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 

    Jonusas, Julius; Mitchell, J. D.; Pfeiffer, M. (2017-06-19) - Journal article
    In this paper, we present two algorithms based on the Froidure-Pin 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 

    Fraser, Jonathan MacDonald; Sahlsten, Tuomas (2018) - Journal article
    In 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 real-valued function on R is bounded above by 1. This partially answered ...
  • Root sets of polynomials and power series with finite choice of coefficients 

    Baker, Simon; Yu, Han (2017-10-09) - Journal article
    Given 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 star-height of subword counting languages and their relationship to Rees zero-matrix semigroups 

    Bourne, Tom; Ruškuc, Nik (2016-11-15) - Journal article
    Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in ...
  • Self-similar sets: projections, sections and percolation 

    Falconer, Kenneth John; Jin, Xiong (Birkhäuser, 2017) - Conference item
    We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of ...

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