The Centre for Mathematics and its Applications (CMA) has the primary function of a research institute in the mathematical sciences, fulfilling both national and international roles in this capacity. It comprises all the Institute members of the School together with some members of The Faculties. A high percentage of our staff are employed on contracts of two to five years, including several people on ARC Research Fellowships.
The principal research activities of the School, which are administered through the CMA, are divided into seven research programs and are grouped as follows:
Mathematics:
Statistics:
Applied Mathematics:
Members of the CMA participate with staff from the Department of Mathematics in these programs to form the focal point of research interaction in the School, (refer to SMS Research Programs).
Each program has a large number of visitors and extensive international contacts. As shown later in this report, there is a wealth of powerful international collaboration. A large number of leading mathematicians and statisticians visit us from overseas as well as from within Australia. Our members regularly visit their colleagues overseas, and are invited to participate in international conferences. Indeed, the CMA has an exceptional international profile for its size.
A selection of significant achievements by members of the CMA during the year follows. In collaborative work with the French mathematicians, Auscher and Tchamitchian, and the Americans, Hofmann and Lacey, Alan McIntosh solved a problem which has aroused a lot of interest since it was posed by Kato forty years ago. Min-Chun Hong resolved a long-standing conjecture about energy-minimizing deformations of a ball. Amnon Neeman obtained results with Ranicki about higher-dimensional knot invariants by applying Thomason's localisation theorem to the K-theory of non-commutative rings. Rodney Baxter has given a new formulation of the combinatorial meander problem in terms of the well known Temperley-Lieb algebra.
The CMA conducts several seminar series as well as a weekly colloquium. It publishes a series of research monographs and has extensive series of mathematical and statistical reports.
In its national role, the CMA organises and sponsors programs and conferences involving Australian and overseas researchers. In particular it supports a scheme of National Research Symposia. In 2000, there were 5 such symposia, individual reports of which appear later. The program was overseen by a national committee, while the organisers come from the Australian mathematical and statistical community. The program will continue in 2001, though on a reduced scale. It will be a challenge for the CMA to find support to maintain its national role in the coming years, but every effort will be made to do so. However, its national and international profile remains exceptional, and is expected to continue.
This year Derek Robinson, a long-standing and highly valued member of the CMA, retired; he will continue his association with the CMA as a Visiting Fellow and holds an ARC grant. The next few years will see several more retirements. This presents us with the opportunity and the challenge of assessing our role and determining the areas in which to concentrate our resources and build our future strength. We are already committed to development of the applied and computational areas, and have recently appointed Markus Hegland who has strong connections with other sections of the University and with the Australian Partnership in Advanced Computation. Sue Wilson developed substantial links between our School and the John Curtin School of Medical Research through the establishment of the Centre in Bioinformation Science. The theoretical core of activities must also be kept at its current high level of strength. In this way, the CMA will remain the strongest mathematical and statistical research group in this country and maintain its international reputation.
Joe Gani was awarded Membership of the Order of Australia (AM) for his contribution to mathematical research, in particular applied probability and mathematical biology. He was also awarded the Moyal Medal when he gave the inaugural Moyal Lecture at Macquarie University. Peter Hall was elected to Fellowship of the Royal Society of London.
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