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. With Attila Egri-Nagy, James Mitchell and Yann Péresse: Computing finite semigroups. J. Symbolic Comput, to appear.
  2. Presentations for (singular) partition monoids: a new approach. Math. Proc. Cambridge Philos. Soc., to appear.
  3. With Igor Dolinka: Twisted Brauer monoids. Proc. Roy. Soc. Edinburgh Sect. A, to appear.
  4. With Igor Dolinka: The idempotent-generated subsemigroup of the Kauffman monoid. Glasg. Math. J., to appear.
  5. With Igor Dolinka: Semigroups of rectangular matrices under a sandwich operation. Semigroup Forum, to appear.
  6. With Attila Egri-Nagy and James Mitchell: Enumerating transformation semigroups. Semigroup Forum, to appear.
  7. With Alexei Vernitski: Ranks of ideals in inverse semigroups of difunctional binary relations. Semigroup Forum, to appear.
  8. Infinite dual symmetric inverse monoids. Period. Math. Hungar., to appear.
  9. With Robert Gray: Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals. J. Combin. Theory Ser. A, 146 (2017), 63--128.
  10. With Igor Dolinka and Robert Gray: Motzkin monoids and partial Brauer monoids. J. Algebra, 471 (2017), 251–298.
  11. With Thomas Nordahl: On groups generated by involutions of a semigroup. J. Algebra, 445 (2016), 136--162.
  12. With Igor Dolinka: Idempotent generation in the endomorphism monoid of a uniform partition. Comm. Algebra, 44 (2016), no. 12, 5179--5198.
  13. With Igor Dolinka and James Mitchell: Idempotent rank in the endomorphism monoid of a non-uniform partition. Bull. Aust. Math. Soc., 93 (2016), no. 1, 73--91.
  14. With Igor Dolinka, Athanasios Evangelou, Des FitzGerald, Nicholas Ham, James Hyde and Nicholas Loughlin: Enumeration of idempotents in diagram semigroups and algebras. J. Combin. Theory Ser. A., 131 (2015), 119--152.
  15. With James Mitchell and Yann Péresse: Maximal subsemigroups of the semigroup of all mappings on an infinite set. Trans. Amer. Math. Soc., 367 (2015), no. 3, 1911--1944.
  16. With Igor Dolinka: Variants of finite full transformation semigroups. Internat. J. Algebra Comput., 25 (2015), no. 8, 1187--1222.
  17. A symmetrical presentation for the singular part of the symmetric inverse monoid. Algebra Universalis, 74 (2015), no. 3-4, 207–228.
  18. Singular braids and partial permutations. Acta Sci. Math. (Szeged), 81 (2015), 55--77.
  19. Partition monoids and embeddings in regular *-semigroups. Period. Math. Hungar., 69 (2014), no. 2, 211--221.
  20. Infinite partition monoids. Internat. J. Algebra Comput. 24 (2014), no. 4, 429--460.
  21. Defining relations for idempotent generators in finite partial transformation semigroups. Semigroup Forum 89 (2014), no. 1, 72--76.
  22. Infinity minus infinity. Faith and Philosophy 30 (2013), no. 4, 429--433.
  23. Defining relations for idempotent generators in finite full transformation semigroups. Semigroup Forum 86 (2013), no. 3, 451–485.
  24. With Des FitzGerald: The semigroup generated by the idempotents of a partition monoid. J. Algebra 372 (2012), 108--133.
  25. Generation of infinite factorizable inverse monoids. Semigroup Forum 84 (2012), no.2, 267--283.
  26. Generators and relations for partition monoids and algebras. J. Algebra 339 (2011), 1--26.
  27. With Peter McNamara: On the work performed by a transformation semigroup. Australas. J. Combin. 49 (2011), 95--109.
  28. On the singular part of the partition monoid. Internat. J. Algebra Comput. 21 (2011), no. 1-2, 147--178.
  29. Braids and order-preserving partial permutations. J. Knot Theory Ramifications 19 (2010), no. 8, 1025--1049.
  30. A presentation of the singular part of the full transformation semigroup. Semigroup Forum. 20 (2010), no. 2, 357--379.
  31. Presentations for singular subsemigroups of the partial transformation semigroup. Internat. J. Algebra Comput. 20 (2010), no. 1, 1--25.
  32. Embeddings in coset monoids. J. Aust. Math. Soc. 85 (2008), no. 1, 75--80.
  33. On a class of factorizable inverse monoids associated with braid groups. Comm. Algebra 36 (2008), no. 8, 3155--3190.
  34. With David Easdown and Des FitzGerald: A presentation of the dual symmetric inverse monoid. Internat. J. Algebra Comput. 18 (2008), no. 2, 357--374.
  35. Vines and partial transformations. Adv. Math. 216 (2007), no. 2, 787--810.
  36. Braids and partial permutations. Adv. Math. 213 (2007), no. 1, 440--461.
  37. The factorizable braid monoid. Proc. Edinb. Math. Soc. (2) 49 (2006), no. 3, 609--636.
  38. Factorizable inverse monoids of cosets of subgroups of a group. Comm. Algebra 34 (2006), no. 7, 2659--2665.
  39. A presentation of the singular part of the symmetric inverse monoid. Comm. Algebra 34 (2006), no. 5, 1671--1689.
  40. Birman's conjecture is true for I2(p). J. Knot Theory Ramifications 15 (2006), no. 2, 167--177.
  41. Cellular algebras and inverse semigroups. J. Algebra 296 (2006), no. 2, 505--519.
  42. With David Easdown and Des FitzGerald: Presentations of factorizable inverse monoids. Acta Sci. Math. (Szeged) 71 (2005), no. 3-4, 509--520.
  43. With David Easdown and Des FitzGerald: Braids and factorizable inverse monoids. Semigroups and languages, 86--105, World Sci. Publ., River Edge, NJ, 2004.

