School of Mathematics and Statistics

Analysis Research Group

Group Members


  • Collin Bleak

    My research is in studying infinite groups of homeomorphisms via properties of their actions. In this study I employ tools from various fields including algebra, theoretical computer science, combinatorics, symbolic dynamical systems, and analysis. Webpage.

  • Kenneth Falconer

    My research centres around the geometry of fractals and multifractals, geometric measure theory, dimension theory, dynamical systems and probability. Specific topics include self-affine sets and measures, sections and projections of fractals, random fractals and stochastic processes, and applications of fractals to other areas. Webpage.

  • Jonathan Fraser

    My research interests centre on fractal geometry and its connections with other areas of mathematics, such as: geometric measure theory, ergodic theory, Fourier analysis, and hyperbolic geometry. Particular topics include: self-affine sets, self-similar sets with overlaps, limit sets of Kleinian groups, and Fourier transforms of random measures associated with Brownian motion. Webpage.

  • Jonathan Hickman

    My interests lie in Euclidean harmonic analysis, in particular questions pertaining to operators whose definition depends on some submanifold of Rn such as Fourier restriction/extension operators and generalised Radon transforms. I am also interested in discrete analogues of these objects. Webpage.

  • James Mitchell

    My main research concerns semigroup theory, combinatorics and topology, including studying algebraic and combinatorial properties of functions defined on topological spaces. Webpage.

  • Lars Olsen

    My research covers all aspects of fractal and multifractal geometry and geometric measure theory, including work on self-affine sets and measures, fractal defined by digits of numbers, typical structure of fractal sets and measures, etc. Webpage.

  • Mike Todd

    I work in ergodic theory and dynamical systems, applying ideas from probability and thermodynamic formalism to study expansion and recurrence properties of, mostly, smooth low dimensional systems. Topics include Return Time Statistics, Extreme Value Theory, statistical stability, equilibrium states, phase transitions and transience. Webpage.

Emeritus Staff

  • John McCabe

    My research interests have generally been in rational approximation, and pade approximation and the related continued fractions in particular. In collaboration with others, mainly overseas and including my Ph.D students, I have worked on strong moment problems. Webpage.

  • George Phillips


Ph.D Students

  • Stuart Burrell

    I'm interested in a broad array of topics in fractal geometry, most recently the dimension theory of inhomogeneous sets. Webpage.

  • Douglas Howroyd

    I am currently interested in fractal geometry and dimension theory, notably the study of self-affine sponges. Webpage.

  • Nayab Khalid

    I study the groups of homeomorphisms (rearrangements) of self-similar spaces (fractals). The dynamical properties I'm studying include generation, conjugacy and centralizers - among other things.

  • Lawrence Lee

    I'm currently interested in the dimension theory of self-affine measures. I'm also interested in applications of fractal geometry to other areas of mathematics, particularly Diophantine approximation.

  • Han Yu

    My research interest include dimension theory of fractal geometry, ergodic theory, dynamical systems and number theory. Webpage.

Recent Staff

Recent Ph.D Students