Symmetry and computation. The overall objective of the project is to explore connections between symmetry and computation, especially the theory and algorithms that facilitate the use of groups in computational science. The main outcome will be theoretically fast algorithms and implementations to drive applications in the sciences and for secure communication.
Group actions: combinatorics, geometry and computation. Science today relies on digital technologies using quantised and digital information. Because of the discrete nature of digital information, much of the mathematics underpinning these advances comes from the core disciplines of algebra and combinatorics within which this proposal falls. All aspects of the proposal focus on strengthening theoretical understanding of algebraic and combinatorial structures, and increasing computational power f ....Group actions: combinatorics, geometry and computation. Science today relies on digital technologies using quantised and digital information. Because of the discrete nature of digital information, much of the mathematics underpinning these advances comes from the core disciplines of algebra and combinatorics within which this proposal falls. All aspects of the proposal focus on strengthening theoretical understanding of algebraic and combinatorial structures, and increasing computational power for working with them. The fundamental research outcomes, in terms of theorems, algorithms, and the training of young research mathematicians, will thus both enhance the high international standing of Australian mathematics, and strengthen Australia's capabilities in these important areas.Read moreRead less
Complexity of group algorithms and statistical fingerprints of groups. 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 facto ....Complexity of group algorithms and statistical fingerprints of groups. 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.Read moreRead less