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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Semigroup congruences : computational techniques and theoretical applications
(University of St Andrews, 2019-06-25) - ThesisComputational semigroup theory is an area of research that is subject to growing interest. The development of semigroup algorithms allows for new theoretical results to be discovered, which in turn informs the creation ... -
A capacity approach to box and packing dimensions of projections of sets and exceptional directions
(2019-03-12) - Journal articleDimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set E in ℝn onto almost all m-dimensional subspaces. However, these definitions ... -
Hitting and escaping statistics : mixing, targets and holes
(2018-04-13) - Journal articleThere is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix ... -
Maximal subsemigroups of finite transformation and diagram monoids
(2018-06-15) - Journal articleWe describe and count the maximal subsemigroups of many well-known transformation monoids, and diagram monoids, using a new unified framework that allows the treatment of several classes of monoids simultaneously. The ... -
Computing maximal subsemigroups of a finite semigroup
(2018-07-01) - Journal articleA proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, ...
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