Noncommutative analysis for self-similar structure

自相似结构的非交换分析

• 批准号: DP220101631
• 负责人: Prof Aidan Sims
• 金额: $ 27.64万
• 依托单位: University of Wollongong
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220101631
• 关键词: Noncommutative; analysis; self; similar; structure

This project in pure mathematics aims to develop novel mathematical techniques for understanding self-similar structures using operator algebras. Fractals and self-similarity have many applications both within and outside mathematics, but remain deeply mysterious, while operator algebras are the mathematical language of quantum mechanics. This project expects to provide new connections between self similarity and operator algebras advancing both fields. Expected outcomes include increased understanding of self-similar structures, and novel operator-algebraic phenomena and examples. Benefits include growing Australia's capacity in operator algebras and mathematics more generally, and enhanced international collaboration.

纯数学中的该项目旨在开发新颖的数学技术，以使用操作员代数来理解自相似结构。分形和自相似性在数学内部和外部都有许多应用，但是仍然非常神秘，而操作员代数是量子力学的数学语言。该项目预计将提供自我相似性和运营商代数之间的新联系。预期的结果包括对自相似结构的了解，以及新型的操作员 - 地面现象和实例。好处包括增强澳大利亚在运营商代数和数学方面的能力，并增强了国际合作。