# 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 Building EN, Room 1.33, Parramatta campus J.East@WesternSydney.edu.au +61 2 9685 9108 +61 2 9685 9557

## Teaching

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

• Second Semester 2010 - PHAR1822 - Physical Pharmaceutics and Formulation (Mathematics Component) - old webpage
• First Semester 2010 - PHAR2813 - Therapeutic Principles (Mathematics Component) - old webpage
• Summer School 2010 - MATH2061 - Vector Calculus
• First semester 2009 - MATH1902 - Linear Algebra (Advanced)
• Summer School 2009 - MATH2061/2067 - Vector Calculus
• Second Semester 2008 - MATH2968 - Algebra (Advanced)

## 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:

• diagram algebras and monoids;
• transformation semigroups;
• braid groups and monoids;
• Coxeter groups and Artin monoids/groups.

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. Congruence lattices of finite diagram monoids.
• James East, James Mitchell, Nik Ruškuc, Michael Torpey.
2. Transformation representations of sandwich semigroups.
• James East.
• Exp. Math. to appear.
3. Presentations for rook partition monoids and algebras and their singular ideals.
• James East.
• J. Algebra Appl. to appear.
4. Sandwich semigroups in locally small categories I: Foundations.
• Algebra Universalis, to appear.
5. Sandwich semigroups in locally small categories II: Transformations.
• Algebra Universalis, to appear.
6. Computing finite semigroups.
• James East, Attila Egri-Nagy, James Mitchell, Yann Péresse.
• J. Symbolic Comput, to appear.
7. Presentations for (singular) partition monoids: a new approach.
• James East.
• Math. Proc. Cambridge Philos. Soc., to appear.
8. Twisted Brauer monoids.
• Proc. Roy. Soc. Edinburgh Sect. A, to appear.
9. Semigroups of rectangular matrices under a sandwich operation.
• Semigroup Forum, 96 (2018), no. 2, 253--300.
10. Maximal subsemigroups of finite transformation and diagram monoids.
• James East, Jitender Kumar, James D. Mitchell, Wilf A. Wilson.
• J. Algebra, 504 (2018), 176--216.
11. Ranks of ideals in inverse semigroups of difunctional binary relations.
• James East, Alexei Vernitski.
• Semigroup Forum, 96 (2018), 21--30.
12. The idempotent-generated subsemigroup of the Kauffman monoid.
• Glasg. Math. J., 59 (2017), no. 3, 673--683.
13. Enumerating transformation semigroups.
• James East, Attila Egri-Nagy, James Mitchell
• Semigroup Forum, 95 (2017), 109--125.
14. Infinite dual symmetric inverse monoids.
• James East.
• Period. Math. Hungar., 75 (2017), 273--285.
15. Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals.
• James East, Robert Gray.
• J. Combin. Theory Ser. A, 146 (2017), 63--128.
16. Motzkin monoids and partial Brauer monoids.
• Igor Dolinka, James East, Robert Gray.
• J. Algebra, 471 (2017), 251–298.
17. On groups generated by involutions of a semigroup.
• James East, Thomas Nordahl.
• J. Algebra, 445 (2016), 136--162.
18. Idempotent generation in the endomorphism monoid of a uniform partition.
• Comm. Algebra, 44 (2016), no. 12, 5179--5198.
19. Idempotent rank in the endomorphism monoid of a non-uniform partition.
• Igor Dolinka, James East, James Mitchell.
• Bull. Aust. Math. Soc., 93 (2016), no. 1, 73--91.
20. Enumeration of idempotents in diagram semigroups and algebras.
• Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin.
• J. Combin. Theory Ser. A., 131 (2015), 119--152.
21. Maximal subsemigroups of the semigroup of all mappings on an infinite set.
• James East, James Mitchell, Yann Péresse.
• Trans. Amer. Math. Soc., 367 (2015), no. 3, 1911--1944.
22. Variants of finite full transformation semigroups.
• Internat. J. Algebra Comput., 25 (2015), no. 8, 1187--1222.
23. A symmetrical presentation for the singular part of the symmetric inverse monoid.
• James East.
• Algebra Universalis, 74 (2015), no. 3-4, 207–228.
24. Singular braids and partial permutations.
• James East.
• Acta Sci. Math. (Szeged), 81 (2015), 55--77.
25. Partition monoids and embeddings in regular *-semigroups.
• James East.
• Period. Math. Hungar., 69 (2014), no. 2, 211--221.
26. Infinite partition monoids.
• James East.
• Internat. J. Algebra Comput. 24 (2014), no. 4, 429--460.
27. Defining relations for idempotent generators in finite partial transformation semigroups.
• James East.
• Semigroup Forum 89 (2014), no. 1, 72--76.
28. Infinity minus infinity.
• James East.
• Faith and Philosophy 30 (2013), no. 4, 429--433.
29. Defining relations for idempotent generators in finite full transformation semigroups.
• James East.
• Semigroup Forum 86 (2013), no. 3, 451–485.
30. The semigroup generated by the idempotents of a partition monoid.
• James East, Des FitzGerald.
• J. Algebra 372 (2012), 108--133.
31. Generation of infinite factorizable inverse monoids.
• James East.
• Semigroup Forum 84 (2012), no.2, 267--283.
32. Generators and relations for partition monoids and algebras.
• James East.
• J. Algebra 339 (2011), 1--26.
33. On the work performed by a transformation semigroup.
• James East, Peter McNamara.
• Australas. J. Combin. 49 (2011), 95--109.
34. On the singular part of the partition monoid.
• James East.
• Internat. J. Algebra Comput. 21 (2011), no. 1-2, 147--178.
35. Braids and order-preserving partial permutations.
• James East.
• J. Knot Theory Ramifications 19 (2010), no. 8, 1025--1049.
36. A presentation of the singular part of the full transformation semigroup.
• James East.
• Semigroup Forum. 20 (2010), no. 2, 357--379.
37. Presentations for singular subsemigroups of the partial transformation semigroup.
• James East.
• Internat. J. Algebra Comput. 20 (2010), no. 1, 1--25.
38. Embeddings in coset monoids.
• James East.
• J. Aust. Math. Soc. 85 (2008), no. 1, 75--80.
39. On a class of factorizable inverse monoids associated with braid groups.
• James East.
• Comm. Algebra 36 (2008), no. 8, 3155--3190.
40. A presentation of the dual symmetric inverse monoid.
• David Easdown, James East, Des FitzGerald.
• Internat. J. Algebra Comput. 18 (2008), no. 2, 357--374.
41. Vines and partial transformations.
• James East.
• Adv. Math. 216 (2007), no. 2, 787--810.
42. Braids and partial permutations.
• James East.
• Adv. Math. 213 (2007), no. 1, 440--461.
43. The factorizable braid monoid.
• James East.
• Proc. Edinb. Math. Soc. (2) 49 (2006), no. 3, 609--636.
44. Factorizable inverse monoids of cosets of subgroups of a group.
• James East.
• Comm. Algebra 34 (2006), no. 7, 2659--2665.
45. A presentation of the singular part of the symmetric inverse monoid.
• James East.
• Comm. Algebra 34 (2006), no. 5, 1671--1689.
46. Birman's conjecture is true for I2(p).
• James East.
• J. Knot Theory Ramifications 15 (2006), no. 2, 167--177.
47. Cellular algebras and inverse semigroups.
• James East.
• J. Algebra 296 (2006), no. 2, 505--519.
48. Presentations of factorizable inverse monoids.
• David Easdown, James East, Des FitzGerald.
• Acta Sci. Math. (Szeged) 71 (2005), no. 3-4, 509--520.
49. Braids and factorizable inverse monoids.
• David Easdown, James East, Des FitzGerald.
• Semigroups and languages, 86--105, World Sci. Publ., River Edge, NJ, 2004.

