Symmetries in CR-geometry. This project aims at investigating symmetries of geometric objects called CR-manifolds. It is expected to open new avenues for understanding such symmetries at the infinitesimal level and lead to ground-breaking results in CR-geometry. Expected outcomes include new methodology, solving long-standing problems, and establishing international research collaborations. The benefits are in enhancing the strength of the research in analysis and geometry performed in Australia ....Symmetries in CR-geometry. This project aims at investigating symmetries of geometric objects called CR-manifolds. It is expected to open new avenues for understanding such symmetries at the infinitesimal level and lead to ground-breaking results in CR-geometry. Expected outcomes include new methodology, solving long-standing problems, and establishing international research collaborations. The benefits are in enhancing the strength of the research in analysis and geometry performed in Australia, in fostering the international competitiveness of Australian research and in high-quality research training.Read moreRead less
Nilpotent associative algebras and spherical hypersurfaces. This project concerns pure basic research in mathematics and is based on an important recently discovered relationship between certain geometric and algebraic objects. In the project, this relationship will be applied in a novel way to solve several significant long-standing problems in the research area of complex geometry.
The Reconstruction and Recognition Problems for Hypersurface Singularities. This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Arti ....The Reconstruction and Recognition Problems for Hypersurface Singularities. This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Artinian Gorenstein algebras, this project proposes to clarify the nature of this relationship and utilise it for solving related geometric and algebraic problems. In particular, it aims at obtaining a groundbreaking result in the area of classical invariant theory.Read moreRead less
Proper Group Actions in Complex Geometry. The results of the project will enhance Australia's performance in several key mathematical areas as well as mathematical applications to physics critical for expanding Australia's knowledge base and research capability. The project has strong international aspects, it will foster the international competitiveness of Australian research and establish long-term collaborations between Australian researchers and high profile world experts in the area of the ....Proper Group Actions in Complex Geometry. The results of the project will enhance Australia's performance in several key mathematical areas as well as mathematical applications to physics critical for expanding Australia's knowledge base and research capability. The project has strong international aspects, it will foster the international competitiveness of Australian research and establish long-term collaborations between Australian researchers and high profile world experts in the area of the proposal. It will create an opportunity for a Ph.D. graduate to be involved in top-class research as a Research Associate, and will attract Ph.D. and honours students thus enabling research training in a high-quality mathematical environment.Read moreRead less
Symmetry and geometric structures. This is a fundamental research project in mathematics, especially concerned with the interaction between symmetry, differential equations, and geometry. Based on many classical and recently discovered instances, the aim of the project is to use symmetries to build and understand curved geometric structures from their flat counterparts.
Thermo-electro-chemo-mechanical properties of biological systems. The proposal is aimed at developing a new theoretical framework for piezoelectric biological materials and structures, through theoretical analysis, computation and numerical simulations, as well as experimental investigations, to produce high-reliability, high-performance hydrogel components and smart soft tissue structures. It is envisaged that successful outcomes of this program will give the Australian biological industry a te ....Thermo-electro-chemo-mechanical properties of biological systems. The proposal is aimed at developing a new theoretical framework for piezoelectric biological materials and structures, through theoretical analysis, computation and numerical simulations, as well as experimental investigations, to produce high-reliability, high-performance hydrogel components and smart soft tissue structures. It is envisaged that successful outcomes of this program will give the Australian biological industry a technology edge over their competitors and provide easy-to-use guidelines for the design of smart biological systems.Read moreRead less
Structures and properties of tissue engineering matrices for cartilage and bone: Imaging, visualising and modelling tissue/scaffold constructs in 3D. Tissue engineering of bone and cartilage has the potential to lower costs and improve outcomes. The first stage requires the design of porous 3D scaffolds. To date they have been found less than ideal for clinical applications. Our ability to design and optimise scaffolds has been ad hoc, as local structure and properties have not been measurable ....Structures and properties of tissue engineering matrices for cartilage and bone: Imaging, visualising and modelling tissue/scaffold constructs in 3D. Tissue engineering of bone and cartilage has the potential to lower costs and improve outcomes. The first stage requires the design of porous 3D scaffolds. To date they have been found less than ideal for clinical applications. Our ability to design and optimise scaffolds has been ad hoc, as local structure and properties have not been measurable during tissue growth and repair. In this proposal, an interdisciplinary group from three universities will utilise microCT imaging, visualisation and numerical modelling to determine these structures and properties. This will provide an invaluable understanding for the further development of tissue engineering scaffolds.Read moreRead less
Structural Characterization of Ion Beam Synthesized Metallic Nanocrystals using Advanced Synchrotron based Analytical Techniques. Metallic nanocrystals formed by ion implantation represent a highly relevant class of nanomaterials with significant potential applications in communication technology. A detailed understanding of the structure of such crystals, as proposed in the project, will yield considerable information for efficient utilization of ion beam synthesized nanocrystals. This will enh ....Structural Characterization of Ion Beam Synthesized Metallic Nanocrystals using Advanced Synchrotron based Analytical Techniques. Metallic nanocrystals formed by ion implantation represent a highly relevant class of nanomaterials with significant potential applications in communication technology. A detailed understanding of the structure of such crystals, as proposed in the project, will yield considerable information for efficient utilization of ion beam synthesized nanocrystals. This will enhance Australia's strength in nanotechnology and materials science and create the potential for technical innovation. Furthermore, this project will produce significant know-how in synchrotron based analytical techniques which is invaluable with respect to future research at the forthcoming Australian synchrotron facility.Read moreRead less
Tailoring superconducting hybrid multilayered film systems for electric and electronic applications. This project focuses on the development of new scientific and technological aspects of the fabrication, properties and operation of novel hybrid systems for revolutionizing electricity handling and electronics. It will also solve some existing problems of film structures with promising multilayer technology. Hybrid systems, often make the headlines in science and are gaining an increasingly promi ....Tailoring superconducting hybrid multilayered film systems for electric and electronic applications. This project focuses on the development of new scientific and technological aspects of the fabrication, properties and operation of novel hybrid systems for revolutionizing electricity handling and electronics. It will also solve some existing problems of film structures with promising multilayer technology. Hybrid systems, often make the headlines in science and are gaining an increasingly promising outlook in materials engineering, nanotechnology and electronics, promising eventual application in a broad range of industries. This project will establish Australia's capability at the forefront in this area. The outcomes predicted will benefit existing Australian companies and may establish new companies dealing with these hybrid systems.Read moreRead less