Coarse Geometry of Groups and Spaces

Date: 12 - 16 July 2027

Location: ICMS, Edinburgh

Coarse embeddings are plentiful, natural and highly useful. One famous example of this is Yu’s proof that any (finitely generated) group admitting a coarse embedding into a Hilbert space satisfies the Novikov conjecture, a result which is particularly striking as it has since been proved that most “natural” classes of groups do admit such an embedding. Indeed, the only examples we have of groups which do not embed have been specifically constructed to have this property. This highlights a common theme in the area, progress on the existence and construction of coarse embeddings is comparatively very well understood, but (with the obvious exception of Yu’s result above) there are relatively few known consequences of a particular coarse embedding, as our understanding of obstructions to coarse embeddings has not progressed at the same pace.

Over the last 10 years this situation has changed dramatically. The coarse geometric approach has been employed in a much wider variety of settings (including Lorentz geometry, graph theory, fractal geometry and solid state physics), and a plethora of tools and techniques inspired by these different applications have been developed to obstruct coarse embeddings. This workshop is intended to bring together these different communities, to share current progress and major difficulties, and to introduce younger researchers to this family of ideas.