Research
PDFs of all papers can be obtained directly from me


2019

73. Recent developments in inverse semigroup theory, Semigroup Forum http://doi.org/10.1007/s00233-019-10067-4.

72. A Tribute to John B. Fountain, with V. A. R. Gould, Semigroup Forum https://doi.org/10.1007/s00233-019-10033-0.

2017

71. Tarski monoids: Matui's spatial realization theorem,  Semigroup Forum. 95 (2017), 379--404.

70. Levi categories and graphs of groups, with A. Wallis, TAC 32 (2017), 780--802.

69.  A perspective on non-commutative frame theory, with G. Kudryavtseva,  Adv. Math. 311 (2017), 378--468.

68.  AF inverse monoids and the structure of countable MV-algebras, with P. Scott, J. P. A. A. 221 (2017), 45--74.

2016

67.  Subgroups of the group of homeomorphisms of the Cantor space and a duality between a class of inverse monoids and a class of Hausdorff etale groupoids, J. Alg. 462 (2016), 77--114.

66. Invariant means on Boolean inverse monoids, with G. Kudryavtseva, D. H. Lenz, P. Resende, Semigroup Forum 92 (2016), 77--101.

65. Boolean sets, skew Boolean algebras, and a non-commutative Stone duality, with G. Kudryavtseva,  Alg. Univ. 75 (2016), 1--19.
 
2015

64. A correspondence between a class of monoids and self-similar group actions II, with A. Wallis, IJAC 25 (2015), 633--668.

63. The classifying space of an inverse semigroup, with G. Kudryavtseva, Periodica Math. Hung. 70 (2015), 122--129.

2014

62. David Rees 1918--2013, with L. O'Carroll, S. Rees, Semigroup Forum 88 (2014), 513--522.

61. Graph inverse semigroups: their characterization and completion, with D. Jones, Journal of Algebra 409 (2014), 444--473.

60. The structure of generalized inverse semigroups, with G. Kudryavtseva, Semigroup Forum 89 (2014), 199--216.

59. The etale groupoid of an inverse semigroup as a groupoid of filters,  with S. W. Margolis and B. Steinberg,  J. Aust. Math. Soc. 94 (2014), 234--256.

2013


58. Pseudogroups and their etale groupoids, with D. Lenz, Advances in Maths 244 (2013), 117--170.

57. Morita equivalence of inverse semigroups, with B. Afara, Periodica math Hung. 66 (2013), 119--130.

2012

56. Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras, IJAC 22, 1250058 (2012), 47pp.

55. Morita equivalence of semigroups with locally commuting idempotents, with B. Afara, Communications in Algebra 40, 1982--1996.

54. Strong representation of the polycyclic inverse monoids: cycles and atoms, with D. Jones,  Periodica Math. Hung. 64, 53-87.

2011

53. Characterizations of Morita equivalent inverse semigroups, with J. Funk and B. Steinberg,  J. Pure Appl. Algebra 215, 2262-2279.

52. Morita theory for semigroups with local units,  J. Pure Appl. Algebra 215, 455--470.

51. Generalized heaps, inverse semigroups and Morita equivalence, Algebra Universalis 66 (2011), 317--330.

2010


50. Compactable semilattices, Semigroup Forum 81, 187--199.

49. A non-commutative generalization of Stone duality,  J. Austral. Math. Soc. 88, 385--404. This paper won the Mahoney-Neumann-Room Prize of the Australian Mathematical Society 2017.

2009

48. Primitive partial permutation representations of the polycyclic monoids and branching function systems, Periodica Math. Hung. 52, 189--207.

2008

47. Semigroups related to subshifts of graphs, Mathematics Studies of the Estonian Mathematical Society 3, (edited by V. Laan, S. Bulman-Fleming, R. Kaschek), 92--107.

46. A correspondence between a class of monoids and self-similar group actions I, Semigroup Forum 76, 489-517.

2007

45. The polycyclic monoids P_{n} and the Thompson groups V_{n,1}, Communications in algebra 35, 4068--4087.

44. A class of subgroups of Thompson's group V, Semigroup Forum 75, 241--252.

43. In McAlister's footsteps: a random ramble around the P-theorem, with S. Margolis  Proceedings of the International Conference on
Semigroups and Languages, Lisbon 2005,
(eds Andre, Fernandes, Branco, Gomes, Fountain and Meakin) World Scientific, 2007, 145--163.

42. Orthogonal completions of the polycyclic monoids, Communications in Algebra 35,  1651--1660.

2006

41. A correspondence between balanced varieties and inverse monoids, Inter. J. Alg. and Computation 16, 887--924.

40. Expansions of inverse semigroups, with S. Margolis and B. Steinberg Journal of the Australian Mathematical Society 80, 205--228.

