William Pettersson

William Pettersson

Headshot of William Pettersson
William Pettersson, Research Fellow
School of Science, RMIT University ,
Melbourne, Victoria, Australia

Email: william@ewpettersson.se
XMPP: william@ewpettersson.se
Languages: English, Swedish

About Me

I am a mathematician, and currently employed as a research fellow at RMIT. My research has taken me from graph decompositions through combinatorial toplogy, and I am currently looking at using linear and integer programming solutions to solve problems in computational topology.

I also have a strong interest in computing, reaching from the algorithms I use in my research to the complex world of information security. I have practical experience with coding at all levels, from assembly for the HC12 through C, and C++ all the way to Python, PHP and Perl. Details on some of these projects are available at Github.

As a student I have played integral roles in the organisation of various social functions as a part of the Mathematics Students Society. I was a member of the Host Scientific Committee for the 2013 International Olympiad in Informatics and was involved with the Queensland Informatics & Programming Club to train high school students in informatics.
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Research Interests

Graph Decompositions

A decomposition of K7 I study the existence of decompositions and factorisations of
  • complete graphs,
  • circulant graphs, and
  • multigraphs.
I also apply computational techniques to problems in this field.

Combinatorial and computational topology

The Regina logo
  • Development of Regina, a mathematical software suite for 3-manifold topologists
  • Census enumeration algorithms, and their complexity
  • Spine codes of 3-manifolds
  • Properties of Pachner graphs
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Publications

Published
  1. W. Pettersson. Computational Graph Theory, PhD Thesis Oct 17 2014; (Available online)
  2. B. Burton and W. Pettersson. Fixed parameter tractable algorithms in combinatorial topology, Lecture Notes in Computer Science vol. 8591, 2014, pp.200-311. (Publisher, arXiv)
  3. D. Bryant, P. Danziger and W. Pettersson. Bipartite 2-factorisations of complete multipartite graphs, Journal of Graph Theory vol. 78, issue 4. April 2015;, pp.287-294 doi: 10.1002/jgt.21806 (Publisher)
  4. D. Bryant, D. Horsley, and W. Pettersson. Cycle decompositions V: Complete graph into cycles of arbitrary lengths, Proceedings of the London Mathematical Society 2014; doi: 10.1112/plms/pdt051 (Publisher, arXiv)
  5. B. Burton and W. Pettersson. An edge-based framework for enumerating 3-manifold triangulations, SoCG 2015: 31st International Symposium on Computational Geometry, Leibniz International Proceedings in Informatics vol. 34, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2015, pp. 270-284. (Publisher, arXiv)
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Teaching

At The University of Queensland
As a teaching assistant:
  • 2014 : MATH4303 Advanced Combinatorics
  • 2011-2014 : MATH3301 Graph Theory and Design Theory
  • 2010-2014 : MATH3302 Coding and Cryptography
  • 2010-2014 : MATH1061 Discrete Mathematics
  • 2011-2013 : MATH3500 Problems and Applications in Modern Mathematics
  • 2011 : MATH4302 Combinatorial Designs
  • 2010 : MATH3306 Set Theory and Logic
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