Coarse geometry is the study of geometric properties that are invariant under "uniformly bounded error". For example, we can use this language to make precise the idea that the integers Z, the real line R and the direct product of R with any compact set K have the same large scale geometric features (i.e. they are coarsely equivalent). The modern language of coarse geometry was developed by Roe following his investigations on index theory, Roe algebras and assembly maps. It also arises naturally in the framework of geometric group theory.
This course will introduce the language of coarse geometry, with emphasis on its most geometric aspects. Among the topics that will be covered there are coarse invariants, coarse embeddings in Hilbert spaces, Roe-like C*-algebras and rigidity results.
The course is fairly self contained. Some basic knowledge of general topology, differential geometry and functional analysis may be helpful. Knowledge of geometric group theory would help with intuition and motivation. The main reference for the course is Roe's book "Lectures on Coarse Geometry".
- Lehrende/r: Federico Vigolo