These programs are largely administered through the CMA. A report on each one is contained in Section 9.

Here is a selection of significant achievements made by members of the CMA during the year. Trudinger and Wang solved the Bernstein problem for affine maximal surfaces. Baxter solved a problem in Statistical Mechanics which has been outstanding since 1990, namely he verified directly that two known expressions for the free energy of the chiral Potts model are the same, an equivalence that is by no means obvious. Isaev gave a complete description of Kobayashi hyperbolic n-dimesional complex manifolds with automorphism group of dimension larger than n². Kovacs and collaborators identified the nonprojective indecomposable direct summands of free Lie algebras of rank less than 2p over fields of prime characteristic p. Osborne developed a general theory of simplicial algorithms for the class of methods that includes the ubiquitous Dantzig linear programming algorithm. For further details, along with numerous other achievements, see Section 9.

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. Reports of those held during 1999 are presented in Section 5. 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 international conferences. Indeed, the CMA has an exceptional international profile for its size.

There are several seminar series as well as the School's weekly colloquium. The CMA publishes a series of research monographs and has extensive series of mathematical and statistical reports. Details appear later.

This year two long-standing and highly valued members of the CMA retired, namely Mike Newman and Mike Osborne, though both remain with us as Visiting Fellows. 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 which can provide links with other sections of the University. The theoretical core of activities must also be kept at its 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.

A high percentage of our staff are employed on contracts of two to five years. These include several people on ARC Research Fellowships. One of our research fellows, John Urbas, was honoured in 1999 by the award of the prestigious Australian Mathematical Society Medal.

Six CMA National Research Symposia were held in 1999, individual reports of which appear later. These comprise a major component of our national outreach. The program is overseen by a national committee, and administered by the CMA. The organisers come from the Australian mathematical and statistical community, and the symposia are normally, but not always, held in Canberra. Unfortunately, the grant which has been used to subsidize these symposia is now spent, but the program will remain active in 2000 with SMS support, though on a reduced scale. It will be a challenge for the CMA to find support to maintain its current national role in the coming years, but every effort will be made to do so. However, its national and international profile remain exceptional, and hopefully will continue to remain so.