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.
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
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
The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real est ....The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real estate markets together. The research will benefit all Australians as the outcomes will result in improved risk and return performance for superannuation funds, leading to a better standard of living for all retirees.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE100100069
Funder
Australian Research Council
Funding Amount
$640,000.00
Summary
A high resolution environmental scanning electron microscope (HRESEM) for South Australia. Australian researchers need access to state-of-the-art instrumentation in microscopy and microanalysis to remain competitive on the international stage. Nationally Australia has established excellent facilities and access regimes but there still remain areas where access to routine instrumentation is poor. Increased capacity is needed in South Australia for high resolution scanning electron microscopy (HRS ....A high resolution environmental scanning electron microscope (HRESEM) for South Australia. Australian researchers need access to state-of-the-art instrumentation in microscopy and microanalysis to remain competitive on the international stage. Nationally Australia has established excellent facilities and access regimes but there still remain areas where access to routine instrumentation is poor. Increased capacity is needed in South Australia for high resolution scanning electron microscopy (HRSEM), as well as capability for environmental scanning electron microscopy (ESEM). The need is highlighted by the recent establishment of the Centre of Excellence in Photonics and the Australian Centre for Plant Functional Genomics, both of which need this capacity and capability for characterisation at EM levels. Research organisations across the state will benefit from access to the proposed instrumentation.Read moreRead less
The role of fat crystal wettability in altering dairy emulsion properties. The role of fat crystal wettability in altering dairy emulsion properties. This project aims to control fat crystal wettability, to create tailored dairy products with desirable stability, shelf-life and texture. Fat crystals are an essential component of dairy emulsions (fat droplets dispersed in dairy/milk serum) and control product processing, shelf life and texture. Their structuring role involves partial coalescence: ....The role of fat crystal wettability in altering dairy emulsion properties. The role of fat crystal wettability in altering dairy emulsion properties. This project aims to control fat crystal wettability, to create tailored dairy products with desirable stability, shelf-life and texture. Fat crystals are an essential component of dairy emulsions (fat droplets dispersed in dairy/milk serum) and control product processing, shelf life and texture. Their structuring role involves partial coalescence: the formation of complicated network structures of fat droplets. Unless fat crystals are partially wetted by water, they will not be present at the fat droplet interface, and partial coalescence will not occur. Expected outcomes are new dairy products with optimum stability and texture.Read moreRead less
Unveiling the epigenome dynamics through the pluripotency continuum. This project aims to utilise stem cells and genomics based technologies, in combination with new computational algorithms to dissect the fundamental molecular events that drive the first steps during development. The project is expected to unveil the basic mechanisms underpinning how genes driving the developmental master plan are controlled in cells that have the capacity to give rise to the whole organism and placenta. The kn ....Unveiling the epigenome dynamics through the pluripotency continuum. This project aims to utilise stem cells and genomics based technologies, in combination with new computational algorithms to dissect the fundamental molecular events that drive the first steps during development. The project is expected to unveil the basic mechanisms underpinning how genes driving the developmental master plan are controlled in cells that have the capacity to give rise to the whole organism and placenta. The knowledge gained from this work will inform and guide future novel approaches, such as in assisted reproductive technologies or regenerative medicine.Read moreRead less