Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges ....Novel geometric invariants. Quantum theory is the language of fundamental physics, it describes the small scale structure of matter and possibly space-time. Sophisticated models in condensed matter physics and string theory have exposed geometric and topological structure as basic building blocks of the theory. Issues thrown up by quantum theory are very similar to, and have provided techniques to solve, problems in the geometry of three and four dimensional manifolds. Exciting two way exchanges of methods, problems and solutions have emerged. This project aims to settle fundamental questions in the interaction between these two fields.Read moreRead less
New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will ....New approaches to index theory. The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.Read moreRead less
Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
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Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Quantitative Metagenomics. This project aims to revolutionize our view of the microbial world once more by transforming microbiome studies from relative counts of organisms to actual numbers of microbes. This project expects to impact all the microbiome studies that are being performed worldwide by unveiling the actual numbers of microbes. Expected outcomes of this project include new techniques to enumerate the number of bacteria in different environments and new approaches to measure gene expr ....Quantitative Metagenomics. This project aims to revolutionize our view of the microbial world once more by transforming microbiome studies from relative counts of organisms to actual numbers of microbes. This project expects to impact all the microbiome studies that are being performed worldwide by unveiling the actual numbers of microbes. Expected outcomes of this project include new techniques to enumerate the number of bacteria in different environments and new approaches to measure gene expression within individual bacteria in any environment that will be demonstrated with complex microbial communities. This should provide significant benefits because microbes affect every aspect of our lives and those effects are driven by how many microbes are present.Read moreRead less
Human identification, ancient DNA and genomics. This project aims to develop and apply a novel targeted sequence capture and high throughput DNA sequencing approach to simultaneously type thousands of informative identity, ancestry and phenotype markers in a single assay to facilitate identification of unknown suspects and missing persons. DNA based human identification is both critical and central to criminal and coronial investigations, disaster-victim and missing persons identification, repat ....Human identification, ancient DNA and genomics. This project aims to develop and apply a novel targeted sequence capture and high throughput DNA sequencing approach to simultaneously type thousands of informative identity, ancestry and phenotype markers in a single assay to facilitate identification of unknown suspects and missing persons. DNA based human identification is both critical and central to criminal and coronial investigations, disaster-victim and missing persons identification, repatriation of war dead and counter-terrorism operations. Persistent technological and conceptual issues associated with the application of standard procedures to trace degraded DNA, or when profiles have no match in DNA databases, limit their application to real-world human identification problems.Read moreRead less
Diatom lipids to reveal sea-ice history in remote Antarctic regions. This project aims to understand seasonal Antarctic sea-ice extent using molecular, geochemical, elemental and genomic characteristics of specific marine phytoplankton (diatoms). Little is known of the seasonal sea-ice variation and the position of the summer sea-ice extent a million years before satellite records, but this information is critical to determining air-sea gas exchange and ecosystem food web regulation. This projec ....Diatom lipids to reveal sea-ice history in remote Antarctic regions. This project aims to understand seasonal Antarctic sea-ice extent using molecular, geochemical, elemental and genomic characteristics of specific marine phytoplankton (diatoms). Little is known of the seasonal sea-ice variation and the position of the summer sea-ice extent a million years before satellite records, but this information is critical to determining air-sea gas exchange and ecosystem food web regulation. This project will unite geochemical and biological approaches to provide the data to improve past Antarctic ecosystem and climate models where sea-ice data is missing. Studying diatom biomarkers in deep sea cores from Australia’s Southern Ocean will redefine knowledge of Antarctic climate and provide data necessary to improve global ecosystem and climate models.Read moreRead less
Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spre ....Preventing biological growth – a new generation anti-biofouling coatings. The project aims to improve anti-biofouling technology by developing a ‘smart and green’ coating that requires no toxic biocides and makes use of copper already present in the water. Biofouling is the unwanted attachment and growth on surfaces in water; it causes significant problems on ships and in drinking water systems, and damages infrastructure and capital investment. Biofouling also carries a significant risk of spreading diseases and environmental damage through the introduction of invasive marine species. Existing coatings release highly toxic substances into the water, causing untold environmental damage. This project offers a single, comprehensive solution for all of the above problems.Read moreRead less
Evolution of sensory systems in the dark biosphere. This project utilises a unique Australian model system based on multiple, independently-evolved subterranean water beetles to explore the adaptive and regressive changes in the genome that occur when surface species colonise subterranean habitats. We aim to characterise and investigate the evolution of chemosensory and circadian rhythm genes, which play critical roles in the fitness of animals, including the ability to find food and mates in a ....Evolution of sensory systems in the dark biosphere. This project utilises a unique Australian model system based on multiple, independently-evolved subterranean water beetles to explore the adaptive and regressive changes in the genome that occur when surface species colonise subterranean habitats. We aim to characterise and investigate the evolution of chemosensory and circadian rhythm genes, which play critical roles in the fitness of animals, including the ability to find food and mates in a dark, thermally stable environment. Knowledge of chemosensory and circadian genetic systems and how they dynamically evolve is fundamental to a variety of fields, including the process of speciation and biological adaptation (for example, to permanent darkness, pollutants and insecticides).Read moreRead less
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