Research projects

One of the things I most like about my job is supervising students in research projects. From AMSI Vacation Scholarship students to honours students to PhD students, I enjoy collaborating with a student that is seeing a dedicated research problem for the first time, and then becoming a master of their subject.

For PhD supervision, I require that the student know me first: too often do I receive an email from someone who wants to do a PhD in, say, fluid mechanics with me; a subject I have very little idea about! I also require proof that you are capable of research at a high level. This gruelling test consists of asking the student to write a difficult proof in exquisitely written english on a result of my choosing. So if you are interested in doing a PhD with me, send me an informal chatty email (formal emails will be deleted), and the areas of my research that you are interested in.

Prospective honours students, I have outlined what I think you need to know in making an informed decision on whether you want to work under my supervision. The styles of projects can be roughly categorised as follows:

As for research areas, here is how I describe them for a student:

Group theory

I am mainly interested in finite permutation groups, but I sometimes offer a project where my curiosity has taken me beyond the finite realm. The project is likely to be an abstract investigation and be co-supervised by another member of our research group; the Centre for the Mathematics of Symmetry and Computation are world-renown for their strengths in finite group theory.

Geometry

My research has mostly been in finite projective or polar geometry, generalised polygons, and related structures. Recently I have been interested in the foundations of geometry and the Bachmann school of metric geometry. I have plenty of nice problems in incidence geometry, and this would be my comfort zone in terms of supervision.

Algebraic Combinatorics

The use of association schemes has recently been very successful in the existence and non-existence questions of substructures in finite geometry. This currently a hot topic of mine that I have many side-projects on the fly. There are interesting avenues for computational investigation in this area.

Elementary number theory

First a disclaimer: I am not a number theorist, and I cannot pretend to be at the cutting edge of modern number theory. A lot of students are easily swayed by the beauty of this subject, however, the modern day number theory is quite a deep and complicated profession. The research projects I would offer under this heading would not be cutting edge research problems, only curiosities that have come up in my day-to-day research. If you would like a problem that trains you to be at the forefront of modern research in number theory, there is an excellent group at Macuqarie University and ANU that I would suggest you contact. However, if you like the style of mathematics of number theory, then you might also like combinatorics too, and we can certainly offer projects under that broad heading.

Students I have supervised

I have been enormously lucky to have supervised some remarkable students. Here is a list of the students and their projects.

Current students

Past students

PhD Students

Masters/MPhil Students

Honours Students