Coarse Geometry of Groups and Spaces

Monotone Coarse Invariants (MCIs) are POset valued Coarse-invariants of metric spaces
which behave monotonically with respect to Coarse embeddings i.e if X coarsely em-
beds in Y the invariants for X and Y , say fX and fY satisfy fX fY . Classical examples
include Growth and Asymptotic Dimension. MCIs allow us to create obstructions to
Coarse embeddings. In the last ten years, the number and diversity of MCIs have in-
creased dramatically, with new MCIs inspired by techniques from combinatorics, anal-
ysis, topology, electrical network theory, and neural networks. The goal of the project
is to further develop these MCIs as tools to tackle key problems in geometric group
theory, fractal geometry, and beyond. This project falls under the EPSRC research theme 'Mathematical Sciences'.