New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to w ....New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to wave scattering by objects with complex scattering mechanisms, as typified by cavity structures. This new formulation is obtained by a process of analytical regularisation of the equations describing the scattering process. It generates algorithms more reliable and computationally accurate than current codes.
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Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by t ....Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by the CI. All indications are that the new ideas relating integrable structures and random matrices underpinning this proposal will fulfil this goal. For the postdoctral researcher involved the stimulating atmosphere of discovery should provide ideal training in mathematical research.Read moreRead less
Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, a ....Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, another line of applications will be emphasized, and a new axis of international linkage formed.Read moreRead less