I am an Academic Visitor in the Department of Mathematics at Imperial College London.

I am interested in group theory, combinatorics, discrete geometry and representation theory.

I obtained my PhD at the University of Cambridge, working with Jan Saxl on bases of primitive permutation groups. I then worked as a Research Associate in the Centre for the Mathematics of Symmetry and Computation at The University of Western Australia. After this, I was an LMS Grace Chisholm Young Fellow in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. Most recently, I was a Marie Skłodowska-Curie Individual Fellow in the Department of Mathematics at Imperial College London.

Publications

Bases of twisted wreath products, J. B. Fawcett, to appear in J. Algebra. (See arXiv or journal.)

Partial linear spaces with a rank 3 affine primitive group of automorphisms, J. Bamberg, A. Devillers, J. B. Fawcett, C. E. Praeger, J. London Math. Soc. 104, 1011-1084 (2021). (See arXiv or journal.)

On k-connected-homogeneous graphs, A. Devillers, J. B. Fawcett, C. E. Praeger, J.-X. Zhou, J. Combin. Theory Ser. A 173 (2020). (See arXiv or journal.)

Regular orbits of sporadic simple groups, J. B. Fawcett, J. Müller, E. A. O'Brien, R. A. Wilson, J. Algebra 522, 61-79 (2019). (See arXiv or journal.)

Information transmission and signal permutation in active flow networks, F. G. Woodhouse, J. B. Fawcett, J. Dunkel, New J. Phys. 20, 035003 (2018). (See arXiv or journal.)

Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5, J. B. Fawcett, M. Giudici, C. H. Li, C. E. Praeger, G. Royle, G. Verret, J. Combin. Theory Ser. A 157, 247-266 (2018). (See arXiv or journal.)

Bruck nets and partial Sherk planes, J. Bamberg, J. B. Fawcett, J. Lansdown, J. Austral. Math. Soc. 104, 1-12 (2018). (See arXiv or journal.)

Stochastic cycle selection in active flow networks, F. G. Woodhouse, A. Forrow, J. B. Fawcett, J. Dunkel, Proc. Natl. Acad. Sci. U.S.A. 113, 8200-8205 (2016). (See arXiv or journal.)

Locally triangular graphs and normal quotients of the n-cube, J. B. Fawcett, J. Algebraic Combin 44, 119-130 (2016). (See arXiv or journal. See also erratum.)

Regular orbits of symmetric and alternating groups, J. B. Fawcett, E. A. O'Brien, J. Saxl, J. Algebra 458, 21-52 (2016). (See preprint or journal.)

Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples, J. B. Fawcett, C. E. Praeger, Arch. Math. 106, 305-314 (2016). (See arXiv or journal.)

Locally triangular graphs and rectagraphs with symmetry, J. Bamberg, A. Devillers, J. B. Fawcett, C. E. Praeger, J. Combin. Theory Ser. A 133, 1-28 (2015). (See arXiv or journal.)

The base size of a primitive diagonal group, J. B. Fawcett, J. Algebra 375, 302-321 (2013). (See arXiv or journal.)

Other

Bases of primitive permutation groups, PhD Thesis, University of Cambridge, 2013.

The O'Nan-Scott Theorem for finite primitive permutation groups, and finite representability, Master's Thesis, University of Waterloo, 2009.