Pure Mathematics
Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.
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Solvable quotients of subdirect products of perfect groups are nilpotent
(2018-08-09) - Journal articleWe prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by Holt. -
Triple arrays from difference sets
(2017-11) - Journal articleThis paper addresses the question whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having −1 as multiplier is both a necessary ... -
On the Π^0_γ-completeness and Σ^0_γ-completeness of multifractal decomposition sets
(2018) - Journal articleThe purpose of this paper twofold. Firstly, we establish Π^0_γ-completeness and Σ^0_γ-completeness of several different classes of multifractal decomposition sets of arbitrary Borel measures (satisfying a mild non-degeneracy ... -
Analytic analysis of auxetic metamaterials through analogy with rigid link systems
(2018-02-21) - Journal articleIn recent years many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic ... -
On plausible counterexamples to Lehnert's conjecture
(University of St Andrews, 2018) - ThesisA group whose co-word problem is a context free language is called co𝐶𝐹 . Lehnert's conjecture states that a group 𝐺 is co𝐶𝐹 if and only if 𝐺 embeds as a finitely generated subgroup of R. Thompson's group V . In this ...
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