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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Rearrangement groups of connected spaces
(University of St Andrews, 2020-07-28) - ThesisWe develop a combinatorial framework that assists in finding natural infinite “geometric” presentations for a large subclass of rearrangement groups of fractals – defined by Belk and Forrest, namely rearrangement groups ... -
Modern computational methods for finitely presented monoids
(2024-06-11) - ThesisIn this thesis we are mainly interested in the development of practical algorithms for semigroups and monoids defined by finite presentations. Although in general nearly every problem about finitely presented semigroups ... -
Finiteness conditions on semigroups relating to their actions and one-sided congruences
(University of St Andrews, 2020-12-01) - ThesisThe purpose of this thesis is threefold: firstly, to develop a systematic theory of presentations of monoid acts; secondly, to study finiteness conditions on semigroups relating to finite generation of one-sided congruences; ... -
On constructing topology from algebra
(University of St Andrews, 2022-06-14) - ThesisIn this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, ... -
Interpolating between Hausdorff and box dimension
(2023-11-28) - ThesisHausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all sets in the cover have the same diameter, but ...
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