Cluster Algebras and their implementation on the computer

研究背景这个项目将着眼于纯数学中相对较新的主题，即簇代数和曲面的三角剖分的组合学。重点将放在探索簇代数之间的自然映射上。在此背景下，将探索团簇代数的极限，从而为理解无限秩团簇组合学中的组合现象及其在数学物理领域的可能应用铺平道路。这属于EPSRC涵盖的数学科学研究的范围，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。目的和目标寻找方法扩展当前受限的簇代数范畴的概念，并根据簇代数的限制来正式解释组合现象，以期在数学物理和计算机科学中应用。研究方法论新奇：该项目的中心方法是通过在符号计算软件中实现簇代数来实现。

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.