The geometry of braids and triangulated categories

辫子的几何形状和三角类别

• 批准号: DE240100447
• 负责人: Dr Asilata Bapat
• 金额: $ 30.39万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE240100447
• 关键词: geometry; braids; triangulated; categories

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.

三角类别在几何，代数和拓扑中起着核心作用。他们的研究可以发现连接数学不同领域的深层结构。该项目旨在使用新颖的方法来回答有关三角类别及其对称性的基本问题。这些对称性是由辫子编码的，辫子是具有许多科学应用的重要对象。预计该项目将通过刺激数学和计算机科学研究来使澳大利亚受益。它将邀请与世界各地的主要专家和学生建立联系，并鼓励海外合作。网络安全具有潜在的长期利益，以制定基于辫子的新加密方案。