My research interests fall into three broad areas:
- algebraic and metric graph theory,
- combinatorial design theory, and
- permutation groups,
although all three are linked. I've also worked on topics including coding theory, hypergraphs, matroids, enumeration, and combinatorial matrix theory.
Along with some student research assistants, I have developed www.distanceregular.org, an online catalogue of distance-regular graphs, with graphs available to be downloaded for use in computations.
A lot of my time in recent years has been devoted to the relationship between base sizes of permutation groups and the metric dimension of graphs. A survey article on this topic, with Peter Cameron, was published in the Bulletin of the London Mathematical Society in 2011. In particular, I've investigated the metric dimension of numerous families of distance-regular graphs.
In combinatorial design theory, my recent work has focused on packing and covering versions of so-called "generalized t-designs", which should keep me busy for a while.
My research is funded by an NSERC Discovery Grant (2016–21), as well as a university start-up grant.
Students and Postdocs
- Adam Jackson, undergraduate research assistant (full time), May–August 2016.
- Courtney Weir, undergraduate research assistant (part time), October 2016–April 2017.
In addition, a postdoctoral fellowship in algebraic graph theory is currently available.
Travelling around the world (literally, on one occasion) to attend conferences and give talks is definitely one of the more enjoyable aspects of being a mathematician. A list of conferences I have attended (or may attend soon) is here.
Previously, I was responsible for organizing, or co-organizing, the following conferences (or conference sessions):
- Session on Graphs, Designs and Hypergraphs, Canadian Mathematical Society Summer Meeting, University of Prince Edward Island, 5–9 June 2015.
- Prairie Discrete Mathematics Workshop 2011, University of Regina, 22–23 July 2011.
- Graphs, Designs and Algebraic Combinatorics, University of Regina, 18–21 July 2011.
- From Higman-Sims to Urysohn: Peter Cameron's 60th birthday conference, Ambleside, UK, 23–26 August 2007.
- 15th Postgraduate Combinatorial Conference, Queen Mary, University of London, 20–22 April 2004.