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 the University of Western Sydney 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 and Mathematics University of Western Sydney Locked Bag 1797, Penrith NSW 2751 Australia Office: Building ER, Room G.18, Parramatta campus Email: j.east@uws.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:

• 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 lies in combinatorial semigroup theory, the study of semigroups (including monoids and groups) via presentations (generators and relations). The kinds of semigroups and monoids I am particularly interested in are all somehow related to:

• braid groups; and
• symmetric groups and generalizations such as:
  • transformation semigroups;
  • partition monoids/algebras and dual symmetric inverse monoids; and
  • 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

In print

1. On the singular part of the partition monoid. Internat. J. Algebra Comput. 21 (2011), no 1-2, 147--178.
2. Braids and order-preserving partial permutations. J. Knot Theory Ramifications 19 (2010), no. 8, 1025--1049.
3. A presentation of the singular part of the full transformation semigroup. Semigroup Forum. 20 (2010), no. 2, 357--379.
4. Presentations for singular subsemigroups of the partial transformation semigroup. Internat. J. Algebra Comput. 20 (2010), no. 1, 1--25.
5. Embeddings in coset monoids. J. Aust. Math. Soc. 85 (2008), no. 1, 75--80.
6. On a class of factorizable inverse monoids associated with braid groups. Comm. Algebra 36 (2008), no. 8, 3155--3190.
7. With David Easdown and Des FitzGerald: A presentation of the dual symmetric inverse monoid. Internat. J. Algebra Comput. 18 (2008), no. 2, 357--374.
8. Vines and partial transformations. Adv. Math. 216 (2007), no. 2, 787--810.
9. Braids and partial permutations. Adv. Math. 213 (2007), no. 1, 440--461.
10. The factorizable braid monoid. Proc. Edinb. Math. Soc. (2) 49 (2006), no. 3, 609--636.
11. Factorizable inverse monoids of cosets of subgroups of a group. Comm. Algebra 34 (2006), no. 7, 2659--2665.
12. A presentation of the singular part of the symmetric inverse monoid. Comm. Algebra 34 (2006), no. 5, 1671--1689.
13. Birman's conjecture is true for I₂(p). J. Knot Theory Ramifications 15 (2006), no. 2, 167--177.
14. Cellular algebras and inverse semigroups. J. Algebra 296 (2006), no. 2, 505--519.
15. With David Easdown and Des FitzGerald: Presentations of factorizable inverse monoids. Acta Sci. Math. (Szeged) 71 (2005), no. 3-4, 509--520. Preprint version.
16. With David Easdown and Des FitzGerald: Braids and factorizable inverse monoids. Semigroups and languages, 86--105, World Sci. Publ., River Edge, NJ, 2004. Preprint version.

Preprints

1. With Peter McNamara: On the work performed by a transformation semigroup. Australas. J. Combin. To appear.
2. Generators and relations for partition monoids and algebras. J. Algebra To appear.
3. Cellularity of inverse semigroup algebras. Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear.
4. Coset monoids and embeddings. Proceedings of the Special Interest Meeting on Semigroups, University of Sydney, 2006. To appear.
5. Singular braids and partial permutations. Preprint, 2010.
6. Infinite dual symmetric inverse semigroups. Preprint, 2011.
7. Infinite partition monoids. Preprint, 2011.
8. Generation of infinite factorizable inverse monoids. Preprint, 2011.
9. Dual reflection monoids I--III. Three papers, in preparation.

Conference Talks and Seminars

• Generators and relations for semigroups of singular transformations - ICGS Nebraska (2009)
• Dual reflection monoids - BMC Edinburgh (2010)
• Braids and Transformation Semigroups - Heriot-Watt, St Andrews, Manchester, York (2010)
• Applications of order-preserving partial permutations - York (2010)
• Infinite partition monoids - USyd, UTas (2010) and Amiens (2011)
• Idempotent generators in partition monoids - St Andrews, Porto, Lisbon, USyd (2011)

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.

Random

• Dot Paper Version I
• Dot Paper Version II