### Preprints

1. Idempotents and one-sided units in infinite partial Brauer monoids.
• James East.
• Preprint. 2017.
2. Integer polygons of given perimeter.
• James East, Ron Niles.
• Preprint. 2017.
3. On transformation semigroups based on digraphs.
• James East, Maximilien Gadouleau, James Mitchell.
• Preprint. 2017.
4. Presentations for singular wreath products.
• Preprint. 2016.
5. Constructing Embeddings and Isomorphisms of Finite Abstract Semigroups.
• James East, Attila Egri-Nagy, James Mitchell, Andrew Francis.
• Preprint. 2016.
6. Idempotent statistics of the Motzkin and Jones monoids.
• Igor Dolinka, James East, Athanasios Evangelou, Des FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin.
• Preprint. 2015.
7. Finite diagram semigroups: expanding the computational horizon.
• James East, Attila Egri-Nagy, James Mitchell, Andrew Francis.
• Preprint. 2015.
8. Congruences of infinite partition and partial Brauer monoids
• James East, Nik Ruškuc.
• In preparation.
9. Can God count to infinity?
• James East.
• In preparation.
10. Methuselah's diary: a response to Ben Waters on the finitude of the past.
• James East.
• In preparation.
11. Diagram categories and sandwich semigroups.
• Ivana Ðurđev, Igor Dolinka, James East.
• In preparation.
12. Maximal subsemigroups of the symmetric inverse monoid.
• James East, James Mitchell, Yann Péresse.
• In preparation.
13. Maximal subsemigroups of the dual symmetric inverse monoid.
• James East, James Mitchell, Yann Péresse.
• In preparation.
14. Dual reflection monoids.
• James East.
• In preparation.
15. Cellularity of inverse semigroup algebras.
• James East.
• Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear?
16. Coset monoids and embeddings.
• James East.
• Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear?

## 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.