A topic in fractal geometry

Roughly speaking, a fractal is an object which displays interesting geometrical features at arbitrarily small scales. Such objects appear naturally in numerous areas of pure and applied science and fractal geometry is the subject which tries to develop a rigorous mathematical framework for studying them.

This project will focus on, but not necessarily be limited to, the pure side of fractal mathematics. We will set out with an open mind and a flexible programme, but specific topics could include: the geometry of iterated function systems, dimension theory in dynamical systems, or multifractal analysis.

Since we are interested in infinitesimal properties, fractal geometry falls naturally under the umbrella of pure analysis. However, it has many links to other areas and would be appropriate for students with a background in: geometric measure theory, ergodic theory or dynamical systems, and could be linked when appropriate to: probability theory, number theory, hyperbolic geometry, Fourier analysis, functional analysis, harmonic analysis or aspects of topology.


Three SMSTC modules
University induction for new PhD students
University tutor training course
Weekly(approx) Pure Maths Colloquia