Cluster Algebras and their implementation on the computer

簇代数及其在计算机上的实现

• 批准号: 2126134
• 金额: --
• 依托单位: University of Glasgow
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2126134
• 关键词: Cluster; Algebras; their; implementation; computer

Context of the ResearchThis project will look at the relatively new topic within pure mathematics, the combinatorics of cluster algebras and triangulations of surfaces. A particular emphasis will lie on exploring natural maps between cluster algebras. In this context, limits of cluster algebras will be explored, leading the way to understanding combinatorial phenomena in infinite rank cluster combinatorics and their possible applications in the area of mathematical physics. This falls within the remit of mathematical sciences research covered by EPSRC and will strengthen intradisciplinary links between different areas, algebra, combinatorics, mathematical physics.Aims and ObjectivesFind ways of extending the current, restricted, notion of a category of cluster algebras, and formally interpret combinatorial phenomena in terms of limits of cluster algebras with a view towards applications in mathematical physics and computer science.Novelty of Research Methodology: A central approach to the project is via the implementation of cluster algebras in symbolic computational software.

研究背景本项目将研究纯数学中相对较新的主题，簇代数的组合学和曲面的三角剖分。一个特别的重点将在于探索簇代数之间的自然映射。在这种情况下，集群代数的限制将被探索，导致的方式来理解组合现象在无限秩集群组合数学和它们可能的应用领域的数学物理。这福尔斯属于EPSRC所涵盖的数学科学研究的职权范围，并将加强不同领域，代数，组合学，数学物理之间的学科内联系。Aims and ObjectivesFind ways of extending the current，restricted，concept of a category of cluster algebras，并以簇代数的极限形式解释组合现象，以期应用于数学物理和计算机科学。新奇研究方法：该项目的一个中心方法是通过在符号计算软件中实现簇代数。