The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - t ....The Sakai scheme-Askey table correspondence, analogues of isomonodromy and determinantal point processes. The Australian mathematical sciences enjoys two research groups with active interests on Painleve equations in applied mathematics which are able to address difficult problems. Such a problem is to give a formulation of Sakai's 2001 classification of the Painleve equations in a form most suitable for applications. For this links will be made with a seemingly distinct area of mathematics - the Askey table from the theory of hypergeometric orthogonal polynomials. A number of tractable PhD projects are suggested by this proposal.Read moreRead less
Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions ....Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions will be used to improve the accuracy of regional economic models and will contribute to efficient regional resource management. This has the potential to positively affect the economic growth and employment in the region. The expected outcomes of the project are especially important taking into account the need for predicting the socio-economic consequences of the 1994 COAG water reforms. Read moreRead less
Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathe ....Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathematical physics experts in Australia. The research in these exciting areas of mathematics will contribute to maintaining Australia's position as a research leader in pure mathematics.
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The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to com ....The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to computational mathematics, particularly elliptic curve cryptosystems; - a huge boost to the development of number theory Australia-wide.
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Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of th ....Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of the modern methods in the theory require expertise in mathematics as well as a high level of programming skills. This combination provides a unique training ground for higher degree students aiming at careers in financial mathematics, weather/climate forecasting and internet security.
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Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Generalized group characters. With its numerous international visitors, Ganter's program will be a significant gain for Melbourne as a centre of science and research. Students at all levels will benefit from training in a scientific environment of world-rank.
Ganter plans to build a research community in her field, involving individuals across the nation; this will be a good addition to the Australian research landscape. Finally, she hopes that her past experience in working with minority stud ....Generalized group characters. With its numerous international visitors, Ganter's program will be a significant gain for Melbourne as a centre of science and research. Students at all levels will benefit from training in a scientific environment of world-rank.
Ganter plans to build a research community in her field, involving individuals across the nation; this will be a good addition to the Australian research landscape. Finally, she hopes that her past experience in working with minority students will enable her to contribute to creating a more diverse research community in pure mathematics in Melbourne and across Australia.Read moreRead less
Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
Random Structures and Asymptotics. Discrete random structures have many uses in algorithms in computer science (for instance, random networks modelling computer link-ups), biology (for instance, random sequences modelling DNA) and engineering. New techniques for studying these structures will lead to powerful new results on their properties. The emphasis will be on the behaviour of the random structures when their size becomes large. With the advent of
more powerful computing techniques, it is ....Random Structures and Asymptotics. Discrete random structures have many uses in algorithms in computer science (for instance, random networks modelling computer link-ups), biology (for instance, random sequences modelling DNA) and engineering. New techniques for studying these structures will lead to powerful new results on their properties. The emphasis will be on the behaviour of the random structures when their size becomes large. With the advent of
more powerful computing techniques, it is often the large-scale behaviour which has relevance to the more diffucult computations being undertaken. The results are also of potential application to other areas of mathematics.Read moreRead less
Rigidity in measured group theory and geometric group theory. Elite universities throughout the world have all made a point of being leaders in the field of pure mathematics. Geometric group theory and orbit equivalence are currently topical areas which attract many of the best young pure mathematicians as is demonstrated by recent invited talks at the International Congress of Mathematicians. This project will foster the development of these fields in Australia as well as nurturing existing e ....Rigidity in measured group theory and geometric group theory. Elite universities throughout the world have all made a point of being leaders in the field of pure mathematics. Geometric group theory and orbit equivalence are currently topical areas which attract many of the best young pure mathematicians as is demonstrated by recent invited talks at the International Congress of Mathematicians. This project will foster the development of these fields in Australia as well as nurturing existing efforts and international links. This proposal will also provide training and research experience for Australian honours and graduate students in mathematics.Read moreRead less