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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Recent Submissions

Parallel algorithms for computing finite semigroups
(20170619)  Journal articleIn this paper, we present two algorithms based on the FroidurePin Algorithm for computing a finite semigroup. If U is any semigroup, and A be a subset of U, then we denote by ⟨A⟩ the least subsemigroup of U containing A. ... 
On the Fourier analytic structure of the Brownian graph
(2018)  Journal articleIn a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any realvalued function on R is bounded above by 1. This partially answered ... 
Root sets of polynomials and power series with finite choice of coefficients
(20171009)  Journal articleGiven H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H, {z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0}, and the set of zeros of a power series with coefficients in H, {z∈C:∃(an)∈HN,∑n=0∞anzn=0}. ... 
On the starheight of subword counting languages and their relationship to Rees zeromatrix semigroups
(20161115)  Journal articleGiven a word w over a finite alphabet, we consider, in three special cases, the generalised starheight of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in ... 
Selfsimilar sets: projections, sections and percolation
(Birkhäuser, 2017)  Conference itemWe survey some recent results on the dimension of orthogonal projections of selfsimilar sets and of random subsets obtained by percolation on selfsimilar sets. In particular we highlight conditions when the dimension of ...