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
The effect of aerial spraying of two pesticides on semi-arid grasslands. The project will investigate how two pesticides, fipronil and metarrhizium, used to control locusts, affect semi-arid ecosystems by examining impacts on invertebrates, their predators, lizards and soil processes. The effects will be followed through time in a large scale experiment to determine recovery and compare each pesticide.
Testing our knowledge on the dawn of animal life: evidence from the fossil record against modern ecological and morphological analogues. The Cambrian 'Explosion', half a billion years ago, is regarded as one of the most important events in the history of the Earth, when most major animal groups first appear in the rock record, and for which South Australia has recently become a significant source of spectacular fossils. However, important questions remain regarding their Ediacaran roots, the spe ....Testing our knowledge on the dawn of animal life: evidence from the fossil record against modern ecological and morphological analogues. The Cambrian 'Explosion', half a billion years ago, is regarded as one of the most important events in the history of the Earth, when most major animal groups first appear in the rock record, and for which South Australia has recently become a significant source of spectacular fossils. However, important questions remain regarding their Ediacaran roots, the speed of evolution at the time, and the environments in which the radiation took place. Studying the fossil evidence in the light of present-day ecological frameworks, and in comparison with modern behavioural and morphological analogues, as well as living relatives, can help us better assess our understanding of this first radiation of animals.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
Ecology, morphology and the diversification of Australian lizards. This project aims to determine the factors driving the spectacular radiation of lizards in Australia. To date, most investigations of lizard anatomy have focused exclusively on external characteristics. This project will examine the underlying internal anatomy to investigate whether morphological innovation is associated with enhanced rates of ecological, life-history and species diversification. The project expects to shed light ....Ecology, morphology and the diversification of Australian lizards. This project aims to determine the factors driving the spectacular radiation of lizards in Australia. To date, most investigations of lizard anatomy have focused exclusively on external characteristics. This project will examine the underlying internal anatomy to investigate whether morphological innovation is associated with enhanced rates of ecological, life-history and species diversification. The project expects to shed light on the evolution of Australia’s most diverse vertebrate lineage, and provide comparative data with which to interpret the lizard fossil record in Australia, and the range declines and relative extinction risks of native lizard species.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.
Resilience in biogeochemical pathways along a catchment-to-coast continuum. Aquatic systems have degraded more in the past 50 years than any other time in history. Global pressures are further threatening their sustainability, but their complexity makes it difficult to understand how they are responding. This project will combine numerous state-of-the-art approaches to unravel pathways that shape their response.
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.