Advanced Topics in Geometry
Asymptotic geometry is concerned with properties of metric spaces which are insensitive to small-scale structure. It is a well-known theme in many areas of mathematics, such as the geometry of Riemannian manifolds or singular spaces, geometric group theory, the theory of discrete subgroups of Lie groups, geometric topology (especially 3-manifolds), graph theory, and recently in theoretical computer science. The course will begin with asymptotic invariants such as growth rates, isoperimetric inequalities, coarse topology, and boundaries, followed by a discussion of Mostow rigidity and variants. Subsequent topics will chosen according to the interests of the audience.
