Tractable topological computing: Escaping the hardness trap

计算拓扑学是一个年轻而充满活力的领域，它利用计算机解决由纯数学驱动的复杂几何问题，并在生物学、信号处理和数据挖掘中有多种应用。一个主要的障碍是，这些问题中的许多被认为是根本性的、难以解决的难题。该项目旨在通过将几何技术与参数化复杂性领域的技术相融合，为这些问题创造强大而实用的解决方案，从而克服典型现实世界输入的这些障碍。它有望揭示理论与实践之间巨大而令人困惑的差距，并为研究人员提供快速的新软件工具，用于大规模实验和尖端的计算机证明。

Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project aims to defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from the field of parameterised complexity, creating powerful, practical solutions for these problems. It is expected to shed much-needed light on the vast and puzzling gap between theory and practice, and give researchers fast new software tools for large-scale experimentation and cutting-edge computer proofs.