Pure Mathematics Research
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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(2018-08-09) - Journal articleWe prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by Holt.
(2017-11) - Journal articleThis paper addresses the question whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having −1 as multiplier is both a necessary ...
(2018) - Journal articleThe purpose of this paper twofold. Firstly, we establish Π^0_γ-completeness and Σ^0_γ-completeness of several different classes of multifractal decomposition sets of arbitrary Borel measures (satisfying a mild non-degeneracy ...
(2018-02-21) - Journal articleIn recent years many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic ...
(2017-09) - Journal articleFor a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant ...