Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manif ....Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.Read moreRead less
Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical an ....Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical and it will provide a unified approach to important results in several areas, including Lie groups and functions of several complex variables. 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.
The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the ....The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the crossroads of the paths connecting the most important areas of applications of mathematics with its most abstract parts. Analytic Singularity Theory is a central part of Singularity Theory. This project would lead to substantially new advancements in Analytic Singularity Theory.Read moreRead less
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 implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real est ....The implications for greying Australia of international property market interlinkages. Recent events in global financial markets have had a major effect on the retirement plans of Australians and the living standards of retirees. This research will permit pension fund managers to better gauge the fundamental links that exist across international property markets, as well as provide a better understanding for both academics and practitioners on the driving forces that link international real estate markets together. The research will benefit all Australians as the outcomes will result in improved risk and return performance for superannuation funds, leading to a better standard of living for all retirees.Read moreRead less
Early settlements in Upper Burma (Myanmar): an experiment in urban living. This project directly increases access for Australian research to a previously self-isolated nation, Myanmar. It contributes to better understanding of our region and our world by examining how past communities worked together and how they dealt with social and environmental stress.
Chorasmian temples: an archaeological study of early Zoroastrianism and its precursors in Central Asia. The project is a collaboration with the Uzbek Academy of Sciences. National benefits to Australia are in international relations and in broadening our understanding of cultural issues in the potentially volatile and politically significant region of Central Asia. The team has developed a high profile in Uzbekistan and internationally, reflecting well on Australia's cultural strengths, intern ....Chorasmian temples: an archaeological study of early Zoroastrianism and its precursors in Central Asia. The project is a collaboration with the Uzbek Academy of Sciences. National benefits to Australia are in international relations and in broadening our understanding of cultural issues in the potentially volatile and politically significant region of Central Asia. The team has developed a high profile in Uzbekistan and internationally, reflecting well on Australia's cultural strengths, international involvement and support for developing countries in Asia. Our research features regularly in the Uzbek media and has the personal approval of President Karimov. We are involved with Zoroastrian and Parsi communities in Australia and overseas, particularly in India and the USA, and our results are published regularly in the community press.Read moreRead less
East meets West: an archaeological study of early contact between China and Eurasia. The project will link Chinese and Australian researchers in a collaborative programme exploring the origins of cultural contact between China and the West. Through the work of a team of international specialists, this fresh initiative will bring western analytical techniques together with Chinese archaeological experience to create a new and robust picture of the evidence for early cultural contact. From this we ....East meets West: an archaeological study of early contact between China and Eurasia. The project will link Chinese and Australian researchers in a collaborative programme exploring the origins of cultural contact between China and the West. Through the work of a team of international specialists, this fresh initiative will bring western analytical techniques together with Chinese archaeological experience to create a new and robust picture of the evidence for early cultural contact. From this we will study the early movements of Indo-European populations and examine the question of the origins of early metal production in China.Read moreRead less
With or without pots: Investigating the archaeology of human settlement on Santa Isabel, western Solomon Islands. Following the recent civil unrest in the Solomon Islands, the SI National and Provincial Governments, as well as community bodies, have identified a better understanding of the past and the revival of traditional systems and knowledge (Kastom) as a route to stability and cohesion throughout the region. This study responds to direct requests from the Santa Isabel community for assist ....With or without pots: Investigating the archaeology of human settlement on Santa Isabel, western Solomon Islands. Following the recent civil unrest in the Solomon Islands, the SI National and Provincial Governments, as well as community bodies, have identified a better understanding of the past and the revival of traditional systems and knowledge (Kastom) as a route to stability and cohesion throughout the region. This study responds to direct requests from the Santa Isabel community for assistance with archaeological research and the recording of cultural histories. By assisting a Pacific neighbour to develop a more durable, internally generated basis for social and economic development, Australia not only encourages security in the region, but also increases its engagment with and understanding of adjacent cultures.Read moreRead less