## Heilbronn Research Fellow

**University of Bristol**

*“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root and it would be hard to find a better one on which to demonstrate the working of mathematical intellect.”*Hermann Weyl

I am a Heilbronn Research Fellow at the University of Bristol. 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 the STEM for Britain event in parliament. If that gets you hooked, then read my slightly longer (but equally friendly and colourful) leaflet The Art of Measuring Symmetry.

Much of my recent research has focussed on group generation, probabilistic group theory and permutation group theory. Two key themes of this work are the subgroup structure and conjugacy of (finite and infinite) simple groups, which are topics that have many applications across mathematics. More generally, I am interested in representation theory, geometric group theory, combinatorics and fractal geometry, and I am always keen to explore new areas.

In a paper recently accepted to the Annals of Mathematics, Tim Burness, Robert Guralnick and I recently proved some long-standing questions about the generation of finite groups, including the question: “In which finite groups is every nontrivial element contained in a generating pair?”

Until June 2019, I was a PhD student under the supervision of Prof Tim Burness. In 2017, I was awarded the Cecil King Travel Scholarship from the London Mathematical Society, with which I visited the University of Auckland and the University of Western Australia. Immediately following my PhD, I was an LMS Early Career Fellow based at the University of Padua. In 2020, I participated in the Groups, Representations and Applications programme at the Isaac Newton Institute in Cambridge.

My Erdős number is three via four disjoint paths, for example

(Harper → Praeger → Cameron → Erdős)

(Harper → Guralnick → Brenner → Erdős)

(Harper → Burness → Seress → Erdős)

(Harper → Glasby → Palfy → Erdős).

Feel free to contact me at the details below.