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
A shipload of consequences: studying the impact of Old World diseases on native South American populations via ancient DNA. This pioneering project will give the first real-time picture of the genetic changes induced by epidemics in human populations. This will reveal important new information about the likely impact of future epidemics on the genetic diversity of the immune system in modern human populations and will be of substantial use in building epidemiological models. By proposing to comb ....A shipload of consequences: studying the impact of Old World diseases on native South American populations via ancient DNA. This pioneering project will give the first real-time picture of the genetic changes induced by epidemics in human populations. This will reveal important new information about the likely impact of future epidemics on the genetic diversity of the immune system in modern human populations and will be of substantial use in building epidemiological models. By proposing to combine state-of-the-art science with global problems of humanity, we will address Australia's interests in expanding scientific expertise beyond its borders and place Australia at the leading edge of disease impact studies.Read moreRead less
Investigation of the fundamental roles of class Ib MHC (major histocompatibility complex) molecules in immunity. The proposed research program, using laboratory-based and synchrotron-based radiation, will provide insight into the roles of a poorly understood class of immune molecules. This will improve our understanding of the regulation of immunity, and the knowledge gained will increase Australia's international research profile.
Molecular mechanisms regulating Ca2+ channels formed by Orai and STIM proteins. Store-operated calcium channels play a central role in the functions of all animal cells. They participate in generating the cellular responses to hormones, antigens, growth factors and other physiological stimuli. The aims of this project are to elucidate cellular mechanisms that regulate interaction between the molecular components of store-operated calcium channel, Orai and STIM. Using techniques of electrophysiol ....Molecular mechanisms regulating Ca2+ channels formed by Orai and STIM proteins. Store-operated calcium channels play a central role in the functions of all animal cells. They participate in generating the cellular responses to hormones, antigens, growth factors and other physiological stimuli. The aims of this project are to elucidate cellular mechanisms that regulate interaction between the molecular components of store-operated calcium channel, Orai and STIM. Using techniques of electrophysiology and molecular biology we expect to answer a fundamental question how STIM and Orai proteins interact to form functional store-operated calcium channels, and how the expression of STIM and Orai is regulated.Read moreRead less
Investigating the evolution of innate and adaptive cellular immunity. This proposal aims to assess the impact of geographical and genetic isolation of the Australian Indigenous population on adaptive and innate immune systems. The project will use novel DNA sequencing approaches to generate the high resolution sequences of two genetic loci that regulate innate and adaptive immune responses, the major histocompatibility complex locus and the killer cell immunoglobulin-like receptor locus. In an i ....Investigating the evolution of innate and adaptive cellular immunity. This proposal aims to assess the impact of geographical and genetic isolation of the Australian Indigenous population on adaptive and innate immune systems. The project will use novel DNA sequencing approaches to generate the high resolution sequences of two genetic loci that regulate innate and adaptive immune responses, the major histocompatibility complex locus and the killer cell immunoglobulin-like receptor locus. In an initial screen, distinct variants and combinations of these genes were identified. This project aims to interrogate how variation in these critical genes impacts on the function of cytotoxic lymphocytes, providing insights into the evolutionary drivers of immune recognition mechanisms.Read moreRead less