I work in geometric group theory. I study infinite discrete groups via associated metric spaces, Riemannian manifolds, graphs and cell complexes, and I focus on geometric features such as curvature, the shapes of balls, and characteristics of discs spanning loops (which can be called soap-film ge...
I work in geometric group theory. I study infinite discrete groups via associated metric spaces, Riemannian manifolds, graphs and cell complexes, and I focus on geometric features such as curvature, the shapes of balls, and characteristics of discs spanning loops (which can be called soap-film geometry). The setting for much of my research to date has been the geometry of the word problem for groups — a meeting-point of algebra, algorithmic complexity, geometry, topology and formal languages. My work has also touched on graph theory and cryptography.