Interactions between geometric and topological structures

该项目旨在为高维几何想象开发必要的工具，并弥合低维和高维之间的差距。拓扑学是对空间形状的数学研究。几何赋予空间额外的结构，如距离、角度和曲率。模空间编码了将几何图形分配给空间的不同方式。该项目的预期成果包括可计算不变量的构建，实现问题的解决和对几何退化的理解。

This project aims to develop the necessary tools for a geometric imagination in higher dimensions and to bridge the gap between low and high dimensions. Topology is the mathematical study of the shape of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Moduli space encodes the different ways in which a geometry can be assigned to a space. Expected outcomes of the project include construction of computable invariants, solution of realisation problems and understanding degeneration of geometries.