Research Group: Topology

Research interests in the group broadly fall into two categories.

1. Polyhedral products . These are functorial generalisations of moment-angle complexes, which are central to toric topology. They unify a wide variety of of constructions from many different areas of mathematics, and the study of their homotopy theoretic properties has multiple applications. This is a new and rapidly growing subject with high impact.
2. Unstable homotopy theory . This is the modern formulation of classical homotopy theory. It is concerned with fundamental spaces that are of enduring interest, such as spheres, Moore spaces, Lie groups, and manifolds. The methods have wider application, and we use them to study spaces that arise in other areas of mathematics and physics, such as gauge groups, free loop spaces and configuration spaces.