p-Adic Methods in Arithmetic Geometry. This project concerns algorithms for determining the number of
solutions to systems of polynomial equations over finite fields
by p-adic methods. Our goal is to determine a fundamental
invariant, the zeta function, appearing in arithmetic geometry,
whose characterization was the subject of the famous Weil
conjectures.
....p-Adic Methods in Arithmetic Geometry. This project concerns algorithms for determining the number of
solutions to systems of polynomial equations over finite fields
by p-adic methods. Our goal is to determine a fundamental
invariant, the zeta function, appearing in arithmetic geometry,
whose characterization was the subject of the famous Weil
conjectures.
We seek to understand and develop p-adic methods for determining
zeta functions, taking as point of departure the methods of Satoh
and Mestre for elliptic curves. Applications of this work include
public key cryptography and coding theory, having direct impact
in e-commerce and telecommunications.
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Avatars and Identities. The avatar, a virtual representation of its user, is the key element of interface technology for everyday computer use in the twenty-first century. While specialist aspects of the avatar have received intensive attention from the technology industries and scholars, the focus of the work to date has been on the technical efficiency of the interface, rather than understanding the full social implications of its use. Through a historical, ethnographic and critical analysis o ....Avatars and Identities. The avatar, a virtual representation of its user, is the key element of interface technology for everyday computer use in the twenty-first century. While specialist aspects of the avatar have received intensive attention from the technology industries and scholars, the focus of the work to date has been on the technical efficiency of the interface, rather than understanding the full social implications of its use. Through a historical, ethnographic and critical analysis of the role of the avatar, in consultation with industry, this project offers a unique opportunity to develop a wider perspective that will contribute to an understanding of the uses and policies for the digital economy.Read moreRead less
Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific lo ....Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific location. The research carried out will be in collaboration with international experts, creating and strengthening existing ties of Australian research institutions with other world class research institutes overseas.Read moreRead less
A Design History of Australian HIV/AIDS Public Health Campaigns 1983-2004. This project investigates the differing roles of governments and community organisations as influential factors in the formulation of graphic representations which characterise the prevention campaigns used in the HIV/AIDS epidemic in Australia 1983-2004. It explains how graphic representations, functioning as an index of official and public responses to the epidemic, impact on the aesthetic and professional autonomy of t ....A Design History of Australian HIV/AIDS Public Health Campaigns 1983-2004. This project investigates the differing roles of governments and community organisations as influential factors in the formulation of graphic representations which characterise the prevention campaigns used in the HIV/AIDS epidemic in Australia 1983-2004. It explains how graphic representations, functioning as an index of official and public responses to the epidemic, impact on the aesthetic and professional autonomy of the designer. Complimenting existing quantitative assessments this study uses a textual-visual analysis and triangulation method to demonstrate the agency of these institutional constraints placed within the broader range of material forms relating to the campaigns including brochures, posters, and videos.Read moreRead less
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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Fingerprinting the soil microbial metagenome. The understanding of the impact of current farming systems on soil biology is in its infancy. Technology previously used to examine soil biology only investigates a very small percentage of all soil organisms. We will use an innovative new technology (DArT) to rapidly gain an overview of all soil microbial biodiversity. We will then evaluate the impact of agricultural practices on that biodiversity, firstly based on our long term trial site exhibiti ....Fingerprinting the soil microbial metagenome. The understanding of the impact of current farming systems on soil biology is in its infancy. Technology previously used to examine soil biology only investigates a very small percentage of all soil organisms. We will use an innovative new technology (DArT) to rapidly gain an overview of all soil microbial biodiversity. We will then evaluate the impact of agricultural practices on that biodiversity, firstly based on our long term trial site exhibiting common farming practices, and then by a broader regional survey. Our longer term goal is to find microbiological indicators of healthy soil through a vastly improved ability to determine a wide range of beneficial and disease organisms to identify sustainable farming practices.Read moreRead less
Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's meth ....Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's methods will surprise some longstanding problems into submission and in particular will lead them to reveal full data on torsion on hyperelliptic curves of low genus.
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Signatures of Order, Chaos and Symmetry in Algebraic Dynamics. The project in the breakthrough science of algebraic dynamics will help inform and sustain both algebraic number theory and dynamical systems in Australia. Thus far, Australia is not well represented in this cutting edge international area, and international research prominence and teaching benefits will flow from the pioneering and innovative topics to be addressed. The research incorporates the synergy of an existing highly-product ....Signatures of Order, Chaos and Symmetry in Algebraic Dynamics. The project in the breakthrough science of algebraic dynamics will help inform and sustain both algebraic number theory and dynamical systems in Australia. Thus far, Australia is not well represented in this cutting edge international area, and international research prominence and teaching benefits will flow from the pioneering and innovative topics to be addressed. The research incorporates the synergy of an existing highly-productive international collaboration and creates possibilities for many more such linkages. It affords Australia a strategic opportunity to considerably increase its profile in the algebraic dynamics community, particularly in the Pacific region.Read moreRead less
Dynamic media: innovative social and artistic developments in new media in Australia, Britain, Canada and Scandinavia since 1990. This study will foreground strengths and remedy weaknesses in Australian new media arts and innovative social uses of new media. By studying the international strategies for social use of dynamic media, this study will provide information for Australians to more extensively implement dynamic media within a social context. It will highlight the innovation of Australian ....Dynamic media: innovative social and artistic developments in new media in Australia, Britain, Canada and Scandinavia since 1990. This study will foreground strengths and remedy weaknesses in Australian new media arts and innovative social uses of new media. By studying the international strategies for social use of dynamic media, this study will provide information for Australians to more extensively implement dynamic media within a social context. It will highlight the innovation of Australian artists and researchers in the development of dynamic media and position these internationally. A major long-term benefit of this study will be an online database that will both profile and be accessible to Australian artists, arts organizations, new media researchers and social innovators. Read moreRead less
Biofertiliser technology for improved yields and environmental sustainability of rice and wheat crops. Australia faces the double challenge of improving the efficiency of its crop production while minimising the agricultural impact on its fragile biodiversity. Our project will meet this challenge by providing the technology for using natural biofertilisers in cereal crops. This will reduce our heavy reliance on chemical fertilisers - with associated soil loss, salinity and acidity, and high dema ....Biofertiliser technology for improved yields and environmental sustainability of rice and wheat crops. Australia faces the double challenge of improving the efficiency of its crop production while minimising the agricultural impact on its fragile biodiversity. Our project will meet this challenge by providing the technology for using natural biofertilisers in cereal crops. This will reduce our heavy reliance on chemical fertilisers - with associated soil loss, salinity and acidity, and high demand on scarce water resources - and significantly increase our crop yields. Our advances will help Australian farmers to reduce the costs and increase the productivity of our substantial export crops while improving their environmental sustainability.Read moreRead less