Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic s ....Symmetry in Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic science and unexpected technological benefits can easily arise (for example, in medical imaging). Fundamental mathematical research is absolutely necessary if Australia is to maintain a presence on the international scientific stage.
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Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular i ....Classification and Invariants in Complex Differential Geometry. Differential geometry is the study of shape using calculus and differential equations. This is a fundamental research project in this area. Complex differential geometry refers to geometry based on the complex numbers, generally a rich and intriguing setting. Geometries will be distinguished by the construction of suitable invariants, both algebraic and analytic. Classification problems will be solved by these means. Of particular interest are geometries with a high degree of symmetry, a critical feature that pervades both mathematics and physics. Twistor theory provides the unifying theme for this project.Read moreRead less
Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, c ....Homotopical structures in algebraic, analytic, and equivariant geometry. This is a project for fundamental research in pure mathematics. It is focused on an emerging subfield of complex geometry concerned with spaces and maps that exhibit exceptional flexibility properties, which often go hand-in-hand with a high degree of symmetry. The project aims to develop the foundations of this new area, solve several open problems, and pursue interconnections with and applications to algebraic geometry, complex analysis, geometric invariant theory, and topology.Read moreRead less
Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
The impact of strategic alignment on IT outsourcing success in a complex service setting. Improved conceptual and methodological understanding of strategic alignment is essential for better IT outsourcing decisions. This research will improve the performance of Australian industry by investigating how strategically well aligned ITO investments can lead to improved performance and greater competitive advantage.
Flexibility and symmetry in complex geometry. Differential equations play a fundamental role in science and technology. The aim of the project is to study important differential equations that arise in geometry, their symmetries, and obstructions to solving them.
A Platform for Rapid and Flexible Development of Context-Aware Web Services. Context awareness is one of the most exciting trends in computing today, and it holds the potential to make our daily life more productive, convenient and enjoyable. The proposed project will produce a comprehensive platform for developing context-aware Web services, which will facilitate ready implementation of many innovative applications and make important contributions to Australian society and the national economy. ....A Platform for Rapid and Flexible Development of Context-Aware Web Services. Context awareness is one of the most exciting trends in computing today, and it holds the potential to make our daily life more productive, convenient and enjoyable. The proposed project will produce a comprehensive platform for developing context-aware Web services, which will facilitate ready implementation of many innovative applications and make important contributions to Australian society and the national economy. One such application is an intelligent seniors assistance service that will improve quality of life for senior citizens while helping them maintain an independent lifestyle. This project will also place Australia at the forefront of Web service development.Read moreRead less
Normalizing XML Documents. Our work will be of great benefit, both to the research community and to the ICT industry. The project addresses one of the most important problems in XML usage and we expect our results to be published in important international forums, as has our preliminary research on the topic. This will significantly improve Australia's reputation in research in the ICT area. In the longer term, we intend to build commercial software tools based on the results of our research ....Normalizing XML Documents. Our work will be of great benefit, both to the research community and to the ICT industry. The project addresses one of the most important problems in XML usage and we expect our results to be published in important international forums, as has our preliminary research on the topic. This will significantly improve Australia's reputation in research in the ICT area. In the longer term, we intend to build commercial software tools based on the results of our research and this will be of direct benefit to the Australian economy and the Australian ICT industry.Read moreRead less
Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
Integration of Object Behavior in Federated Information Systems. Integration of autonomous object-oriented systems requires the integration
of object structure and object behaviour. Research in federated information
systems has so far mainly addressed integration of object structure. This
project will investigate the integration of object behaviour, especially object
life cycles. A major application area is the integration of business processes,
which is typically required when companies me ....Integration of Object Behavior in Federated Information Systems. Integration of autonomous object-oriented systems requires the integration
of object structure and object behaviour. Research in federated information
systems has so far mainly addressed integration of object structure. This
project will investigate the integration of object behaviour, especially object
life cycles. A major application area is the integration of business processes,
which is typically required when companies merge or enter into
consumer-producer relationships and constitutes a key capability for B2B e-commerce
systems. Consistency criteria for behaviour integration
will be defined and applied in a graphical integration tool that guides the
definition of global behavioural views upon autonomous object-oriented systems.
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