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.
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
Benchmarking the neurophysiology of human cortex models in vitro. This project aims to improve human brain models in vitro by developing an analytical tool benchmarking biophysical similarities to the adult human cortex. This project expects to generate new knowledge by testing for the first time the theory that integrating sensory-like inputs and awake/sleep-like cycles of electrical activity in vitro may complete the maturation of human brain organoid models. It will also generate new methods ....Benchmarking the neurophysiology of human cortex models in vitro. This project aims to improve human brain models in vitro by developing an analytical tool benchmarking biophysical similarities to the adult human cortex. This project expects to generate new knowledge by testing for the first time the theory that integrating sensory-like inputs and awake/sleep-like cycles of electrical activity in vitro may complete the maturation of human brain organoid models. It will also generate new methods to simplify the analysis of multimodal path-clamping data (Patch-seq). Expected outcomes will facilitate research collaboration and the reproducibility of accurate experimental replicates of the human brain. This will provide significant benefits in the global race to understand human brain computation mechanisms.Read moreRead less
EGF Peptide Signalling Improves Oocyte Maturation And Quality
Funder
National Health and Medical Research Council
Funding Amount
$586,891.00
Summary
Infertility is common and although IVF is widely accepted, the procedure is expensive and is associated with health risks. Using laboratory animals, we have developed significant new insights into mechanisms regulating egg quality. These insights have allowed us to develop a new approach to infertility treatment - crucially, one that eliminates the need for ovarian hormone therapy used in IVF. This project will investigate the basic mechanisms underlying our new approach to enable safe clinical ....Infertility is common and although IVF is widely accepted, the procedure is expensive and is associated with health risks. Using laboratory animals, we have developed significant new insights into mechanisms regulating egg quality. These insights have allowed us to develop a new approach to infertility treatment - crucially, one that eliminates the need for ovarian hormone therapy used in IVF. This project will investigate the basic mechanisms underlying our new approach to enable safe clinical implementation.Read moreRead less
Impaired Bone Remodelling Leads To Failure Of Orthopaedic Prostheses
Funder
National Health and Medical Research Council
Funding Amount
$515,917.00
Summary
The failure of bone prostheses is becoming a major health problem. More than 26,000 hip, and an equal number of knee, replacements were performed in Australia in 2002 with the number increasing between 5%-10% each year for the previous 10 years. Disturbingly, the incidence of revision hip surgery in Australia is now more than 15%, meaning that, despite the impressive success of joint replacement surgery, a significant number of arthroplasties fail. It is becoming more common for young, active in ....The failure of bone prostheses is becoming a major health problem. More than 26,000 hip, and an equal number of knee, replacements were performed in Australia in 2002 with the number increasing between 5%-10% each year for the previous 10 years. Disturbingly, the incidence of revision hip surgery in Australia is now more than 15%, meaning that, despite the impressive success of joint replacement surgery, a significant number of arthroplasties fail. It is becoming more common for young, active individuals to receive joint replacement surgery to improve their quality of life. This, combined with increasing life expectancy, and the known higher rate of failure of joint replacements in younger patients, means that the morbidity of a failed replacement, and the mobidity and associated mortality of revision surgery, will become an increasingly important health issue, with a major impact upon health budgets. The overwhelming majority of hip and knee prostheses have metal or ceramic on polyethylene bearing surfaces. It is now apparent that most implants fail due to bone loss around them leading to loosening, and evidence is accumulating that polyethylene wear particles are a major contributing factor to this process. It is therefore vital that we obtain better understanding of the causes of implant failure in order to extend the life of these implants and this project is designed to do so.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0989226
Funder
Australian Research Council
Funding Amount
$340,000.00
Summary
Multi-photon imaging for infection, immunity, and self recognition. This proposal will address a gap in our imaging capabilities, allowing us to visualise the movement of immune cells and infectious agents such as bacteria and viruses within living tissues. This will immensely improve our capacity to understand interactions between the immune system, invading organisms and the rest of our body. The intravital imaging system will provide novel insights into how the immune system works, which will ....Multi-photon imaging for infection, immunity, and self recognition. This proposal will address a gap in our imaging capabilities, allowing us to visualise the movement of immune cells and infectious agents such as bacteria and viruses within living tissues. This will immensely improve our capacity to understand interactions between the immune system, invading organisms and the rest of our body. The intravital imaging system will provide novel insights into how the immune system works, which will benefit the design of vaccines, the treatment of cancer, and our understanding of allergy. This state-of-the-art facility will also provide vital training in an emerging technology that will have application in many areas of biology.
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