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
Engaging Students during the Early Years of Secondary School. This project aims to design, test and share sustainable strategies to support teachers and enable students from low socioeconomic communities to achieve success. The greatest decreases in students’ interest and effort occur when they transition into secondary school, with students from low socioeconomic communities at greatest risk of disengagement. What can teachers do to engage their students during this key life transition? This pr ....Engaging Students during the Early Years of Secondary School. This project aims to design, test and share sustainable strategies to support teachers and enable students from low socioeconomic communities to achieve success. The greatest decreases in students’ interest and effort occur when they transition into secondary school, with students from low socioeconomic communities at greatest risk of disengagement. What can teachers do to engage their students during this key life transition? This project plans to identify teacher behaviours that motivate students in their first year at secondary school. Using an experimental design with a representative sample of 150 teachers and 1500 students in low socioeconomic areas across three states, the project plans to test whether an online professional learning program for teachers can improve student engagement and achievement. This cost-effective and scalable intervention is designed for widespread dissemination to Australian teachers.Read moreRead less
Evolution. Morphodynamics and History of the Younghusband Peninsula. This project will examine the history and evolution of the Sir Richard-Younghusband Peninsula (SRYP) complex barrier in SA. The aims are to derive a understanding of how the influences of relative sea-level changes, neotectonics, and sediment supply, can produce remarkably different responses in barrier development. No complex barrier (i.e. foredune ridges in one portion, transgressive dunefields in another) has ever been compr ....Evolution. Morphodynamics and History of the Younghusband Peninsula. This project will examine the history and evolution of the Sir Richard-Younghusband Peninsula (SRYP) complex barrier in SA. The aims are to derive a understanding of how the influences of relative sea-level changes, neotectonics, and sediment supply, can produce remarkably different responses in barrier development. No complex barrier (i.e. foredune ridges in one portion, transgressive dunefields in another) has ever been comprehensively drilled, dated, modelled, or examined in the context of indigenous occupation and oral histories in Australia. The study provides excellent analogues for barrier and dune response, and shoreline translation to varying rates of sea level rise, paralleling pressures facing all coastlines today.Read moreRead less
Diversity in large crop genomes via enhanced recombination. The project aims to understand genetic and environmental factors that limit how fast genomic combinations can be generated by modifying the recombination rates between chromosomes. Plant breeding is based around genetic diversity, but modern breeding programs have captured only a small proportion of the variation available in wild relatives and land races. Knowledge of diversity in this wild germplasm pool is increasing and the challeng ....Diversity in large crop genomes via enhanced recombination. The project aims to understand genetic and environmental factors that limit how fast genomic combinations can be generated by modifying the recombination rates between chromosomes. Plant breeding is based around genetic diversity, but modern breeding programs have captured only a small proportion of the variation available in wild relatives and land races. Knowledge of diversity in this wild germplasm pool is increasing and the challenge is to quickly and efficiently introduce this variation into elite lines. This project’s findings are expected to transform wheat and barley breeding methods by unlocking the genetic diversity to produce new varieties. This will enhance and protect a critical and valuable rural industry.Read moreRead less