Noncommutative analysis for self-similar structure

这个纯数学项目的目的是开发新的数学技术，以便使用算子代数来理解自相似结构。分形和自相似在数学内外都有许多应用，但仍然非常神秘，而算符代数是量子力学的数学语言。这个项目期望在自相似和推进这两个领域的算子代数之间提供新的联系。预期的结果包括增加对自相似结构的理解，以及新的算子-代数现象和例子。好处包括澳大利亚在算符代数和更广泛的数学方面的能力不断增强，以及加强国际合作。

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.