Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
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Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and sta ....Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and statistical mechanics and is likely to have flow-on effects in real-world disciplines such as network communication. This project will also strengthen Australia's international presence in discrete mathematics and will further strengthen ties between Australian and international mathematicians.Read moreRead less
Global Lithospheric Architecture Mapping II. The continents have been rifted, or broken up, and collided, or re-assembled, along major zones of weakness many times throughout Earth's history. Boundaries between such continental domains focus large-scale movements of fluids that can produce giant ore deposits. This study will provide new perspectives on the localisation of world-class economic deposits, the Earth resources on which society depends. Innovations in imaging the deep Earth beneath co ....Global Lithospheric Architecture Mapping II. The continents have been rifted, or broken up, and collided, or re-assembled, along major zones of weakness many times throughout Earth's history. Boundaries between such continental domains focus large-scale movements of fluids that can produce giant ore deposits. This study will provide new perspectives on the localisation of world-class economic deposits, the Earth resources on which society depends. Innovations in imaging the deep Earth beneath continents, and in numerical modelling, will maintain our high international profile in research relevant to National Priority 1.6 (Developing Deep Earth Resources). Unique 3D geological maps of regions down to 250km will make the composition of deep Earth regions newly accessible to geoscientists and all potential endusers.Read moreRead less