Research
PDFs of all papers can be obtained directly from me


2021

80. A generalization of higher rank graphs, with A. Vdovina, Bull. Austral. Math. Soc, appeared online 26 July 2021.

79. Morita equivalence of pseudogroups, with P. Resende, Journal of Algebra 586, 718--755.

78. The polycyclic inverse monoids and the Thompson groups revisited, in (P. G. Romeo, A. R. Rajan eds) Semigroups, categories and partial algebras ICSAA 2019, Springer, Proc. in Maths and Stats, volume 345.

77. On Ehresmann semigroups, Semigroup Forum, published online June.

76. The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations, with Alina Vdovina,  Journal of Noncommutative Geometry  15, 279--304.

2020

75. Higher dimensional generalizations of the Thompson groups, with Alina Vdovina, Advances in Mathematics 369, 107191.

74. The Booleanization of an inverse semigroup, Semigroup Forum 100 (2020), 283--314.

73. Recent developments in inverse semigroup theory, Semigroup Forum 100 (2020), 103--118.

2019

72. A Tribute to John B. Fountain, with V. A. R. Gould, Semigroup Forum 99 (2019), 1--8.

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.

2013

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, 234--256.

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 Mahony-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, Cahiers de topologie et geometrie differentielle categoriques 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. Ordered groupoids and left cancellative categories, Semigroup Forum 68, 458--476.

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

34. Universal groups for point-sets and tilings, with J. Kellendonk Journal of 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,  Journal of Algebra 202, 276--294.

21. The Moebius inverse monoid,  Journal 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: Section A Mathematics, 127 , 127--143.

1996

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

17. A class of actions of inverse semigroups,  Journal 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,  Journal 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: Section A Mathematics, 107, 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.