Research project: Coarse geometry of non-positively curved spaces
Non positively curved spaces play a central role in geometry, topology and geometric group theory. Natural examples arise from the study of right angled Artin groups, Coxeter groups, knot groups and limit groups. The work of Connes, Higson, Yu and others has shown that asymptotic properties, as encoded by coarse geometry, play a surprising role in determining their structure, linking the unitary representation theory of their fundamental groups with the topology of the spaces themselves.