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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(University of St Andrews, 1924) - Thesis
(University of St Andrews, 2021-12-01) - ThesisThis thesis is based on three papers the author wrote during his time as a PhD student [28, 17, 33]. In Chapter 2 we study 𝐿[sup]𝑞-spectra of planar self-affine measures generated by diagonal matrices. We introduce ...
(University of St Andrews, 2021-06-29) - ThesisComputational semigroup theory involves the study and implementation of algorithms to compute with semigroups. Efficiency is of central concern and often follows from the insight of semigroup theoretic results. In turn, ...
(University of St Andrews, 2021-06-29) - ThesisWe investigate the dimension and structure of four fractal families: inhomogeneous attractors, fractal projections, fractional Brownian images, and elliptical polynomial spirals. For each family, particular attention is ...
(University of St Andrews, 2020-12-01) - ThesisSubdirect products are special types of subalgebras of direct products. The purpose of this thesis is to initiate a study of combinatorial properties of subdirect products and fiber products of semigroups and monoids, ...