Symmetry: Groups, Graphs, Number Fields and Loops

利用对称性可以大大简化复杂的数学问题。本项目旨在应用有限单群的强大分类来推进我们对数域、高度对称图和与拉丁平方相关的代数结构的内部结构的理解。该项目希望利用群论产生新的结构和分类。预期的结果包括解决每个领域的主要开放问题，以及研究基于群体行为的代数和组合结构的创新方法。预期的好处包括加强国际合作，培养训练有素的数学家，以加强澳大利亚在基础科学领域的研究地位。

Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major open problems in each area as well as innovative methods for studying algebraic and combinatorial structures based on group actions. Expected benefits include enhanced international collaboration, and highly trained mathematicians to strengthen Australia’s research standing in fundamental science.