Mathematical Sciences: Rewriting Systems and Geometric Group Theory

数学科学：重写系统和几何群论

• 批准号: 9623088
• 负责人: Susan Hermiller
• 金额: $ 5.82万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623088&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rewriting; Systems; Geometric

9623088 Hermiller This grant supports the research of Professor S. Hermiller to work on problems in geometric group theory. She will study rewriting systems for Artin groups, triangles of groups and small cancellation products of groups in the hope of finding normal forms or automatic structures. She will also study extensions of the properties of almost convexity and rational growth that will be independent of presentation. She also hopes to extend the theory of finite derivation type to higher dimensions. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.

小行星9623088 这项拨款支持S教授的研究。赫米勒工作的问题，几何群论。她将研究重写系统阿廷组，三角形的群体和小取消产品的群体，希望找到正常的形式或自动结构。她还将研究几乎凸性和理性增长的属性的扩展，这将是独立的演示。她还希望将有限导出类型的理论扩展到更高的维度。 这是群论领域的研究。群论可以被认为是对抽象对称性的研究。因此，这一领域直接应用于物理和化学的许多领域。此外，在过去的30年里，许多与数据传输问题有关的问题已经用群论的技术解决了。也有直接连接到纠错码是至关重要的现代计算，如与光盘的工作。