Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing th ....Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing the global behaviour of such elusive solutions, particularly when the systems depend on many variables.Read moreRead less
Fusion Energy and the Physics of Burning Plasmas. The world faces a global energy crisis. Our standard of living, which is largely powered by base-load electricity supply, is unsustainable. Fusion power is a near zero greenhouse gas technology, which promises millions of years of base-load electricity, free from weapon proliferation. This promise has galvanised the international community to accelerate fusion development by committing to the next-step technology-enabling $16 billion experiment, ....Fusion Energy and the Physics of Burning Plasmas. The world faces a global energy crisis. Our standard of living, which is largely powered by base-load electricity supply, is unsustainable. Fusion power is a near zero greenhouse gas technology, which promises millions of years of base-load electricity, free from weapon proliferation. This promise has galvanised the international community to accelerate fusion development by committing to the next-step technology-enabling $16 billion experiment, International Thermonuclear Experimental Reactor (ITER). In anticipation of ITER, this fellowship will foster growth of Australian fusion research, and address a grand science challenge facing ITER: how do we maintain burn in the face of potentially damaging plasma instabilities? The answer will affect both ITER and the viability of fusion power.Read moreRead less
Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will ....Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will enable Australia to maintain a position at the forefront of Pure Mathematics, and by recruiting a recent winner of the highly prestigious Karp prize the country will be instantly established as one of the leading centers of Mathematical Logic.Read moreRead less