Coarse Geometry of Groups and Spaces

单调粗不变量（MCIs）是度量空间的偏置值粗不变量，它对粗嵌入表现单调性，即如果X粗嵌入Y，则X和Y的不变量，例如fX和fY满足fX fY。经典的例子包括增长和渐近维数。MCIs允许我们创建粗嵌入的障碍。在过去的十年中，mci的数量和多样性急剧增加，新的mci受到组合学、分析学、拓扑学、电网络理论和神经网络等技术的启发。该项目的目标是进一步发展这些MCIs，使其成为解决几何群论、分形几何等关键问题的工具。该项目属于EPSRC的研究主题“数学科学”。

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'.