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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  • Faithful semigroup diagram representations of homeomorphism groups 

    Stott, Liam Kevin (2024-12-03) - Thesis
    In this thesis we investigate two different classes of objects. The first is the class of Dénes cycles of a tree; we show a ‘strong’ correspondence between such cycles and certain partial orders on the edges of the tree. ...

  • Volume rigidity of simplicial complexes 

    Southgate, Jack Oliver (2024-12-03) - Thesis
    This thesis develops a theory of rigidity of frameworks of simplicial complexes subject to maximal-simplex-volume constraints inspired by the well-studied theory of rigidity of frameworks of graphs subject to edge-length ...

  • Disjoint and external partial difference families and cyclotomy 

    Johnson, Laura (2024-12-03) - Thesis
    In this Thesis, we introduce two new combinatorial objects known as Disjoint Partial Difference Families and External Partial Difference Families: these objects generalise Disjoint Difference Families (DDFs), External ...

  • Statistical properties and rare events for chaotic dynamical systems 

    Couto, Raquel (2024-12-03) - Thesis
    The application of Extreme Value Theory to Dynamical Systems has been a topic of interest for a few years now (see the influential work in [FFT10] which built on [Col01] and [FF08]) opening up a whole new framework for the ...

  • 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 ...

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