Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less
An investigation of the impacts of increased power supply to the national grid by wind generators on the Australian electricity industry. The aim of this project is to discover the most economical and effective way to accommodate large increases in wind power into the national grid and to understand the effects on the national electricity market. This is crucial to ensure stability of electricity supply and affordable prices in the transition towards a low carbon economy.