# Doctor James East

## Senior Lecturer - Pure Mathematics,

Mathematics

## Biography

I obtained my PhD in pure mathematics from the University of Sydney, where I also did my BSc (Adv Math), gaining first class honours and the university medal. Since then, I held postdoctoral research positions at La Trobe University and the University of Sydney, before beginning a lecturing position in the School of Computing and Mathematics at the University of Western Sydney in 2011.

My research comes under the broad heading of abstract algebra, but I am particularly interested in braid groups, reflection groups and semigroup theory, and their many areas of intersection. My recent focus has been on transformation semigroups (semigroups that somehow generalize the well-known symmetric groups), and related objects including partition monoids and algebras. My main avenue for studying these structures has been to utilise (and find) presentations in terms of generators and relations.

Outside of mathematical research, I enjoy cricket, Rubiks puzzles, and a nice scotch.

*This information has been contributed by Doctor East.*

### Qualifications

- PhD University of Sydney

### Interests

- Algebra
- Braid Groups
- Pure Mathematics
- Reflection Groups
- Semigroup Theory

### Organisational Unit (School / Division)

- Mathematics

## Contact

Email: | J.East@westernsydney.edu.au |
---|---|

Phone: | (02) 9685 9108 |

Mobile: | |

Location: | EN.1.33 Parramatta |

Website: |

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## Publications

### Chapters in Books

- Easdown, D., East, J. and FitzGerald, D. (2004), 'Braids and factorizable inverse monoids',
*Proceedings of a Workshop: Semigroups and Languages*, World Scientific 9812389172.

