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.

该纯数学项目旨在开发新颖的数学技术，使用算子代数来理解自相似结构。分形和自相似性在数学内外都有许多应用，但仍然很神秘，而算子代数是量子力学的数学语言。该项目期望在自相似性和算子代数之间提供新的联系，推动这两个领域的发展。预期成果包括增强对自相似结构的理解以及新颖的算子代数现象和示例。好处包括提高澳大利亚在算子代数和数学方面的能力，并加强国际合作。