The geometry of braids and triangulated categories

三角分类在几何、代数和拓扑学中起着核心作用。他们的研究可以揭示连接不同数学领域的深层结构。这个项目旨在用新颖的方法来回答关于三角分类及其对称性的基本问题。这些对称性是由辫状体编码的，辫状体是在科学领域有许多应用的重要对象。该项目有望通过刺激数学和计算机科学的研究而使澳大利亚受益。它将邀请与世界各地的顶尖专家和学生建立联系，并鼓励海外合作。对于网络安全来说，基于编织的新加密方案的发展是一个潜在的长期利益。

Triangulated categories play a central role in geometry, algebra, and topology. Their study can uncover deep structure connecting different areas of mathematics. This project aims to use novel approaches to answer fundamental questions about triangulated categories and their symmetries. These symmetries are encoded by braids, which are important objects with many applications across science. The project is expected to benefit Australia by stimulating research in mathematics and computer science. It will invite connections with leading experts and students around the world and encourage overseas collaboration. There is a potential long-term benefit to cybersecurity, towards the development of new encryption schemes based on braids.