Local-Global Interactions in Combinatorics

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A fundamental question in many parts of the mathematical sciences is how local and global structure interact. For instance, what can we say about the local structures of a large, complicated network? How is global structure constrained by what we see locally? Problems of this type arise in many areas, including for example model theory, geometric group theory, topology, combinatorics, computer science, statistical physics, biology, probability, network science, and data analysis. Practical examples include DNA sequencing, where fragments of a genetic sequence need to be assembled to a global sequence, and problems in big data, where the global structure is too large to access directly and its properties must be inferred from 'local' information. The aim of this research is to address fundamental questions about the relationship between local and global structure in graphs and networks. This will generate new theory and new structural understanding, as well as leading to new insights into the analysis of algorithms.