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.
Read moreRead less
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.
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.
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
Development of advanced lithium ion battery and battery management system for electric /hybrid electric vehicle applications. This project represents a significant scientific and economic development for Australia as it aims to create advanced, high performing, energy storage devices with a focus on safety, that will provide enormous benefits for the environment. An added advantage will be the establishment of local and national expertise in the area of electrochemical energy storage systems, th ....Development of advanced lithium ion battery and battery management system for electric /hybrid electric vehicle applications. This project represents a significant scientific and economic development for Australia as it aims to create advanced, high performing, energy storage devices with a focus on safety, that will provide enormous benefits for the environment. An added advantage will be the establishment of local and national expertise in the area of electrochemical energy storage systems, that will place Australia at the forefront of lithium ion battery research and development. Flow-on benefits will also be created for Australian organizations involved in the manufacturing of electric vehicles and portable devices.Read moreRead less
The development of super-toughened epoxies using a novel nanomaterial. Epoxy resins are widely used as structural adhesives and coatings in engineering structures. This project will address the problem of the intrinsic brittleness of epoxy by making it significantly tougher with superior performance and cost-effectiveness. Our technology for producing super-toughened epoxy will lead to a wide range of applications for new and existing products in the construction, automotive, aerospace, adhesive ....The development of super-toughened epoxies using a novel nanomaterial. Epoxy resins are widely used as structural adhesives and coatings in engineering structures. This project will address the problem of the intrinsic brittleness of epoxy by making it significantly tougher with superior performance and cost-effectiveness. Our technology for producing super-toughened epoxy will lead to a wide range of applications for new and existing products in the construction, automotive, aerospace, adhesive and microelectronics industries.Read moreRead less
Advanced Nanoscale Materials Engineered from Diatomaceous Earth. Using natural materials of diatomaceous earth (DE) as a cheap and available resource by applying synthetic routes this project is directed towards the innovative development of new nanoscale materials with advanced properties. New mesoporous materials with intricate 3-D structures and nano sized features will be engineered from diatom silica for use in demanding applications such as separation and catalysis. These research outcomes ....Advanced Nanoscale Materials Engineered from Diatomaceous Earth. Using natural materials of diatomaceous earth (DE) as a cheap and available resource by applying synthetic routes this project is directed towards the innovative development of new nanoscale materials with advanced properties. New mesoporous materials with intricate 3-D structures and nano sized features will be engineered from diatom silica for use in demanding applications such as separation and catalysis. These research outcomes will enhance Australia's capacity in frontier technology and advanced materials, as well as bringing a competitive advantage to local industry through the development of such advanced materials.Read moreRead less
Novel Waterborne Multifunctional Sealer for Asphalt Pavement. One of the long-term challenges and most serious problems faced by the asphalt surfacing and road construction industry is the rapid deterioration of asphaltic surfaces to the extent that they become unfit/unsafe for use in short time. The length of the Australian local government road system is approximately 810,000 kilometres and currently approximately $2,460 million/year is spent on road maintenance; the replacement value of ....Novel Waterborne Multifunctional Sealer for Asphalt Pavement. One of the long-term challenges and most serious problems faced by the asphalt surfacing and road construction industry is the rapid deterioration of asphaltic surfaces to the extent that they become unfit/unsafe for use in short time. The length of the Australian local government road system is approximately 810,000 kilometres and currently approximately $2,460 million/year is spent on road maintenance; the replacement value of the road asset exceeds $106,000 million. Thus providing satisfactory tough protective shield on asphalt pavements that locks out destructive elements and provide long-term protection is of enormous economic importance and national/community benefit.Read moreRead less