Complexity of group algorithms and statistical fingerprints of groups

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This project aims to shape the next generation of efficient randomised algorithms in the field of group theory, the mathematics of symmetry. Fundamental mathematics underpins modern technological tasks such as web searches, sorting and data compression. This project aims to determine characteristic statistical fingerprints of key building-block groups. These group statistics lead to much faster procedures to essentially factor huge groups into smaller building-block groups in a manner akin to factoring an integer into its prime factors. The anticipated goal is to include the outcomes in publicly available symbolic algebra computer packages. As the theory of symmetry has broad applications in the mathematical and physical sciences, there is the potential for far reaching benefits.