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
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.
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
Tapasin And Major Histocompatibility Complex Class I Antigen Presentation
Funder
National Health and Medical Research Council
Funding Amount
$226,650.00
Summary
An effective T cell response (cellular immune response) to infections is vital to a functional immune system. Normally, proteins are cleaved into small molecules called peptides and these peptides are in turn presented by Major Histocompatibility Complex molecules to T cells. However, we have only partial understanding of what determines the choice of peptides that are finally presented to T cells. Recent research suggests that a molecule called tapasin may also influence the choice of peptides. ....An effective T cell response (cellular immune response) to infections is vital to a functional immune system. Normally, proteins are cleaved into small molecules called peptides and these peptides are in turn presented by Major Histocompatibility Complex molecules to T cells. However, we have only partial understanding of what determines the choice of peptides that are finally presented to T cells. Recent research suggests that a molecule called tapasin may also influence the choice of peptides. This research proposal aims to examine the role of tapasin in this regard. A thorough understanding of the basic principles of peptide presentation to T cells is crucial to the design of effective vaccines. Furthermore it will also broaden our understanding of immunological responses to cancer, autoimmune diseases and infections.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE100100069
Funder
Australian Research Council
Funding Amount
$640,000.00
Summary
A high resolution environmental scanning electron microscope (HRESEM) for South Australia. Australian researchers need access to state-of-the-art instrumentation in microscopy and microanalysis to remain competitive on the international stage. Nationally Australia has established excellent facilities and access regimes but there still remain areas where access to routine instrumentation is poor. Increased capacity is needed in South Australia for high resolution scanning electron microscopy (HRS ....A high resolution environmental scanning electron microscope (HRESEM) for South Australia. Australian researchers need access to state-of-the-art instrumentation in microscopy and microanalysis to remain competitive on the international stage. Nationally Australia has established excellent facilities and access regimes but there still remain areas where access to routine instrumentation is poor. Increased capacity is needed in South Australia for high resolution scanning electron microscopy (HRSEM), as well as capability for environmental scanning electron microscopy (ESEM). The need is highlighted by the recent establishment of the Centre of Excellence in Photonics and the Australian Centre for Plant Functional Genomics, both of which need this capacity and capability for characterisation at EM levels. Research organisations across the state will benefit from access to the proposed instrumentation.Read moreRead less