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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Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces
(2017-08) - Journal articleIn this paper we show that the transfer operator of a Rauzy–Veech–Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and ... -
Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups
(2017-05-09) - Journal articleThe purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the ... -
Constructing 2-generated subgroups of the group of homeomorphisms of Cantor space
(University of St Andrews, 2017) - ThesisWe study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we ... -
Decision problems for word-hyperbolic semigroups
(2016-07-22) - Journal articleThis paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be ... -
Generalized Bernstein polynomials and total positivity
(University of St Andrews, 1999) - Thesis"This thesis submitted for Ph.D. degree deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a one-parameter family of polynomials. It also provides ...
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