Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is ....Exploring the Frontiers of Feasible Computation. The project aims to delineate the boundary between feasible and infeasible computational problems. A problem is considered feasible if there is an algorithm to solve it in worst-case time bounded by a polynomial in the input size. This is probably impossible for the important class of NP-complete problems. However, typical examples of NP-complete problems can often be solved in polynomial time, because worst-case problems are rare. The project is relevant to public-key cryptography, where breaking an encryption scheme should be infeasible, and to many real-life situations where NP-complete problems need to be solved, either exactly or approximately.Read moreRead less
Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their ....Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their collective behaviour. The project will investigate in detail the geometry, topology, materials science and statistical physics of networks, leading to design and characterization of robust self-assembled materials and complex systems.Read moreRead less
Conformal Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic sci ....Conformal Differential Geometry. Differential geometry is a major branch of mathematics studying shape by using calculus and differential equations. This is a fundamental research project in this area, especially concerned with the interaction between geometry, differential equations, and symmetry. The mathematical notion of symmetry was already formalised early last century and nowadays lies at the very heart of mathematics and physics. Advances in this area provide essential tools in basic science and unexpected technological benefits can easily arise (for example, in medical imaging). Fundamental mathematical research is absolutely necessary if Australia is to maintain a presence on the international scientific stage.Read moreRead less
COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet i ....COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet illustrate the need for research on modelling, analysis of behaviour, planning and control in such networks. This project aims to establish research in this area for Australia's benefit.Read moreRead less