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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Flatness, extension and amalgamation in monoids, semigroups and rings
(University of St Andrews, 1986) - ThesisWe begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in ... -
Dimension theory of random self-similar and self-affine constructions
(University of St Andrews, 2017-06-23) - ThesisThis thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give ... -
Restricted permutations, antichains, atomic classes and stack sorting
(University of St Andrews, 2003) - ThesisInvolvement is a partial order on all finite permutations, of infinite dimension and having subsets isomorphic to every countable partial order with finite descending chains. It has attracted the attention of some celebrated ... -
Topological graph inverse semigroups
(2016-08-01) - Journal articleTo every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E . These semigroups generalize polycyclic monoids, and they arise in the study of Leavitt ... -
ℤ4-codes and their Gray map images as orthogonal arrays
(2017-07) - Journal articleA classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of ...
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