James East

I was a Postdoctoral Research Fellow in the School of Mathematics and Statistics at the University of Sydney during 2008-2010. I am still an honorary associate in the School.

I began a position as lecturer in Pure Mathematics at Western Sydney University in 2011. Here is my personal page there -- it will hopefully be updated some time soon.


Current postal address: Dr James East
School of Computing, Engineering and Mathematics
Western Sydney University
Locked Bag 1797, Penrith NSW 2751
Australia
Office: Building EN, Room 1.33, Parramatta campus
Email: J.East@WesternSydney.edu.au
Phone: +61 2 9685 9108
Department Fax: +61 2 9685 9557

Teaching

Here are the last few courses I taught at the University of Sydney:


Research

I am a member of the Algebra Research Group. My main interest is in (algebraic and combinatorial) semigroup theory. The kinds of semigroups and monoids I am particularly interested in are all somehow related to:

My PhD thesis, supervised by David Easdown and entitled ``On Monoids Related to Braid Groups and Transformation Semigroups'', may be found here.


Publications

My arXiv and ResearchGate pages have most papers (arXiv goes back to about 2011).

In print

  1. Structural aspects of semigroups based on digraphs.
  2. Transformation representations of sandwich semigroups.
  3. Green's relations and stability for subsemigroups.
  4. Integer triangles of given perimeter: A new approach via group theory.
  5. Idempotents and one-sided units in infinite partial Brauer monoids.
  6. Enumeration of idempotents in planar diagram monoids.
  7. Integer polygons of given perimeter.
  8. Presentations for singular wreath products.
  9. Presentations for rook partition monoids and algebras and their singular ideals.
  10. Computing finite semigroups.
  11. Congruence lattices of finite diagram monoids.
  12. Sandwich semigroups in locally small categories I: Foundations.
  13. Sandwich semigroups in locally small categories II: Transformations.
  14. Presentations for (singular) partition monoids: a new approach.
  15. Twisted Brauer monoids.
  16. Semigroups of rectangular matrices under a sandwich operation.
  17. Maximal subsemigroups of finite transformation and diagram monoids.
  18. Ranks of ideals in inverse semigroups of difunctional binary relations.
  19. The idempotent-generated subsemigroup of the Kauffman monoid.
  20. Enumerating transformation semigroups.
  21. Infinite dual symmetric inverse monoids.
  22. Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals.
  23. Motzkin monoids and partial Brauer monoids.
  24. On groups generated by involutions of a semigroup.
  25. Idempotent generation in the endomorphism monoid of a uniform partition.
  26. Idempotent rank in the endomorphism monoid of a non-uniform partition.
  27. Enumeration of idempotents in diagram semigroups and algebras.
  28. Maximal subsemigroups of the semigroup of all mappings on an infinite set.
  29. Variants of finite full transformation semigroups.
  30. A symmetrical presentation for the singular part of the symmetric inverse monoid.
  31. Singular braids and partial permutations.
  32. Partition monoids and embeddings in regular *-semigroups.
  33. Infinite partition monoids.
  34. Defining relations for idempotent generators in finite partial transformation semigroups.
  35. Infinity minus infinity.
  36. Defining relations for idempotent generators in finite full transformation semigroups.
  37. The semigroup generated by the idempotents of a partition monoid.
  38. Generation of infinite factorizable inverse monoids.
  39. Generators and relations for partition monoids and algebras.
  40. On the work performed by a transformation semigroup.
  41. On the singular part of the partition monoid.
  42. Braids and order-preserving partial permutations.
  43. A presentation of the singular part of the full transformation semigroup.
  44. Presentations for singular subsemigroups of the partial transformation semigroup.
  45. Embeddings in coset monoids.
  46. On a class of factorizable inverse monoids associated with braid groups.
  47. A presentation of the dual symmetric inverse monoid.
  48. Vines and partial transformations.
  49. Braids and partial permutations.
  50. The factorizable braid monoid.
  51. Factorizable inverse monoids of cosets of subgroups of a group.
  52. A presentation of the singular part of the symmetric inverse monoid.
  53. Birman's conjecture is true for I2(p).
  54. Cellular algebras and inverse semigroups.
  55. Presentations of factorizable inverse monoids.
  56. Braids and factorizable inverse monoids.

Preprints

  1. Idempotents and one-sided units II. Lattice invariants and a semigroup of functors on the category of monoids.
  2. Lattice paths and submonoids of Z2.
  3. Congruences on infinite partition and partial Brauer monoids.
  4. Constructing Embeddings and Isomorphisms of Finite Abstract Semigroups.
  5. Finite diagram semigroups: expanding the computational horizon.
  6. Congruence lattices of ideals in categories and (partial) semigroups.
  7. Generating wreath products of symmetric and alternating groups.
  8. Sandwich semigroups in diagram categories.
  9. Structure of principal one-sided ideals.
  10. Presentations for diagram categories.
  11. Presentations for Temperley-Lieb algebras.
  12. Reflection monoids, partial dual symmetric inverse monoids, and rook partition algebras.
  13. Can God count to infinity?
  14. Methuselah's diary: a response to Ben Waters on the finitude of the past.
  15. Maximal subsemigroups of the symmetric inverse monoid.
  16. Maximal subsemigroups of the dual symmetric inverse monoid.
  17. Dual reflection monoids.
  18. Cellularity of inverse semigroup algebras.
  19. Coset monoids and embeddings.

Conference Talks and Seminars (very out-of-date)


Algebra Seminar

I was the organizer of the Sydney University Algebra Seminar in 2009--2010. For information about upcoming talks, or to be added to the mailing list, please visit the website.