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
Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the ....Invariants, geometric and discrete structures on manifolds. This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the first aim is to construct structures with good geometric properties on 3- and 4-manifolds, using triangulations. The second aim is to study combinatorial decompositions of n-manifolds, using our new technique of multisections and also searching for polyhedral metrics of non-positive curvature. The third aim is to connect quantum invariants and geometric structures, again using triangulations.Read moreRead less
Triangulations in dimensions 3 and 4: discrete and geometric structures. Recently there have been spectacular advances in understanding 3-dimensional spaces and the interaction between ideas in mathematical physics (quantum invariants) and such spaces. This project aims at practical methods for finding geometric structures and advancing our understanding of the information that physics is providing about these spaces.
Role Of IGF Binding Protein-3 (IGFBP-3) And IGFBP-5 As Modulators Of Nuclear Hormone Signalling
Funder
National Health and Medical Research Council
Funding Amount
$465,750.00
Summary
The insulin-like growth factors are small proteins involved in the growth of most tissues. Their actions are regulated by binding to larger proteins (known as IGFBPs) in the bloodstream and outside the cell. However, some IGFBPs are also found inside cells, where they seem to carry out other functions. We believe that two of these binding proteins, IGFBP-3 and IGFBP-5, change the way cells respond to vitamin A and vitamin D. These two vitamins are important in cell growth and in the way certain ....The insulin-like growth factors are small proteins involved in the growth of most tissues. Their actions are regulated by binding to larger proteins (known as IGFBPs) in the bloodstream and outside the cell. However, some IGFBPs are also found inside cells, where they seem to carry out other functions. We believe that two of these binding proteins, IGFBP-3 and IGFBP-5, change the way cells respond to vitamin A and vitamin D. These two vitamins are important in cell growth and in the way certain cells perform specialised functions. In test-tube experiments, IGFBP-3 and IGFBP-5 interact directly with the receptors that regulate the effects of these hormones. If the same thing happens inside the cell, IGFBP-3 and IGFBP-5 could change the way these receptors respond to signals from outside the cell. We will investigate what effect these IGFBPs have in living cells and in whole animals and how this may relate to human disease. If we are able to understand how IGFBP-3 and IGFBP-5 affect the way cells respond to vitamin A and D, then we may be able to develop new ways to treat certain human diseases.Read moreRead less
Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we ....Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we will forge connections between the geometry of curved spaces, and the physics of operators therein. The significant benefits of this project include increasing fundamental mathematical knowledge, building capacity in Australia’s world-class geometric analysis community, and strong links with international partners.Read moreRead less
Whole Body Vibration For Osteoporosis: Shaking Up Our Treatment Options
Funder
National Health and Medical Research Council
Funding Amount
$961,017.00
Summary
Our aim is to examine the ability of vibration alone and in combination with osteoporosis drugs to reduce hip fracture in postmenopausal women. In Australia, 1 in 2 women >60yrs, will sustain an osteoporotic fracture. Only drugs notably decrease fracture; however none are entirely effective and some patients don’t respond. Whole body vibration has emerged as a potentially effective therapy. A combination of vibration and drugs may enhance the effects of both and revolutionise treatment.
Trisections, triangulations and the complexity of manifolds. This project aims at practical representations of 3-dimensional and 4-dimensional spaces as needed in applications. Topology is the mathematical study of the shapes of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Special combinatorial structures, such as minimal triangulations, are often closely connected to geometric structures or topological properties. This project aims to construct ....Trisections, triangulations and the complexity of manifolds. This project aims at practical representations of 3-dimensional and 4-dimensional spaces as needed in applications. Topology is the mathematical study of the shapes of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Special combinatorial structures, such as minimal triangulations, are often closely connected to geometric structures or topological properties. This project aims to construct computable invariants, connectivity results for triangulations, and algorithms to recognise fundamental topological properties and structures such as trisections and bundles.Read moreRead less
Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable s ....Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.Read moreRead less
Targeting Bone Marrow Mediated Angiogenesis And Metastasis In Breast Cancer
Funder
National Health and Medical Research Council
Funding Amount
$463,006.00
Summary
Despite advances in treatment and diagnostics breast cancer (BC) remains one of the leading causes of death in women. Metastases and tumour blood vessel recruitment are linked. Work by Dr Mellick and others has shown that host bone marrow contributes endothelial progenitor cells (EPCs) to tumour vasculature. The chemokines and their receptors, which differentiate EPCs from tumour vessels, will be knocked down in the tumour cells and EPC progenitors with the aim of preventing tumour spread.
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.