Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asympt ....Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asymptotics is proposed, allowing the rate to be quantified for a large class of model
ensembles, and providing predictions in the various applied settings. The broad project is to be networked with researchers in the Asia-Oceania region, with the aim of establishing leadership status for Australia.Read moreRead less
An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE170100171
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to i ....Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to improve magneto-hydrodynamic flow control in future energy-generating technology, using theoretical and numerical tools that are mathematically consistent with the high-speed limit of the governing equations. More efficient electric generators could improve Australia’s future energy supply with fewer emissions of global warming gases.Read moreRead less