Finite linearly representable geometries and symmetry

有限线性可表示的几何形状和对称性

• 批准号: DP140100416
• 负责人: Prof Cheryl Praeger
• 金额: $ 33.07万
• 依托单位: The University of Western Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2019-05-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100416
• 关键词: Finite; linearly; representable; geometries; symmetry

Finite geometry has profound mathematical connections to the theory of symmetry. Advances in finite geometry and in symmetry have historically led to advances in diverse areas such as algebra, computing, and theoretical physics. The project aims to characterise basic geometric objects called "projective planes'' and "generalised polygons'' using their symmetry properties. To achieve these aims, conceptual links between certain elements in classical symmetry groups and geometric planes and polygons must be developed. The density of these certain elements has important applications to probabilistic geometric algorithms.

有限几何与对称理论有着深刻的数学联系。有限几何和对称性的进步在历史上导致了不同领域的进步，如代数，计算和理论物理。该项目的目的是利用它们的对称性来描述被称为“投影平面”和“广义平面”的基本几何对象。为了实现这些目标，必须发展经典对称群中某些元素与几何平面和多边形之间的概念联系。这些特定元素的密度在概率几何算法中有重要的应用。