Infinite combinatorics 

Permutation groups

Groups acting on graphs

PGR Supervision:

Geometric and combinatorial group and semigroup theory

Homogeneous structures

Presentations and string rewriting systems

Groups acting on graphs


Teaching Interests

Over the course of his ten years of teaching he has been involved in teaching activities ranging from tutoring and lecturing to undergraduates, teaching research level material to postgraduate students, to supporting advanced undergraduate research by giving lectures at summer schools, and supervising undergraduate projects, and PhD students.

Key Responsibilities

  • ·         Organiser of the pure mathematics research seminars, autumn 2013.