2005

39. Constructing ordered groupoids, Cah. Topol. Geom. Differ. Categ. 46, 123--138.

2004

38. Partial actions of groups, with J. Kellendonk,  International Journal of Algebra and Computation 14, 87--114.

37. Ordered groupoids and etendues, with B. Steinberg Cahiers de topologie et geometrie differentielle categoriques XLV, 82--108. 

36. One dimensional tiling semigroups, Semigroup Forum 68, 159--176.

35. Ordered groupoids and left cancellative categories, Semigroup Forum 68, 458--476.

34. Universal groups for point-sets and tilings, with J. Kellendonk J. Algebra 276, 462--492.

2002

33. E*-unitary inverse semigroups, in Semigroups, algorithms, automata and languages (eds G M S Gomes, J-E Pin, P V Silva) World Scientific, 195--214.

32. The homotopy theory of inverse semigroups, with J. Matthews and T. Porter International Journal of Algebra and Computation 12, 755--790.

2001

31. Rees matrix covers for a class of semigroups with locally commuting idempotents, with T. Khan Proc. Edinburgh Math. Soc. 44, 173--186.

30. Variants of regular semigroups, with T. Khan Semigroup Forum 62, 358--374.

2000

29. A characterisation of a class of semigroups with locally commuting idempotents, with T. Khan  Periodica Mathematica Hungarica 40, 85--107.

28. Tiling semigroups, with J. Kellendonk  Journal of Algebra 224, 140--150.

27. Enlargements and coverings by Rees matrix semigroups, with L. Marki Monatshefte fuer Mathematik 129, 191--195.

26. Rees matrix semigroups over semigroupoids and the structure of a class of abundant semigroups, Acta Scientiarum Mathematicarum 66, 517--540.

1999

25. An application of groupoids of fractions to inverse semigroups, with H. James Periodica Mathematica Hungarica 38 , 43--54.

24. The structure of 0-E-unitary inverse semigroups I: the monoid case,  Proc. Edinburgh Math. Soc. 42, 497--520.

23. Constructing inverse semigroups from category actions,  J. of Pure and Applied Algebra 137, 57--101.

1998

22. McAlister semigroups,  J. of Algebra 202, 276--294.

21. The Moebius inverse monoid,  J. of Algebra 200, 428--438.

20. An application of polycyclic monoids to rings,  with P. Hines Semigroup Forum 56, 146--149.

1997

19. Unit regular monoids,  with J. B. Hickey Proc. Royal Soc. Edinburgh 127A , 127--144.

1996

18. Enlargements of regular semigroups,  Proc. Edinburgh Math. Soc. 39, 425--460.

17. A class of actions of inverse semigroups,  J. of Algebra 179, 570--598.

1994

16. Almost factorisable inverse semigroups,  Glasgow Mathematical J. 36, 97--111.

15. Extending partial isomorphisms and McAlister's covering theorem ,  Semigroup Forum 48 , 18--27.

1993

14. A note on a paper of Joubert,  Semigroup Forum 47, 389--392.

13. Coverings and embeddings of inverse semigroups,  Proc. Edinburgh Math. Soc. 36, 399--419.

12. Congruences on ordered groupoids,  Semigroup Forum 47, 150--167.

11. An equivalence theorem for inverse semigroups,  Semigroup Forum 47, 7--14.

1992

10. The geometric theory of inverse semigroups II:  E-unitary covers of inverse semigroups,  J. Pure and Applied Algebra 83, 121--139.  

1991

9. Semigroups and ordered categories I: the reduced case,  J. of Algebra 141, 422--462.

1990

8. The geometric theory of inverse semigroups I: $E$-unitary inverse semigroups,  J. Pure and Applied Algebra 67, 151--177.

7. Rees matrix semigroups, Proc. Edinburgh Math. Soc. 33, 23--37.

1989

6. An order theoretic characterisation of  locally orthodox semigroups,  Semigroup Forum 39, 113--116.

1987

5. Rees matrix covers for a class of abundant semigroups,  Proc. Royal Soc. Edinburgh 107A, 109--120.

4. Abundant  Rees matrix semigroups,  J. Australian Math. Soc.  (Series~A)  42, 132--142.

3. The natural partial order on an abundant semigroup,  Proc. Edinburgh Math. Soc. 30, 169--186.

1986

2. The structure of type A semigroups, Quart. J. Maths. 37, 279--298.

1985

1. The translational hull of an adequate semigroup, with J. B. Fountain Semigroup Forum 32, 79--86.