Cluster Algebras and their implementation on the computer

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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.