I am the Denman Baynes Fellow at Clare College, Cambridge, and a member of the Department of Pure Mathematics and Mathematical Statistics.
I work in Geometric Group Theory -- a field of Mathematics that studies groups, and the geometric and topological spaces on which they act. Thus, I use geometry to understand groups, and algebra to understand geometry. While this is the guiding principle, the tools and techniques of many other areas of Maths enrich and permeate the subject, making it into an ever-growing domain.
My research, specifically, concerns hyperbolic and non-positively curved groups and spaces, non-positively curved cube complexes, and the geometric topology of curves and surfaces; one stream of my work focuses on quantifying geometric and algebraic properties of groups and their topological counterparts, the other on producing examples and structural results.