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

  • 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 ...
  • Diameters of graphs related to groups and base sizes of primitive groups 

    Freedman, Saul Daniel (2022-11-29) - Thesis
    In this thesis, we study three problems. First, we determine new bounds for base sizes b(G,Ω) of primitive subspace actions of finite almost simple classical groups G. Such base sizes are useful statistics in computational ...
  • Synchronisation and separation permutation groups through graphs 

    Aljohani, Mohammed (2022-06-14) - Thesis
    About 15 years ago, Araújo, Arnold and Steinberg introduced the notion of synchronisation to the theory of finite permutation groups. Synchronisation property is closely related to another property which is called separation, ...
  • Base size and generating graphs of primitive permutation groups 

    Kelsey, Veronica (University of St Andrews, 2022-06-14) - Thesis
    In this thesis we consider base size and properties of the generating graph for finite groups. Let Ω = {1,...,n}, let Sₙ = Sym({1,...,n}) and let G ≤ Sₙ. A base for G is a sequence Λ = (ω₁, . . . , ωₖ) of points in Ω ...
  • On singular pencils of matrices 

    Ledermann, Walter (University of St Andrews, 1936) - Thesis
    "This thesis is a study of Singular Matrix Pencils under various aspects. In part (I) a new derivation of the Canonical Form of matrix pencils is given. This suggests investigation of the transformations of a pencil into ...

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