William Pettersson

Contents
About me
Research interests
Teaching history
Side projects and tidbits

William Pettersson
Department of Mathematics,
The University of Queensland,
QLD, 4072,
Australia

Email: william at ewpettersson.se
Phone: (07) 3346 6256
Languages: English, Swedish

About Me

I am currently a Mathematics PhD student in the School of Mathematics and Physics at the University of Queensland. As a student I have played integral roles in the organisation of various social functions as a part of the Mathematics Students Society.
I am also a part of the technical committee for the 2013 International Olympiad in Informatics and am currently involved with the Queensland Informatics & Programming Club to train high school students in informatics.

Research Interests

Graph decompositions

Cycle decompositions of circulants
Cycle factorisations of circulants
Cycle decompositions of multigraphs

Completed project: Cycle decomposition problem for complete graphs

(in conjunction with Prof. Darryn Bryant and Dr. Daniel Horsley)
We show that the complete graph on n vertices can be decomposed into t cycles of specified lengths m₁,...,m_t if and only if n is odd, 3 ≤ m_i ≤ n for i=1,...,t, and m₁+...+m_t=n(n-1)/2. We also show that the complete graph on n vertices can be decomposed into a perfect matching and t cycles of specified lengths m₁,...,m_t if and only if n is even, 3 ≤ m_i ≤ n for i=1,...,t, and m₁+...+m_t=n(n-2)/2.
http://arxiv.org/abs/1204.3709

Combinatorial topology

Manifold Census Generation by Cycle Decompositions (PDF, 1.4MB), awarded First Place for returning presenters at University of Queensland SMP Poster Day, 21^st September, 2012.
Spine codes of 3-manifolds
Properties of Pachner graphs

Ongoing work: Regina - Software for 3-manifold topology and normal surface theory

Regina is a suite of mathematical software for 3-manifold topologists. It focuses on the study of 3-manifold triangulations and normal surfaces.
For official downloads for other distributions, see http://regina.source-forge.net.

ArchLinux
Note that the x86_64 files are pre-compiled. This is nice, but updates to Arch can therefore break these packages so I would recommend using the AUR tarball. For installation instructions, see https://wiki.archlinux.org/index.php/Arch_User_Repository#Installing_packages.
Gentoo - Gentoo packages are available in a layman overlay. Once layman has been installed, you can install the overlay by running
# layman -f -o http://github.com/enigma-/regina-gentoo/raw/master/overlays.xml -a regina-gentoo
You will then be able to install Regina with # emerge regina. Note that version 9999 of Regina in the overlay will always update to the latest SVN revision, which may or may not work at any given time.