Coarse Geometry of Groups and Spaces, Autumn 2022

Coarse embeddings (also known as ``uniform embeddings'', or ``placements'' in certain older papers) arise in fields as diverse as group theory, topology, Lorentzian geometry and theoretical computer science.

One key motivation for studying coarse embedding is that the inclusion of one finitely generated group into another is always a coarse embedding with respect to word metrics. We therefore view coarse embeddings as a natural geometric generalisation of subgroup inclusion amongst finitely generated groups.

The goal of this coarse is to study obstructions to coarse embeddings. While there are some classical invariants (growth and asymptotic dimension) which have been extensively studied, the majority of techniques in the course are extremely new, and as a result there are many fundamental open questions regarding them, as well as many elementary (at least to state!) open questions regarding the existence of coarse embeddings between various spaces.