Coarse Geometry of Groups and Spaces

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Monotone Coarse Invariants (MCIs) are POset valued Coarse-invariants of metric spaceswhich 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 examplesinclude Growth and Asymptotic Dimension. MCIs allow us to create obstructions toCoarse 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 projectis to further develop these MCIs as tools to tackle key problems in geometric grouptheory, fractal geometry, and beyond. This project falls under the EPSRC research theme 'Mathematical Sciences'.