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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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, ... -
On average Hewitt-Stromberg measures of typical compact metric spaces
(2019-01-24) - Journal articleWe study average Hewitt-Stromberg measures of typical compact metric spaces belonging to the Gromov-Hausdorff space (of all compact metric spaces) equipped with the Gromov-Hausdorff metric. -
Multi-part balanced incomplete-block designs
(2019-01-23) - Journal articleWe consider designs for cancer trials which allow each medical centre to treat only a limited number of cancer types with only a limited number of drugs. We specify desirable properties of these designs, and prove some ... -
Rigidity for sticky disks
(2019-01-14) - Journal articleWe study the combinatorial and rigidity properties of disk packings with generic radii. We show that a packing of n disks in the plane with generic radii cannot have more than 2n − 3 pairs of disks in contact. The allowed ... -
On the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞
(2019-02) - Journal articleLet (X,ε,μ) be a measure space and let ƒ:X→ ℝ be a measurable function such that ||ƒ||p < ∞ for all p ≥ 1 and ||ƒ||∞ >0. In this paper, we describe the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞.
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