Leverhulme Early Career Fellow
I am a Leverhulme Early Career Fellow in the School of Mathematics and Statistics at the University of St Andrews. My general research area is group theory: the mathematical study of symmetry.
For a friendly nontechnical introduction to my research, take a look at my poster that won a Gold Medal at STEM for Britain. For more detail, see my slightly longer (but equally friendly) leaflet The Art of Measuring Symmetry.
Much of my recent research has focussed on generation of groups (both finite and infinite) and permutation group theory, and I'm particularly interested in the overlap between the two. However, I am also interested in representation theory, geometric group theory, combinatorics, fractal geometry among other topics. For more infomation see my Research and Publications pages.
One recent highlight is a paper that appeared in the Annals of Mathematics last year, in which Tim Burness, Robert Guralnick and I answered some old questions about the generation of finite groups, including: “In which finite groups is every nontrivial element contained in a generating pair?”
Before moving to St Andrews in October 2022, I was at the University of Bristol where I was a Heilbronn Fellow for three years and, before that, a PhD student supervised by Prof Tim Burness. Over the past few years I have also spent time at the University of Auckland and the University of Western Australia (both with a Cecil King Travel Scholarship), the University of Padua (as an LMS Early Career Fellow) and the Isaac Newton Institute in Cambridge (for the Groups, Representations and Applications programme).
My Erdős number is three via at least four disjoint paths, for example
(Harper → Praeger → Cameron → Erdős)
(Harper → Guralnick → Brenner → Erdős)
(Harper → Burness → Seress → Erdős)
(Harper → Glasby → Palfy → Erdős).
Sometimes I think about less important things, such as why Dobble is disappointing, whether you can tie a trefoil knot walking around the Fry building and what is to Wordle as a sudoku is to a crossword?
[“University flag flying from St Salvator's Chapel tower”,
© The University of St Andrews 2020, CC BY-NC 4.0]