Research
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.
My favourite mathematical topic is distance-regular graphs. Along with some student research assistants, I have developed distanceregular.org, an online catalogue of distance-regular graphs, with graphs available to be downloaded for use in computations. This work led to some interesting new observations and is the subject of ongoing research.
A lot of my time 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, and is my most cited work. In particular, I've investigated the metric dimension of numerous families of distance-regular graphs.
In combinatorial design theory, my main contributions have focused on packing and covering versions of so-called "generalized t-designs", along with resolvability and block-colourings of designs.
Details of my publications are available here, or (if you have a subscription) MathSciNet. I also have a Google Scholar profile. Preprints since 2010 are available on the arXiv.
Research funding
My research is supported by an NSERC Discovery Grant (2024–29), and has previously also been funded by a university start-up grant, the university's "Seed, Bridge & Multidisciplinary Fund", and the Grenfell Campus Research Fund, as well as a prior NSERC Discovery Grant.
Students and Postdocs
- Daniel Hawtin, postdoctoral fellow, January 2018–April 2019.
- Iren Darijani, postdoctoral fellow, September 2021–August 2022.
- Adam Jackson, undergraduate research assistant (full time), May–August 2016.
- Courtney Weir, undergraduate research assistant (part time), October 2016–April 2017.
- Brittany Pittman, undergraduate research assistant (full time, NSERC USRA), May–August 2018.
- Keenan Nicholson, undergraduate research assistant (full time, NSERC USRA), January–April 2019.
- Cindy Bowers, undergraduate research assistant (part time), January–April 2019.
- Fabien Bosquet, undergraduate research assistant (part time), January–April 2020.
- Dylan Ruth, undergraduate research assistant (full time, NSERC USRA), May–August 2020.
- Aaron Dwyer, undergraduate research assistant (full time, NSERC USRA), May–August 2021.
- Alaina Pardy, undergraduate research assistant (full time, NSERC USRA), May–August 2021 and May–August 2022.
- Abigail Rowsell, undergraduate research assistant (full time, NSERC USRA), May–August 2021 and May–August 2022.
- Daniel O'Neill, undergraduate research assistant (full time, May–August 2024; part time, November 2023–April 2024).
Conferences organized
I am responsible for organizing, or co-organizing, the following conferences, workshops or conference sessions:
- 16th East Coast Combinatorics Conference, Grenfell Campus, 13–14 May 2024.
- Symmetry Breaking in Discrete Structures, workshop at the Casa Matemática Oaxaca, Oaxaca, Mexico, 16–21 September 2018.
- 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.
Erdős number
My Erdős number is 2, via the route Bailey–Cameron–Erdős. (For a few years, this was not mentioned in the Erdős Number Project's data, as they thought I was someone else....)