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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Recent Submissions
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Existence and non-existence results for strong external difference families
(2018-01) - Journal articleWe consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external differences that occur, and were first defined in the context of ... -
Some group presentations with few defining relations
(University of St Andrews, 1990) - ThesisWe consider two classes of groups with two generators and three relations. One class has a similar presentation to groups considered in the paper by C.M. Campbell and R.M. Thomas, ‘On (2,n)-Groups related to Fibonacci ... -
Automorphism groups of linearly ordered structures and endomorphisms of the ordered set ( Q ,≤) of rational numbers
(2018-08-28) - Journal articleWe investigate the structure of the monoid of endomorphisms of the ordered set ( Q ,≤) of rational numbers. We show that for any countable linearly ordered set Ω, there are uncountably many maximal subgroups of End( Q ,≤) ... -
Decision problems in groups of homeomorphisms of Cantor space
(University of St Andrews, 2018-12-06) - ThesisThe Thompson groups $F, T$ and $V$ are important groups in geometric group theory: $T$ and $V$ being the first discovered examples of finitely presented infinite simple groups. There are many generalisations of these groups ... -
Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs
(2017-07) - Journal articleA countable graph is ultrahomogeneous if every isomorphism between finite induced subgraphs can be extended to an automorphism. Woodrow and Lachlan showed that there are essentially four types of such countably infinite ...
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