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
Centre For Clinical Research Excellence In Aboriginal Health: Sexually Transmitted And Bloodborne Viral Infections
Funder
National Health and Medical Research Council
Funding Amount
$2,553,623.00
Summary
This proposed new CCRE will bring together the leading Australian institution dedicated to clinical research on sexually transmitted and blood borne viral infections, and the peak organisation for Aboriginal Community Controlled Health Services. Working with nominated Aboriginal community controlled health services, the Centre will conduct innovative research that will identify new approaches to diagnosing and managing these infections while at the same time developing improved clinical guidelin ....This proposed new CCRE will bring together the leading Australian institution dedicated to clinical research on sexually transmitted and blood borne viral infections, and the peak organisation for Aboriginal Community Controlled Health Services. Working with nominated Aboriginal community controlled health services, the Centre will conduct innovative research that will identify new approaches to diagnosing and managing these infections while at the same time developing improved clinical guidelines and research capacity within the sector.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.
Deadly Liver Mob: Engaging Aboriginal People In Viral Hepatitis, HIV And Sexual Health Services
Funder
National Health and Medical Research Council
Funding Amount
$848,441.00
Summary
Rates of blood-borne viruses and sexually transmissible infections are high among the Aboriginal and Torres Strait Islander population. A local initiative in western Sydney has trialed a new approach to engagement and care of Aboriginal people. We will implement this approach in services across NSW and evaluate its effectiveness as a sustainable and acceptable model for engaging Aboriginal people in care and develop an implementation plan for future roll-out to other services.
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 Role Of UPF3B And Nonsense Mediated MRNA Decay Surveillance In The Pathology Of Intellectual Disability.
Funder
National Health and Medical Research Council
Funding Amount
$789,954.00
Summary
Proper functioning of the nonsense mediated mRNA decay (NMD or 'mRNA police') is crucial for any cell to ensure normal development and function. When NMD is compromised the outcome is learning and memory problems, autism or schizophrenia. Under this project we study malfunctioning NMD using stem and neuronal cells derived from patients' skin cells. Some of the affected genes might be considered for therapeutic interventions. NMD is relevant to 1000s of human disorders and as such it is of fundam ....Proper functioning of the nonsense mediated mRNA decay (NMD or 'mRNA police') is crucial for any cell to ensure normal development and function. When NMD is compromised the outcome is learning and memory problems, autism or schizophrenia. Under this project we study malfunctioning NMD using stem and neuronal cells derived from patients' skin cells. Some of the affected genes might be considered for therapeutic interventions. NMD is relevant to 1000s of human disorders and as such it is of fundamental importance.Read moreRead less
About one in eight known genetic disorders involve DNA alteration that activates a cellular quality control mechanism that disables the affected gene. This mechanism is more efficient in some individuals than others. It can influence disease outcomes and severity. We will engineer and apply tools and models to measure and manipulate this crucial cellular mechanism. This will allow us to predict disease severity as well as to intervene where a manipulation of this mechanism will be beneficial.