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
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.
Identification Of Genes For X-linked Mental Retardation.
Funder
National Health and Medical Research Council
Funding Amount
$675,228.00
Summary
We propose to identify novel heritable causes of intellectual disability using 22 large and well-characterised families from Australia. In these families we have refined the location of the genetic defect to the chromosome X and excluded the contribution of all so far known genes. We will achieve this using the technology of massive parallel sequencing. At the completion of the project we will have identified novel causes of intellectual disability and devised tests to identify them.
Genetic dissection of a regulatory deubiquitlyation network. The potential impact of this work is widespread, because although it is known that ubiquitlyation has regulatory consequences in multicellular eukaryotes, individual networks have not been completely described in higher eukaryotes. Knowledge gained about fundamental processes in the A. nidulans model system is directly applicable to fungi used in biotechnology in the food, beverage, enzyme and pharmaceutical production industries, and ....Genetic dissection of a regulatory deubiquitlyation network. The potential impact of this work is widespread, because although it is known that ubiquitlyation has regulatory consequences in multicellular eukaryotes, individual networks have not been completely described in higher eukaryotes. Knowledge gained about fundamental processes in the A. nidulans model system is directly applicable to fungi used in biotechnology in the food, beverage, enzyme and pharmaceutical production industries, and to fungal pathogens. Since the fungal genes that form the basis of this project are conserved in higher eukaryotes including humans, the knowledge will be transferable to these systems. A further benefit that cannot be overstated is the research education and training opportunities provided.
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