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

  • On the Hausdorff dimension of microsets 

    Fraser, Jonathan MacDonald; Howroyd, Douglas Charles; Käenmäki, Antti; Yu, Han (2019-03-05) - Journal article
    We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dimension of the set. We prove that the lower ...
  • A capacity approach to box and packing dimensions of projections of sets and exceptional directions 

    Falconer, Kenneth John (2019-03-12) - Journal article
    Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set E in ℝn onto almost all m-dimensional subspaces. However, these definitions ...
  • Some results in support of the Kakeya conjecture 

    Fraser, Jonathan MacDonald; Olson, Eric; Robinson, James (2017-10-01) - Journal article
    A Besicovitch set is a subset of Rd that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support ...
  • The Assouad spectrum and the quasi-Assouad dimension : a tale of two spectra 

    Fraser, Jonathan MacDonald; Hare, Kathryn E.; Hare, Kevin G.; Troscheit, Sascha; Yu, Han (2019-01-17) - Journal article
    We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the 'upper Assouad spectrum'. These spectra are designed to interpolate between the upper box-counting and Assouad ...
  • 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 ...

View more