Pure Mathematics

 

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

  • 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 ...

  • 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; ...

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