Geodetic groups: foundational problems in algebra and computer science

大地测量群：代数和计算机科学的基础问题

• 批准号: DP210100271
• 负责人: Prof Murray Elder
• 金额: $ 30.62万
• 依托单位: University of Technology Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210100271
• 关键词: Geodetic; groups; foundational; problems; algebra

The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being geodetic is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations. The project team's expertise in geodesic properties of groups, the interaction between formal languages and groups, and the theory of rewriting systems, together with recent breakthroughs by the team ensures that significant results can be expected. Benefits include training research students and postdoctoral researchers in cutting-edge techniques, and advancing fundamental knowledge in mathematics and computer science.

该项目旨在解决几何群论和理论计算机科学中重要且长期存在的开放性问题。自20世纪80年代以来，研究人员推测，geodetic的几何性质等同于几个纯粹的代数、算法和语言理论特征。