Constructive Representation Theory and its Applications

开发的算法将使确定一组对称可能最终实现为某一空间的变换的不同方式(表示)成为可能。这些知识在许多领域都是必需的，包括微分方程式、数字信号处理、工程(“支柱和缆索”结构)、电话网络设计、结晶学和量子信息处理。开发的高性能线性代数工具也将在密码学和编码理论中得到应用。这项工作代表了一个长期项目的最新阶段，该项目旨在发现用于阐明复杂代数结构性质的实用算法--澳大利亚在这一领域处于世界领先地位。

The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be  realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools for linear algebra developed will also find application in cryptography and coding theory. This work represents the latest stage in a long-term project to discover practical algorithms for elucidating the properties of complex algebraic structures - an area where Australia is a world-leader.