Preprints

  1. With Maximilien Gadouleau and James Mitchell: On transformation semigroups based on digraphs. Preprint. 2017.
  2. With Ying-Ying Feng, Asawer Al-Aadhami, Igor Dolinka and Victoria Gould: Presentations for singular wreath products. Preprint. 2016.
  3. Presentations for rook partition monoids and algebras and their singular ideals. Preprint. 2016.
  4. With Attila Egri-Nagy, James Mitchell and Andrew Francis: Constructing Embeddings and Isomorphisms of Finite Abstract Semigroups. Preprint. 2016.
  5. With Igor Dolinka, Athanasios Evangelou, Des FitzGerald, Nicholas Ham, James Hyde and Nicholas Loughlin: Idempotent statistics of the Motzkin and Jones monoids. Preprint. 2015.
  6. With Attila Egri-Nagy, James Mitchell and Andrew Francis: Finite diagram semigroups: expanding the computational horizon. Preprint. 2015.
  7. With Igor Dolinka, Ivana Ðurđev, Preeyanuch Honyam, Kritsada Sangkanan, Jintana Sanwong, Worachead Sommanee: Sandwich semigroups in locally small categories. In preparation.
  8. With James Mitchell, Nik Ruškuc and Michael Torpey: Congruence lattices of finite diagram monoids. In preparation.
  9. With Jitinder Kumar, James Mitchell and Wilf Wilson: Maximal subsemigroups of finite semigroups. In preparation.
  10. Can God count to infinity? In preparation.
  11. Methuselah's diary: a response to Ben Waters on the finitude of the past. In preparation.
  12. With Igor Dolinka: Diagram categories and sandwich semigroups. In preparation.
  13. With James Mitchell and Yann Péresse: Maximal subsemigroups of the symmetric inverse monoid. In preparation.
  14. With James Mitchell and Yann Péresse: Maximal subsemigroups of the dual symmetric inverse monoid. In preparation.
  15. Dual reflection monoids I--III. Three papers, in preparation.
  16. Cellularity of inverse semigroup algebras. Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear?
  17. Coset monoids and embeddings. Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear?

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.