Geometric structures in representation theory

数学支撑着人们与自然（如物理学）以及人与人之间（如金融）互动的各个方面。它的用途从制定物理定律以理解和预测自然，到分析金融概念和交易。本计画将拟定并发展三个新的基本数学概念：元胞代数、特征空间几何和图解代数。好处包括加强澳大利亚在世界一流数学研究的前沿地位，以及在物理学、编码理论、信息技术、电子安全和实验设计方面的无数潜在应用。

Mathematics underpins every aspect of people's interactions with nature (e.g. physics) and with each other (e.g. finance). Its uses range from formulating physical laws in order to understand and predict nature, to analysis of financial concepts and transactions. This project will formulate and develop three new fundamental mathematical concepts: cellular algebras, eigenspace geometries, and diagram algebras. Benefits include enhancement of Australia's position at the very frontier of world class mathematical research, and a myriad of potential applications to physics, coding theory, information technology, electronic security and experimental design.