Geometric transforms and duality. This Proposal is fundamental, basic research at the forefront of modern differential geometry and its application to physics. It will ensure that Australia is involved in today's mathematical and physical advances and that we have Australian mathematicians trained to take advantage of the future benefits of these advances.
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.
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.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
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
Improving student outcomes: coaching teachers in the power of feedback. This project aims to investigate how student outcomes can be augmented through coaching teachers in effective feedback practice. The project addresses a critical problem of stagnating levels of student achievement in Australian schools with the innovative research design combining evidence-based, pedagogies of feedback, formative assessment and instructional coaching to improve teacher practice and ultimately raise student a ....Improving student outcomes: coaching teachers in the power of feedback. This project aims to investigate how student outcomes can be augmented through coaching teachers in effective feedback practice. The project addresses a critical problem of stagnating levels of student achievement in Australian schools with the innovative research design combining evidence-based, pedagogies of feedback, formative assessment and instructional coaching to improve teacher practice and ultimately raise student achievement levels. The project aims to guide policy implementation in pedagogy to raise the quality of teaching standards and to improve learning outcomes for Australian students. Ultimately, outcomes from the research will help close the gap for low achieving students, and challenge and extend those who may already be meeting required benchmarks. Read moreRead less
Multiliteracies for addressing disadvantage in senior school science. Multiliteracies for addressing disadvantage in senior school science. This project aims to develop discipline-specific pedagogies in senior physics, chemistry and biology to improve disadvantaged students’ engagement and achievement. Many students from disadvantaged backgrounds fail to develop the linguistic precision and symbolic representational dexterity needed to comprehend and communicate senior school science concepts. T ....Multiliteracies for addressing disadvantage in senior school science. Multiliteracies for addressing disadvantage in senior school science. This project aims to develop discipline-specific pedagogies in senior physics, chemistry and biology to improve disadvantaged students’ engagement and achievement. Many students from disadvantaged backgrounds fail to develop the linguistic precision and symbolic representational dexterity needed to comprehend and communicate senior school science concepts. These pedagogies will ‘infuse’ multiliteracies in senior school science to improve access to science-based pathways for these students, and enable them to understand progressively more complex scientific concepts and demonstrate this in examinations. This project is expected to improve student retention, arrest declining enrolments in senior school science, and increase young people working in science.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
Enhancing phosphorus use efficiency in macadamia for sustainable production. Macadamia nuts are an iconic native Australian product worth $287 million annually at the farm gate. Phosphorus fertiliser management currently threatens price premiums for sustainable production in high value European Union export markets, and ‘social license’ to farm in their densely populated coastal production areas. The project aims to exploit adaptive root and shoot traits for phosphorus efficiency found in Austra ....Enhancing phosphorus use efficiency in macadamia for sustainable production. Macadamia nuts are an iconic native Australian product worth $287 million annually at the farm gate. Phosphorus fertiliser management currently threatens price premiums for sustainable production in high value European Union export markets, and ‘social license’ to farm in their densely populated coastal production areas. The project aims to exploit adaptive root and shoot traits for phosphorus efficiency found in Australian native plants to optimise phosphorus fertiliser management and set the platform for breeding macadamia root stocks/varieties that require less phosphorus fertiliser. The outcome will be a macadamia industry that is able to maintain current market price premiums and maintain social license to farm in coastal Australia.Read moreRead less