Unlocking the potential for linear and discrete optimisation in knot theory and computational topology

计算拓扑学是一个年轻而充满活力的领域，它利用计算机来解决复杂的几何问题，比如一圈绳子是否缠结。这种计算在数学中变得越来越重要，其应用跨越了生物学、物理学和信息科学，然而，除了最简单的情况外，该领域的许多核心问题仍然难以解决。该项目将几何技术与运筹学的强大方法（如线性和离散优化）结合起来，构建快速、强大的工具，首次可以系统地解决大型拓扑问题。从理论上讲，该项目对著名的开放性问题——快速多项式时间内的结度检测有重大影响。

Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.