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 www.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. 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.
My research is funded by an NSERC Discovery Grant (2016–23), and has previously also been supported by a university start-up grant, and the university's "Seed, Bridge & Multidisciplinary Fund".
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.
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.
I was responsible for organizing, or co-organizing, the following conferences, workshops or conference sessions:
- 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.