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
The migration of cancer cells (metastasis) is responsible for most cancer deaths. Central to this is dynamic organisation of the actin cytoskeleton _ an internal structure that provides cell shape and enables movement. We have identified a family of small molecules (called miR-200) that regulates this actin cytoskeleton through specifically downregulating various genes. We are investigating the nature of these genes and their role in cell motility _ an underlying pre-requisite of metastasis.
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
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
Enhanced multivalent vaccine responses using a novel vaccine vector system. Enhanced multivalent vaccine responses using a novel vaccine vector system. This project aims to develop a multicomponent vaccine system to deliver equal effectiveness against several disease targets in a single administration. New and innovative vaccine design strategies incorporating economical commercial production processes are urgently needed for new and existing human and animal health applications. A vaccine capab ....Enhanced multivalent vaccine responses using a novel vaccine vector system. Enhanced multivalent vaccine responses using a novel vaccine vector system. This project aims to develop a multicomponent vaccine system to deliver equal effectiveness against several disease targets in a single administration. New and innovative vaccine design strategies incorporating economical commercial production processes are urgently needed for new and existing human and animal health applications. A vaccine capable of targeting multiple diseases by a single injection is an obvious way to expedite future vaccine development and deployment. However, the recipient’s immune system can repress equivalent responses to these multicomponent vaccines. This project’s research is expected to address these problems, and underpin the future commercial development of this vaccine platform.Read moreRead less
Identification Of The Conformation Dependant Targets Of Autoimmune Disease Linked Variation In Human Regulatory T Cells
Funder
National Health and Medical Research Council
Funding Amount
$1,001,815.00
Summary
Specialised immune cells called regulatory T cells act as the policemen of the immune system, preventing the immune system attacking itself, but still fighting infections. If these cells do not work properly, autoimmune diseases such as type 1 diabetes or IBD can arise, because of immune attack on normal body tissue by mistake. In order to explain how this goes wrong we need to carefully identify all of the gene interactions in these cells including interactions over long distances in the DNA.
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.
Identification of Biological pathways regulated by circular RNAs. Circular RNAs (circRNAs) are a, recently discovered molecule. circRNAs are highly abundant and expressed in a tissue and disease specific manner. Yet, currently the understanding of how circRNAs regulate biological processes is very poor. This project aims to use pooled shRNA libraries to screen a large panel of cell lines and systematically identify cellular activities that are regulated by circRNAs. The expected outcome of this ....Identification of Biological pathways regulated by circular RNAs. Circular RNAs (circRNAs) are a, recently discovered molecule. circRNAs are highly abundant and expressed in a tissue and disease specific manner. Yet, currently the understanding of how circRNAs regulate biological processes is very poor. This project aims to use pooled shRNA libraries to screen a large panel of cell lines and systematically identify cellular activities that are regulated by circRNAs. The expected outcome of this study will be a catalogue of functionally active circRNAs. Over the past decades, the wealth of knowledge on the function of linear mRNAs has had a significant impact on medicine and agriculture. Similarly understanding how circRNAs regulate cellular activities may have an analogous impact on humans.Read moreRead less