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
Breathing disturbances and reflexes in sleep and effects on sleep and daytime function. This project will investigate protective reflexes in sleep and the impact of breathing disturbances and frequent arousal on markers of brain functioning and health. This will also significantly advance the understanding of key mechanisms promoting unstable breathing in sleep and ill health and functioning from disturbed sleep.
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.
Electrophysiological and Anatomical Characterization of the Coronary Sinus Musculature and its Relationship to the Atria. This series of experiments will characterise the normal coronary sinus musculature and its connectivity to the atria of the heart and establish their electrical relationships. The underlying characteristics of the muscular connections will also be evaluated with a view to possible future manipulations of the system. Understanding normal heart impulse propagation is paramount ....Electrophysiological and Anatomical Characterization of the Coronary Sinus Musculature and its Relationship to the Atria. This series of experiments will characterise the normal coronary sinus musculature and its connectivity to the atria of the heart and establish their electrical relationships. The underlying characteristics of the muscular connections will also be evaluated with a view to possible future manipulations of the system. Understanding normal heart impulse propagation is paramount before we can understand and develop treatments for dealing with heart problems. This information will facilitate the development of techniques to treat and prevent heart rhythm disorders that are a common cause of morbidity in the community.Read moreRead less
Detection and viability of waterborne pathogens using a gut-on-chip. This project aims to resolve a significant problem for water utilities. Microbial pathogens Cryptosporidium, norovirus and adenovirus are the main public health concern for drinking water in developed nations. Water monitoring is limited by the lack of fast, reliable detection methods and viability assays for these pathogens. This project will use a novel gut-on-a-chip to develop for the first time rapid infectivity assays for ....Detection and viability of waterborne pathogens using a gut-on-chip. This project aims to resolve a significant problem for water utilities. Microbial pathogens Cryptosporidium, norovirus and adenovirus are the main public health concern for drinking water in developed nations. Water monitoring is limited by the lack of fast, reliable detection methods and viability assays for these pathogens. This project will use a novel gut-on-a-chip to develop for the first time rapid infectivity assays for Cryptosporidium, norovirus and adenovirus. Significant benefits include improved diagnostics and water disinfection assays, improved water treatment and reduced costs with global impact.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
Functional characterisation of poly-histidine triad proteins. This project aims to understand the role and function of a novel family of surface proteins produced by Streptococci. These so-called polyhistidine triad proteins are known to contribute to capacity to cause disease in animals and humans, but we need to know how they work, as they may be excellent targets for novel drugs or vaccines.