James East

I am an associate professor at Western Sydney University, where I am a member of
  • the Centre for Research in Mathematics and Data Science and
  • the School of Computer, Data and Mathematical Sciences.
    During 2020--2023 I was an ARC Future Fellow.

    I obtained my PhD in 2006 at the University of Sydney, under the supervision of David Easdown. Here is my thesis:

  • On Monoids Related to Braid Groups and Transformation Semigroups.

    I had postdoctoral fellowships at La Trobe University (2006--2007) and the University of Sydney (2008--2010), before joining Western Sydney University in 2011.

    My main research interest is in algebraic and combinatorial semigroup theory, especially transformation semigroups, diagram monoids/algebras/categories, and braid groups/monoids. Recurring themes in my work include presentations, congruences, (products of) idempotents, sandwich semigroups, combinatorial invariants and more. A publication list can be found below.

    Journal of the Australian Mathematical Society

    I am on the editorial board of the Journal of the AustMS. For submissions, please follow the links from the journal website.

    Communications in Algebra

    I am on the editorial board of Communications in Algebra. For submissions, please follow the links from the journal website.

    Current students/postdocs

    The following people are currently working with me:
  • Chad Clark (PhD student, recently submitted)
  • Matthias Fresacher (PhD student) -- Matthias is also the president (and founder) of the Association of Australian Mathematics Students
  • Azeef Muhammed Parayil Ajmal (postdoctoral fellow)

  • PhD positions available

    If you are interested in doing a PhD (with scholarship), please get in touch.

    Postal address: James East
    School of Computer, Data and Mathematical Sciences
    Western Sydney University
    Locked Bag 1797, Penrith NSW 2751
    Office: Building EN, Room 1.33, Parramatta campus
    Email: J.East@WesternSydney.edu.au
    Phone: +61 2 9685 9108

    Visual mathematics

    I am a big fan of visualisation in mathematics. The following pictures can be found in various papers listed below. Some were produced with assistance from the Semigroups package for GAP.




    Sometimes an equation can be considered art.

  • Un-named Mathematician 1: That's not a proof, it's a picture!
  • Un-named Mathematician 2 (pointing to equations): These are all pictures!

  • equation


    My arXiv and ResearchGate pages have most of the following papers (though arXiv only goes back to about 2011). MathSciNet has almost all of them (but a subscription is required). If you don't have access to something you want, please get in touch.

    In print

    1. On the diameter of semigroups of transformations and partitions.
    2. A groupoid approach to regular *-semigroups.
    3. Presentations for tensor categories.
    4. Minimum degrees of finite rectangular bands, null semigroups, and variants of full transformation semigroups.
    5. Product decompositions of semigroups induced by action pairs.
    6. Congruence lattices of ideals in categories and (partial) semigroups.
    7. Presentations for wreath products involving symmetric inverse monoids and categories.
    8. On the enumeration of integer tetrahedra.
    9. Congruences on infinite partition and partial Brauer monoids.
    10. Properties of congruences of twisted partition monoids and their lattices.
    11. Classification of congruences of twisted partition monoids.
    12. Presentations for P^K.
    13. Generating wreath products of symmetric and alternating groups.
    14. Presentations for Temperley-Lieb algebras.
    15. Lattice paths and submonoids of Z2.
    16. Sandwich semigroups in diagram categories.
    17. Structure of principal one-sided ideals.
    18. Ehresmann theory and partition monoids.
    19. Transformation representations of sandwich semigroups.
    20. Idempotents and one-sided units: Lattice invariants and a semigroup of functors on the category of monoids.
    21. Green's relations and stability for subsemigroups.
    22. Structural aspects of semigroups based on digraphs.
    23. Integer triangles of given perimeter: A new approach via group theory.
    24. The n-matchstick challenge accepted.
    25. Idempotents and one-sided units in infinite partial Brauer monoids.
    26. Enumeration of idempotents in planar diagram monoids.
    27. Integer polygons of given perimeter.
    28. Presentations for singular wreath products.
    29. Presentations for rook partition monoids and algebras and their singular ideals.
    30. Computing finite semigroups.
    31. Congruence lattices of finite diagram monoids.
    32. Sandwich semigroups in locally small categories I: Foundations.
    33. Sandwich semigroups in locally small categories II: Transformations.
    34. Presentations for (singular) partition monoids: a new approach.
    35. Twisted Brauer monoids.
    36. Semigroups of rectangular matrices under a sandwich operation.
    37. Maximal subsemigroups of finite transformation and diagram monoids.
    38. Ranks of ideals in inverse semigroups of difunctional binary relations.
    39. The idempotent-generated subsemigroup of the Kauffman monoid.
    40. Enumerating transformation semigroups.
    41. Infinite dual symmetric inverse monoids.
    42. Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals.
    43. Motzkin monoids and partial Brauer monoids.
    44. On groups generated by involutions of a semigroup.
    45. Idempotent generation in the endomorphism monoid of a uniform partition.
    46. Idempotent rank in the endomorphism monoid of a non-uniform partition.
    47. Enumeration of idempotents in diagram semigroups and algebras.
    48. Maximal subsemigroups of the semigroup of all mappings on an infinite set.
    49. Variants of finite full transformation semigroups.
    50. A symmetrical presentation for the singular part of the symmetric inverse monoid.
    51. Singular braids and partial permutations.
    52. Partition monoids and embeddings in regular *-semigroups.
    53. Infinite partition monoids.
    54. Defining relations for idempotent generators in finite partial transformation semigroups.
    55. Infinity minus infinity.
    56. Defining relations for idempotent generators in finite full transformation semigroups.
    57. The semigroup generated by the idempotents of a partition monoid.
    58. Generation of infinite factorizable inverse monoids.
    59. Generators and relations for partition monoids and algebras.
    60. On the work performed by a transformation semigroup.
    61. On the singular part of the partition monoid.
    62. Braids and order-preserving partial permutations.
    63. A presentation of the singular part of the full transformation semigroup.
    64. Presentations for singular subsemigroups of the partial transformation semigroup.
    65. Embeddings in coset monoids.
    66. On a class of factorizable inverse monoids associated with braid groups.
    67. A presentation of the dual symmetric inverse monoid.
    68. Vines and partial transformations.
    69. Braids and partial permutations.
    70. The factorizable braid monoid.
    71. Factorizable inverse monoids of cosets of subgroups of a group.
    72. A presentation of the singular part of the symmetric inverse monoid.
    73. Birman's conjecture is true for I2(p).
    74. Cellular algebras and inverse semigroups.
    75. Presentations of factorizable inverse monoids.
    76. Braids and factorizable inverse monoids.


    1. Projection algebras and free projection- and idempotent-generated regular *-semigroups.
    2. Congruences of regular variants of finite full transformation semigroups.
    3. Heights of one- and two-sided congruence lattices of semigroups.


    1. Generating the monoid of 2x2 matrices over max-plus and min-plus semirings.
    2. Constructing Embeddings and Isomorphisms of Finite Abstract Semigroups.
    3. Finite diagram semigroups: expanding the computational horizon.