Pure Mathematics Theses: Recent submissions

Now showing items 1-5 of 72

    • Assouad-type dimensions and the local geometry of fractal sets 

      Rutar, Alex (2024-12-03) - Thesis
      We study the fine local scaling properties of rough or irregular subsets of a metric space. In particular, we consider the classical Assouad dimension as well as two variants: a scale-refined variant called the Assouad ...

    • Separability properties of semigroups and algebras 

      O'Reilly, Gerard Aidan (University of St Andrews, 2021-11-30) - Thesis
      Separability properties can be seen as generalisations of residual finiteness. In this thesis we investigate four such properties: monogenic subalgebra separability, weak subalgebra separability, strong subalgebra ...

    • Groups defined by language theoretic classes 

      Al Kohli, Raad Sameer Al Sheikh (2024-06-11) - Thesis
      In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups. We show this class is ...

    • Rearrangement groups of connected spaces 

      Khalid, Nayab (University of St Andrews, 2020-07-28) - Thesis
      We develop a combinatorial framework that assists in finding natural infinite “geometric” presentations for a large subclass of rearrangement groups of fractals – defined by Belk and Forrest, namely rearrangement groups ...

    • 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 ...