Justin is a mathematician with broad interests throughout algebra, group theory and combinatorics. A common theme of his work involves exploring the links between a group of symmetries of an object and the structure of the object itself, such as a geometry or algebra. He uses both theoretical and computation techniques and has extensive experience programming in Python, Magma and GAP.

Recently his research has focused on some interesting classes of non-associative algebra, such as axial algebras. These have motivations coming from Monstrous Moonshine and mathematical physics, such as string theory and VOAs. In addition to examples from algebra, recently examples have been found across mathematics including in the theory of non-linear PDEs and Ricci flows on manifolds.

Other interests include (in no particular order): non-associative algebras, particularly axial and code algebras; finite groups, classical and sporadic; p-local analysis; fusion systems; group amalgams; diagram geometries; buildings; combinatorics; coding theory; VOAs; Clifford algebras and cluster algebras.