Coarse Geometry of Groups and Spaces

The algebraic properties of groups are intricately linked with the geometric properties of the spaces they act on. For infinite groups, there are typically many choices of "natural" actions on geometric spaces. While these spaces may be locally very different, they have the same coarse (large-scale) structure. This creates a need for coarse interpretations of typical methods of measurement such as cardinality, dimension and connectivity, and also new forms of measurement building connections to other research areas including combinatorics, fractal geometry, topology and computer science. The goal of the PhD project will be to take one or more of these measurements and calculate its behaviour on some relevant classes of groups.

Entry requirements:

We are looking for an enthusiastic and highly-motivated graduate with

- a first class degree in Mathematics at the Master’s level (or equivalent);

- a strong background in group theory, and a a range of other topics in pure mathematics;

- good communication skills (oral and written).

The application procedure and the deadlines for scholarship applications are advertised at https://www.birmingham.ac.uk/study/postgraduate/subjects/mathematics-courses/pure-mathematics-phd