### Journal Articles

- Dolinka, I. and East, J. (2018), 'Semigroups of rectangular matrices under a sandwich operation',
*Semigroup Forum*, vol 96, no 2 , pp 253 - 300. - East, J. (2018), 'Presentations for (singular) partition monoids : a new approach',
*Mathematical Proceedings of the Cambridge Philosophical Society*, vol 165, no 3 , pp 549 - 562. - East, J., Kumar, J., Mitchell, J. and Wilson, W. (2018), 'Maximal subsemigroups of finite transformation and diagram monoids',
*Journal of Algebra*, vol 504 , pp 176 - 216. - East, J. and Vernitski, A. (2018), 'Ranks of ideals in inverse semigroups of difunctional binary relations',
*Semigroup Forum*, vol 96, no 1 , pp 21 - 30. - Dolinka, I. and East, J. (2018), 'Twisted Brauer monoids',
*Proceedings of the Royal Society of Edinburgh. Section A: Mathematics*, vol 148, no 4 , pp 731 - 750. - East, J., Mitchell, J., Ruskuc, N. and Torpey, M. (2018), 'Congruence lattices of finite diagram monoids',
*Advances in Mathematics*, vol 333 , pp 931 - 1003. - East, J. (2018), '[In Press] Transformation representations of sandwich semigroups',
*Experimental Mathematics*, . - Dolinka, I., East, J. and Gray, R. (2017), 'Motzkin monoids and partial Brauer monoids',
*Journal of Algebra*, vol 471 , pp 251 - 298. - East, J. and Gray, R. (2017), 'Diagram monoids and Graham-Houghton graphs : idempotents and generating sets of ideals',
*Journal of Combinatorial Theory, Series A*, vol 146 , pp 63 - 128. - Dolinka, I. and East, J. (2017), 'The idempotent-generated subsemigroup of the Kauffman monoid',
*Glasgow Mathematical Journal*, vol 59, no 3 , pp 673 - 683. - East, J., Egri-Nagy, A. and Mitchell, J. (2017), 'Enumerating transformation semigroups',
*Semigroup Forum*, vol 95, no 1 , pp 109 - 125. - East, J. (2017), 'Infinite dual symmetric inverse monoids',
*Periodica Mathematica Hungarica*, vol 75, no 2 , pp 273 - 285. - East, J. and Nordahl, T. (2016), 'On groups generated by involutions of a semigroup',
*Journal of Algebra*, vol 445 , pp 136 - 162. - Dolinka, I., East, J. and Mitchell, J. (2016), 'Idempotent rank in the endomorphism monoid of a nonuniform partition',
*Bulletin of the Australian Mathematical Society*, vol 93, no 1 , pp 73 - 91. - Dolinka, I. and East, J. (2016), 'Idempotent generation in the endomorphism monoid of a uniform partition',
*Communications in Algebra*, vol 44, no 12 , pp 5179 - 5198. - East, J., Mitchell, J. and Peresse, Y. (2015), 'Maximal subsemigroups of the semigroup of all mappings on an infinite set',
*Transactions of the American Mathematical Society*, vol 367, no 3 , pp 1911 - 1944. - Dolinka, I., East, J., Evangelou, A., FitzGerald, D., Ham, N., Hyde, J. and Loughlin, N. (2015), 'Enumeration of idempotents in diagram semigroups and algebras',
*Journal of Combinatorial Theory. Series A*, vol 131, no 4 , pp 119 - 152. - East, J. (2015), 'A symmetrical presentation for the singular part of the symmetric inverse monoid',
*Algebra Universalis*, vol 74, no 3 , pp 207 - 228. - Dolinka, I. and East, J. (2015), 'Variants of finite full transformation semigroups',
*International Journal of Algebra and Computation*, vol 25, no 8 , pp 1187 - 1222. - East, J. (2015), 'Singular braids and partial permutations',
*Acta Scientiarum Mathematicarum*, vol 81, no 1-2 , pp 55 - 77. - East, J. (2014), 'Infinite partition monoids',
*International Journal of Algebra and Computation*, vol 24, no 4 , pp 429 - 460. - East, J. (2014), 'Defining relations for idempotent generators in finite partial transformation semigroups',
*Semigroup Forum*, vol 89, no 1 , pp 72 - 76. - East, J. (2014), 'Partition monoids and embeddings in 2-generator regular *-semigroups',
*Periodica Mathematica Hungarica*, vol 69, no 2 , pp 211 - 221. - East, J. (2013), 'Defining relations for idempotent generators in finite full transformation semigroups',
*Semigroup Forum*, . - East, J. (2013), 'Infinity minus infinity',
*Faith and Philosophy*, vol 30, no 4 , pp 429 - 433. - East, J. and FitzGerald, D. (2012), 'The semigroup generated by the idempotents of a partition monoid',
*Journal of Algebra*, vol 372 , pp 108 - 133. - East, J. (2012), 'Generation of infinite factorizable inverse monoids',
*Semigroup Forum*, vol 84, no 2 , pp 267 - 283. - East, J. and Mcnamara, P. (2011), 'On the Work Performed by a Transformation Semigroup',
*Australasian Journal of Combinatorics*, vol 49 , pp 95 - 109. - East, J. (2011), 'On the singular part of the partition monoid',
*International Journal of Algebra and Computation*, vol 21, no 40940 , pp 147 - 178. - East, J. (2011), 'Generators and relations for partition monoids and algebras',
*Journal of Algebra*, vol 339, no 1 , pp 1 - 26. - East, J. (2010), 'Presentations for singular subsemigroups of the partial transformation semigroup',
*International Journal of Algebra and Computation*, vol 20, no 1 , pp 1 - 25. - East, J. (2010), 'Braids and order-preserving partial permutations',
*Journal of Knot Theory and its Ramifications*, vol 19, no 8 , pp 1025 - 1049. - East, J. (2010), 'A presentation for the singular part of the full transformation semigroup',
*Semigroup Forum*, vol 81, no 2 , pp 357 - 379. - East, J. (2008), 'On a class of factorizable inverse monoids associated with braid groups',
*Communications in Algebra*, vol 36, no 8 , pp 3155 - 3190. - East, J. (2008), 'Embeddings in coset monoids',
*Journal of the Australian Mathematical Society*, vol 85, no 1 , pp 75 - 80. - East, J., Easdown, D. and Fitzgerald, D. (2008), 'A presentation of the dual symmetric inverse monoid',
*International Journal of Algebra and Computation*, vol 18, no 2 , pp 357 - 374. - East, J. (2007), 'Braids and Partial Permutations',
*Advances in Mathematics*, vol 213, no 1 , pp 440 - 461. - East, J. (2007), 'Vines and Partial Transformations',
*Advances in Mathematics*, vol 216, no 2 , pp 787 - 810. - East, J. (2006), 'Birman's Conjecture is True for I2(p)',
*Journal of Knot Theory and its Ramifcations*, vol 15, no 2 , pp 167 - 177. - East, J. (2006), 'Cellular Algebras and Inverse Semigroups',
*Journal of Algebra*, vol 296, no 2 , pp 505 - 519. - East, J. (2006), 'The Factorizable Braid Monoid',
*Proceedings of the Edinburgh Mathematical Society*, vol 49, no 3 , pp 609 - 636. - East, J. (2006), 'Factorizable Inverse Monoids of Cosets of Subgroups of a Group',
*Communications in Algebra*, vol 34, no 7 , pp 2659 - 2665. - East, J. (2006), 'A Presentation of the Singular Part of the Symmetric Inverse Monoid',
*Communications in Algebra*, vol 34, no 5 , pp 1671 - 1689. - East, J., Easdown, D. and Fitzgerald, D. (2005), 'Presentations of Factorizable Inverse Monoids',
*Acta Scientiarum Mathematicarum*, vol 71, no 3-4 , pp 509 - 520.