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

  • Modern computational methods for finitely presented monoids 

    Tsalakou, Maria (2024-06-11) - Thesis
    In this thesis we are mainly interested in the development of practical algorithms for semigroups and monoids defined by finite presentations. Although in general nearly every problem about finitely presented semigroups ...
  • Finiteness conditions on semigroups relating to their actions and one-sided congruences 

    Miller, Craig (University of St Andrews, 2020-12-01) - Thesis
    The purpose of this thesis is threefold: firstly, to develop a systematic theory of presentations of monoid acts; secondly, to study finiteness conditions on semigroups relating to finite generation of one-sided congruences; ...
  • On constructing topology from algebra 

    Elliott, Luke (University of St Andrews, 2022-06-14) - Thesis
    In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, ...
  • Interpolating between Hausdorff and box dimension 

    Banaji, Amlan (2023-11-28) - Thesis
    Hausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all sets in the cover have the same diameter, but ...
  • Solving decision problems in finitely presented groups via generalized small cancellation theory 

    Jurina, Simon (2023-06-13) - Thesis
    This thesis studies two decision problems for finitely presented groups. Using a standard RAM model of computation, in which the basic arithmetical operations on integers are assumed to take constant time, in Part I we ...

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