Operator algebras associated to product systems, and higher-rank-graph algebras. Operator algebras are used to study a wide range of physical systems in quantum physics and quantum computing, and in electrical engineering. The clearer our picture of how operator algebras work, the better we are able to predict and explain how these physical systems will behave. The proposed research project is aimed at showing that we can describe operator algebras in terms of simple coloured diagrams rather tha ....Operator algebras associated to product systems, and higher-rank-graph algebras. Operator algebras are used to study a wide range of physical systems in quantum physics and quantum computing, and in electrical engineering. The clearer our picture of how operator algebras work, the better we are able to predict and explain how these physical systems will behave. The proposed research project is aimed at showing that we can describe operator algebras in terms of simple coloured diagrams rather than abstract mathematical symbols. Consequently, the project will lead to a simpler and less technical approach to the physical problems which operator algebras are used to study.Read moreRead less
Extension of representations and homogeneous spaces. The CI is an early-career researcher who is establishing her research program. The proposed project will allow her to broaden the scope of this program by involving other young Australians, including students. The project involves taking a new approach to a classical problem in representation theory; the outcomes will be of interest to a broad range of the mathematical community in Australia and overseas.
A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less