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
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
Mechanical modulation of particle-cell interactions. Mechanical forces play critical roles in many biological processes, but how particle mechanical properties modulate particle-cell interactions remains elusive. This project aims to develop new design principles for engineering nano/micromaterials with tunable mechanical properties for improved cell activation and expansion, and to advance knowledge of the role of particle stiffness in modulating receptor-mediated particle-cell interactions. Ex ....Mechanical modulation of particle-cell interactions. Mechanical forces play critical roles in many biological processes, but how particle mechanical properties modulate particle-cell interactions remains elusive. This project aims to develop new design principles for engineering nano/micromaterials with tunable mechanical properties for improved cell activation and expansion, and to advance knowledge of the role of particle stiffness in modulating receptor-mediated particle-cell interactions. Expected outcomes and benefits include new fundamental understanding of the effect of particle mechanical properties on cell function, new insights into T cell activation and expansion, and new classes of stiffness-tunable fit-for-purpose materials for various applications in cell manufacturing.Read moreRead less
Multifunctional Porous Nanospheres Engineered Composite Membranes for Hydrogen and Methanol Fuel Cells. Increasing concerns about greenhouse gas emissions and dwindling petroleum supplies have driven the development and commercialisation of fuel cells. The development of novel nanocomposite membranes will possibly lead to the materials breakthrough necessary for advancing both hydrogen and methanol fuel cell technologies, significantly benefiting Australian clean energy supplies and in particul ....Multifunctional Porous Nanospheres Engineered Composite Membranes for Hydrogen and Methanol Fuel Cells. Increasing concerns about greenhouse gas emissions and dwindling petroleum supplies have driven the development and commercialisation of fuel cells. The development of novel nanocomposite membranes will possibly lead to the materials breakthrough necessary for advancing both hydrogen and methanol fuel cell technologies, significantly benefiting Australian clean energy supplies and in particular transport vehicles and portable devices. The synthesis strategies generated will be applicable to creating other functional nanoporous or nanocomposite materials for wider application. This project will also enhance the international reputation and impact of Australian research in the internationally focused fields of nanomaterials and fuel cell technology.Read moreRead less
A Novel Approach to Polymer/Nanosheet Composites and Their Fundamentals. Multifunctional Polymer/nanosheet composites have not yet been widely scaled up in polymer processing and composite industries mainly due to cost and inhaling hazard. This project proposes a novel methodology which embeds nanosheet preparation within polymer melt to both remove the inhaling hazard and lower the cost; the key is to develop two groups of nanosheet intercalation compounds which can expand at the polymer proces ....A Novel Approach to Polymer/Nanosheet Composites and Their Fundamentals. Multifunctional Polymer/nanosheet composites have not yet been widely scaled up in polymer processing and composite industries mainly due to cost and inhaling hazard. This project proposes a novel methodology which embeds nanosheet preparation within polymer melt to both remove the inhaling hazard and lower the cost; the key is to develop two groups of nanosheet intercalation compounds which can expand at the polymer processing temperature, to exfoliate and disperse nanosheets in polymers. It is expected to generate new knowledge of the structure-property relationships and fracture mechanisms of these composites, for industry to scale up this technology and to develop new product.Read moreRead less