The geometry of braids and triangulated categories

三角范畴在几何、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。这个项目的目的是使用新的方法来回答有关三角范畴及其对称性的基本问题。这些对称性由辫子编码，辫子是在科学上有许多应用的重要对象。该项目预计将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领先专家和学生建立联系，并鼓励海外合作。网络安全有一个潜在的长期利益，即开发基于辫子的新加密方案。

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.