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.

For more information please visit the School of Mathematics and Statistics home page.

Recent Submissions

  • New dimension spectra : finer information on scaling and homogeneity 

    Fraser, Jonathan M.; Yu, Han (2018-04-30) - Journal article
    We introduce a new dimension spectrum motivated by the Assouad dimension; a familiar notion of dimension which, for a given metric space, returns the minimal exponent α > 0 such that for any pair of scales 0 < r < R , any ...
  • Hitting and escaping statistics : mixing, targets and holes 

    Bruin, Henk; Demers, Mark F.; Todd, Mike (2018-04-13) - Journal article
    There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix ...
  • Maximal subsemigroups of finite transformation and diagram monoids 

    East, James; Kumar, Jitender; Mitchell, James D.; Wilson, Wilf A. (2018-06-15) - Journal article
    We describe and count the maximal subsemigroups of many well-known transformation monoids, and diagram monoids, using a new unified framework that allows the treatment of several classes of monoids simultaneously. The ...
  • Regularity of Kleinian limit sets and Patterson-Sullivan measures 

    Fraser, Jonathan MacDonald (2019-02-15) - Journal article
    We consider several (related) notions of geometric regularity in the context of limit sets of geometrically finite Kleinian groups and associated Patterson-Sullivan measures. We begin by computing the upper and lower ...
  • Quantifying inhomogeneity in fractal sets 

    Fraser, Jonathan; Todd, Michael John (2018-04) - Journal article
    An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set ...

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