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.
Read moreRead less
Surfacing urban wetlands in two urban renewal sites in Sydney. Urban wetlands in Australia provide benefits for climate change mitigation, pollution reduction, habitat provision and socioecological connection. However, in large cities like Sydney, urban wetlands are unseen because undergrounded, and, therefore not adequately understood. This illegibility, and loss of understanding by residents, planners and policy makers impedes wetlands' good management. This project surfaces wetlands through v ....Surfacing urban wetlands in two urban renewal sites in Sydney. Urban wetlands in Australia provide benefits for climate change mitigation, pollution reduction, habitat provision and socioecological connection. However, in large cities like Sydney, urban wetlands are unseen because undergrounded, and, therefore not adequately understood. This illegibility, and loss of understanding by residents, planners and policy makers impedes wetlands' good management. This project surfaces wetlands through visualisation in a multimodal knowledge platform focusing on two urban renewal sites, Green Square and Marrickville South. We leverage design ethnography to develop resources for strengthening multiple stakeholders’ socioecological engagement through methods empowering just, creative and open participation.Read moreRead less
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.
Read moreRead less
Gravity and quantum-limited measurements with a fundamental minimum length. This project aims to investigate the effects of a fundamental minimum length on the nature of gravity and on how accurately we can make measurements in our world. The key challenge is to combine our best theories of fundamental physics to model what happens at ultra-short distances. This project will generate new knowledge at this interface by using a novel approach inspired by information theory. The expected outcomes a ....Gravity and quantum-limited measurements with a fundamental minimum length. This project aims to investigate the effects of a fundamental minimum length on the nature of gravity and on how accurately we can make measurements in our world. The key challenge is to combine our best theories of fundamental physics to model what happens at ultra-short distances. This project will generate new knowledge at this interface by using a novel approach inspired by information theory. The expected outcomes are new connections between fundamental limitations on measurements, the nature of gravitation, and ultra-small-scale quantum physics. The benefit of this work is breaking the logjam in answering the most important open question in all of physics: how to unite quantum theory and gravitation.Read moreRead less
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
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.
Read moreRead less