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 joining Western Sydney University in 2011. I am currently a senior lecturer and ARC Future Fellow.
My research comes under the broad headings of abstract algebra and combinatorics, and I am particularly interested in semigroup theory. The main objects of my study are transformation semigroups, diagram monoids (and associated algebras and categories), and braid groups and monoids. Recurring themes in my work include presentations, congruences, (products of) idempotents, sandwich semigroups, combinatorial invariant theory and more.
Outside of mathematical research, I enjoy philosophy, cricket, Rubiks puzzles, and single malt whisky.
This information has been contributed by Doctor East.
Qualifications
 PhD University of Sydney
Professional Memberships
 Australian Mathematical Society (2002  2020)
Awards
 ARC Future Fellowship 20200101
Interests
 Algebra
 Braid groups and monoids
 Combinatorics
 Diagram monoids/algebras/categories
 Reflection groups and monoids
 Semigroup theory
 Transformation semigroups
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
 East, J. (2019), 'Presentations for rook partition monoids and algebras and their singular ideals', Journal of Pure and Applied Algebra, vol 223, no 3 , pp 1097  1122.
 Dolinka, I., East, J., Evangelou, A., FitzGerald, D., Ham, N., Hyde, J., Loughlin, N. and Mitchell, J. (2019), 'Enumeration of idempotents in planar diagram monoids', Journal of Algebra, vol 522 , pp 351  385.
 East, J. and Niles, R. (2019), 'Integer polygons of given perimeter', Bulletin of the Australian Mathematical Society, vol 100, no 1 , pp 131  147.
 Feng, Y., AlAadhami, A., Dolinka, I., East, J. and Gould, V. (2019), 'Presentations for singular wreath products', Journal of Pure and Applied Algebra, vol 223, no 12 , pp 5106  5146.
 East, J. (2019), 'Idempotents and onesided units in infinite partial Brauer monoids', Journal of Algebra, vol 534 , pp 427  482.
 East, J. and Higgins, P. (2019), '[In Press] Green's relations and stability for subsemigroups', Semigroup Forum, .
 East, J. and Niles, R. (2019), 'Integer triangles of given perimeter : a new approach via group theory', American Mathematical Monthly, vol 126, no 8 , pp 735  739.
 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., Durdev, I., East, J., Honyam, P., Sangkhanan, K., Sanwong, J. and Sommanee, W. (2018), 'Sandwich semigroups in locally small categories II : transformations', Algebra Universalis, vol 79, no 3 .
 Dolinka, I., Durdev, I., East, J., Honyam, P., Sangkhanan, K., Sanwong, J. and Sommanee, W. (2018), 'Sandwich semigroups in locally small categories I : foundations', Algebra Universalis, vol 79, no 3 .
 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 GrahamHoughton 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 idempotentgenerated subsemigroup of the Kauffman monoid', Glasgow Mathematical Journal, vol 59, no 3 , pp 673  683.
 East, J., EgriNagy, 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 12 , 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 2generator 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 orderpreserving 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 34 , pp 509  520.
Current Projects
Title:  Diagram categories and transformation semigroups 

Funder: 

Western Researchers:  James East 
Years:  20200101  20231231 
ID:  P00025447 
Supervision
Current Supervision
Thesis Title:  Algebraic Models of Bacterial Genomes Evolving by Inversions and Deletions 

Field of Research: 