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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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 ... -
On the Hausdorff dimension of microsets
(2019-03-05) - Journal articleWe investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dimension of the set. We prove that the lower ... -
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 ... -
Some results in support of the Kakeya conjecture
(2017-10-01) - Journal articleA Besicovitch set is a subset of Rd that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support ... -
The power graph of a torsion-free group
(2019-02) - Journal articleThe power graph P(G) of a group G is the graph whose vertex set is G, with x and y joined if one is a power of the other; the directed power graph P(G) has the same vertex set, with an arc from x to y if y is a power of ...
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