The geometry of braids and triangulated categories

Humans have braided hair and textiles into fascinating patterns for thousands of years. A mathematical study of these complex patterns can significantly advance many scientific fields. These include cryptography, quantum computing, fluid flow, protein folding, chemistry, and robotics. This project will use cutting-edge ideas to better understand the mathematics behind braids, with the intention to deepen Australian expertise in several areas of mathematics. Future applications could advance Australia's leadership across a variety of sciences. Importantly, the project has potential to generate new encryption schemes based on braids. These will help keep Australians safe from the increasing risk of digital threats. Thus the project will potentially strengthen Australia's position in cybersecurity.