Doctor James East

• Biography
• Areas of Research / Teaching Expertise
• Selected Publications
• Contact Details

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.

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Areas of Research / Teaching Expertise

Pure mathematics, algebra, braid groups, reflection groups, semigroup theory.

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Selected Publications

1. “Braids and Factorizable Inverse Monoids”, Semigroups and Languages (I.M. Araujo, M.J.J. Branco, V.H. Fernandes and G.M.S. Gomes, eds), World Scientific, (2004), 86-105. (Joint with D. Easdown and D.G. FitzGerald.)

2. “Presentations of Factorizable Inverse Monoids”, Acta Scientiarum Mathematicarum (Szeged), 71 (2005), no. 3-4, 509–520. (Joint with D. Easdown and D.G. FitzGerald.)

3. “Birman’s Conjecture is True for I2(p)”, Journal of Knot Theory and its Ramifications, 15 (2006), no. 2, 167–177.

4. “Cellular Algebras and Inverse Semigroups”, Journal of Algebra, 296 (2006), no. 2, 505–519.

5. “The Factorizable Braid Monoid”, Proceedings of the Edinburgh Mathematical Society, 49 (2006), no. 3, 609—636.

6. “Factorizable Inverse Monoids of Cosets of Subgroups of a Group”, Communications in Algebra, 34 (2006), no. 7, 2659–2665.

7. “A Presentation of the Singular Part of the Symmetric Inverse Monoid”, Communications in Algebra, 34 (2006), no. 5, 1671–1689.

8. “Braids and Partial Permutations”, Advances in Mathematics, 213 (2007), no. 1, 440–461.

9. “Vines and Partial Transformations”, Advances in Mathematics, 216 (2007), no. 2, 787–810.

10. “On a Class of Factorizable Inverse Monoids Associated with Braid Groups”, Communications in Algebra, 36 (2008), no. 8, 3155–3190.

11. “Embeddings in Coset Monoids”, Journal of the Australian Mathematical Society, 85 (2008), no. 1, 75–80.

12. “A Presentation of the Dual Symmetric Inverse Monoid”, International Journal of Algebra and Computation, 18 (2008), no. 2, 357–374. (Joint with D. Easdown and D.G. FitzGerald.)

13. “Presentations for Singular Subsemigroups of the Partial Transformation Semigroup”, International Journal of Algebra and Computation, 20 (2010), no. 1, 1–25.

14. “A Presentation of the Singular Part of the Full Transformation Semigroup”, Semigroup Forum, 81 (2010), no. 2, 357–379.

15. “Braids and order-preserving partial permutations”, Journal of Knot Theory and its Ramifications, 19 (2010), no. 8, 1025–1049.

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