New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary val ....New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary value problems in the theory of equations. Such problems occur in several areas of modern physics. In addition, results obtained will be useful for studying the structure of the most important spectral triples, called noncommutative manifolds.Read moreRead less
GENETIC PREDICTION OF FRACTURE IN A RISK-STRATIFIED POPULATION
Funder
National Health and Medical Research Council
Funding Amount
$363,000.00
Summary
Osteoporosis is a condition characterised by excessive bone loss and impaired bone quality, which ultimately results in fracture with minimal trauma. Osteoporosis affects 27% of women and 11% of men aged 60 years or above in the community, and costs Australia around $7 billion each year. Individuals with low bone mineral density (BMD) have a significantly higher risk of fracture than those with normal BMD. In the long-term (14-year) Dubbo Osteoporosis Epidemiology Study, more than half of indivi ....Osteoporosis is a condition characterised by excessive bone loss and impaired bone quality, which ultimately results in fracture with minimal trauma. Osteoporosis affects 27% of women and 11% of men aged 60 years or above in the community, and costs Australia around $7 billion each year. Individuals with low bone mineral density (BMD) have a significantly higher risk of fracture than those with normal BMD. In the long-term (14-year) Dubbo Osteoporosis Epidemiology Study, more than half of individuals with osteoporosis (e.g., low BMD) did not sustain a fracture, while approximately 60% of fracture cases had BMD above the high risk levels. Thus, BMD alone is not a good discriminant of fracture versus non-fracture cases. It is widely known that the liability to fracture is determined in part by genes. Previous studies, including from our group, have suggested a number of candidate genes that are associated with fracture risk. The fundamental issue that this study is concerned is that how and whether genetic markers could be used to facilitate case finding. It is proposed that common variations of certain genes are associated with fracture risk independent of BMD. That is, they can identify individuals at relatively high and low fracture risk after stratification for BMD. Hence, some markers may identify those individuals likely (and unlikely) to fracture even with low (osteoporotic) BMD. Similarly, some, possibly the same, markers may identify individuals at high risk of fracture despite relatively good (ie non-osteoporotic) BMD. It is further proposed that no single gene will achieve this outcome, but rather a small set of such gene polymorphisms will provide clinically useful risk information. This effect is entirely analogous to the use of clinical risk indicators (eg, age, weight, sex, family history, etc) to assess the risk of future fracture.Read moreRead less
Myeloma Plasma Cell Dormancy - 'Eradicating The Sleeping Giant'
Funder
National Health and Medical Research Council
Funding Amount
$834,428.00
Summary
Multiple myeloma is a fatal cancer that develops in the skeleton. Current therapies are initially effective, but patients develop resistance and the disease returns. This makes the search for drugs to overcome resistance a priority. Myeloma cells can hide in bone in a dormant state where they are insensitive to chemotherapy. We have identified new drug targets in dormant cells. We are investigating whether these new targets can be used eradicate myeloma cells and cure the disease.
Noncommutative Algebraic Geometry. As algebra moves into the twenty-first century, we see a strong trend towards interactions with geometry. This project is right in the thick of this trend and will keep Australia abreast of some of the most interesting developments in algebra. The project seeks to start up a research group in noncommutative algebraic geometry which will foster a lively intellectual atmosphere. This will involve training postgraduate students, inviting international experts to g ....Noncommutative Algebraic Geometry. As algebra moves into the twenty-first century, we see a strong trend towards interactions with geometry. This project is right in the thick of this trend and will keep Australia abreast of some of the most interesting developments in algebra. The project seeks to start up a research group in noncommutative algebraic geometry which will foster a lively intellectual atmosphere. This will involve training postgraduate students, inviting international experts to give seminar talks and establishing relations with other Australian mathematicians in related areas.Read moreRead less
Towards Mike Artin's conjecture. Non-commutative algebra and algebraic geometry are both classical branches of mathematics with much depth to them. As a result, the recent study of the interactions between the two disciplines has proven to be fertile ground for many important developments in mathematics. This project ensures that Australia remains a part of these developments.
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less
On the Geometry of Liquid Crystals and Biological Membranes. This project will provide fundamental insights via realistic mathematical models into two areas of technological importance in the development of certain advanced materials involving liquid crystals and biomembranes. The use of liquid crystal devices is ubiquitous in the design of optical display units. Biomembranes are of much current importance, in particular, in connection with sophisticated drug delivery systems. The design of adva ....On the Geometry of Liquid Crystals and Biological Membranes. This project will provide fundamental insights via realistic mathematical models into two areas of technological importance in the development of certain advanced materials involving liquid crystals and biomembranes. The use of liquid crystal devices is ubiquitous in the design of optical display units. Biomembranes are of much current importance, in particular, in connection with sophisticated drug delivery systems. The design of advanced `smart' materials which admit solitonic behaviour is an area at the forefront of materials science and as such is important to the continued development of an advanced technological base within Australia.Read moreRead less
Deformation of singularities through Hodge theory and derived categories. Moduli theory, the modern classification theory of mathematical objects, is a branch of algebraic geometry with applications in wide-ranging areas from the theoretical high-energy physics (dark matter and Higgs boson) to data encryption and correction via cryptography. The aim of this project is to resolve central open problems in this theory. This will be achieved by developing new methods and establishing deeper connecti ....Deformation of singularities through Hodge theory and derived categories. Moduli theory, the modern classification theory of mathematical objects, is a branch of algebraic geometry with applications in wide-ranging areas from the theoretical high-energy physics (dark matter and Higgs boson) to data encryption and correction via cryptography. The aim of this project is to resolve central open problems in this theory. This will be achieved by developing new methods and establishing deeper connections between various dynamic branches of these fields. By undertaking research at the forefronts of these highly active areas, this project will both strengthen the current expertise within the Australian mathematical community and precipitate the advance of Australian high-tech industries. Read moreRead less
Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises ....Noncommutative geometry in representation theory and quantum physics. One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises to make fundamental contributions to both mathematics and theoretical physics. Read moreRead less