A safety-preserving ecosystem for autonomous driving. In this project, Macquarie University will collaborate with UTS and SilverQuest to develop an innovative safety-preserving ecosystem for autonomous driving. This system will not only be adopted by SilverQuest’s customers (automotive companies) to secure their latest autonomous driving models, but also be commercialised as a toolset that can be plugged into existing autonomous vehicles to detect and prevent malicious attacks on autonomous driv ....A safety-preserving ecosystem for autonomous driving. In this project, Macquarie University will collaborate with UTS and SilverQuest to develop an innovative safety-preserving ecosystem for autonomous driving. This system will not only be adopted by SilverQuest’s customers (automotive companies) to secure their latest autonomous driving models, but also be commercialised as a toolset that can be plugged into existing autonomous vehicles to detect and prevent malicious attacks on autonomous driving models. The project will lead to two innovations: in theory design an attack detection and prevention ecosystem for autonomous driving and in application implement a safety analysis toolset for industry-scale autonomous systems.Read moreRead less
Harmonic analysis: function spaces and partial differential equations. This project aims to solve a number of important problems at the frontier of harmonic analysis on metric measure spaces. Harmonic analysis has been instrumental to several fields of mathematics including complex analysis and partial differential equations which have had many applications in engineering and technology. This project will solve a number of important problems as well as develop new approaches and techniques for r ....Harmonic analysis: function spaces and partial differential equations. This project aims to solve a number of important problems at the frontier of harmonic analysis on metric measure spaces. Harmonic analysis has been instrumental to several fields of mathematics including complex analysis and partial differential equations which have had many applications in engineering and technology. This project will solve a number of important problems as well as develop new approaches and techniques for research in harmonic analysis and related topics. The project will maintain and enhance the strength of Australian mathematical research in harmonic analysis and contribute to the training of the next generation of mathematical researchers in Australia.Read moreRead less
Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications in ....Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications include medical imaging, fluid dynamics and subatomic modelling using quantum interpretation.
It will solve several important open problems in spectral analysis of partial differential operators and develop new cutting-edge techniques in harmonic analysis with application to nonlinear partial differential equations.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100052
Funder
Australian Research Council
Funding Amount
$2,107,500.00
Summary
Breakthrough methods for noncommutative calculus. This project aims to solve hard, outstanding problems which have impeded our ability to progress in the area of quantum or noncommutative calculus. Calculus has provided an invaluable tool to science, enabling scientific and technological revolutions throughout the past two centuries. The project will initiate a program of collaboration among top mathematical researchers from around the world and bring together two separate mathematical areas int ....Breakthrough methods for noncommutative calculus. This project aims to solve hard, outstanding problems which have impeded our ability to progress in the area of quantum or noncommutative calculus. Calculus has provided an invaluable tool to science, enabling scientific and technological revolutions throughout the past two centuries. The project will initiate a program of collaboration among top mathematical researchers from around the world and bring together two separate mathematical areas into a powerful new set of tools. The outcomes from the project will impact research at the forefront of mathematical physics and other sciences and enhance Australia’s reputation and standing.Read moreRead less
Machine learning, group theory and combinatorics. This project aims to investigate group theory and combinatorics using machine learning techniques. This project expects to generate new knowledge concerning symmetric groups and symmetric functions, using an innovative approach from reinforcement learning. Expected outcomes of this project include a clarification of the types of difficult problems in pure mathematics that can be gainfully attacked via machine learning, and an understanding of the ....Machine learning, group theory and combinatorics. This project aims to investigate group theory and combinatorics using machine learning techniques. This project expects to generate new knowledge concerning symmetric groups and symmetric functions, using an innovative approach from reinforcement learning. Expected outcomes of this project include a clarification of the types of difficult problems in pure mathematics that can be gainfully attacked via machine learning, and an understanding of the role of group theory in machine learning. This should provide significant benefits, such as progress on long standing open problems, the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in a vital area of research.Read moreRead less
Microlocal Analysis - A Unified Approach for Geometric Models in Biology . This project will use microlocal analysis to create a unified approach for predicting the outcome of a broad class of diffusion and reaction-diffusion models. This will replace the traditional theory which is no longer adequate for the level of geometric complexity demanded of current models arising in biology/ecology. This project will address the urgent need for a systematic theoretical underpinning of diffusion/reacti .... Microlocal Analysis - A Unified Approach for Geometric Models in Biology . This project will use microlocal analysis to create a unified approach for predicting the outcome of a broad class of diffusion and reaction-diffusion models. This will replace the traditional theory which is no longer adequate for the level of geometric complexity demanded of current models arising in biology/ecology. This project will address the urgent need for a systematic theoretical underpinning of diffusion/reaction-diffusion in geometric settings whose scope of application is broader than the the existing patchwork of methods.
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Discovery Early Career Researcher Award - Grant ID: DE200101310
Funder
Australian Research Council
Funding Amount
$426,918.00
Summary
Dimension-reduced Reinforcement Learning for Large-scale Fleet Management. This project aims to address the problems in large-scale fleet management to ensure the efficiency of tomorrow’s transportation models, such as on-demand ride-hailing and mobility-as-a-service. The expected outcomes of this project include improved techniques for optimising the utility of large fleets of vehicles, and particularly robust dimension-reduced reinforcement learning algorithms that are capable of handling the ....Dimension-reduced Reinforcement Learning for Large-scale Fleet Management. This project aims to address the problems in large-scale fleet management to ensure the efficiency of tomorrow’s transportation models, such as on-demand ride-hailing and mobility-as-a-service. The expected outcomes of this project include improved techniques for optimising the utility of large fleets of vehicles, and particularly robust dimension-reduced reinforcement learning algorithms that are capable of handling the complex dynamics of supply and demand in transportation. The results should advance both research and technology in academia and the transportation industry and will also provide significant benefits to Australia and the international community by enhancing the energy-efficiency of and access to the mobility of the future.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL230100256
Funder
Australian Research Council
Funding Amount
$3,359,669.00
Summary
Unlocking the secrets of modular representations. This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently p ....Unlocking the secrets of modular representations. This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently possible and a new understanding of the arithmetic difficulties present. Key benefits will be seen in the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in sophisticated theory and large-scale computation in concert.Read moreRead less
A Functional Analysis of the Hypoelliptic Laplacian. Strike a bell, a sphere, or any geometrical object, and it rings. The frequencies of ringing are the mathematical spectrum, which encodes deep secrets about the shape of the object. The spectrum of the hypoelliptic laplacian is known to carry deep truths in mathematics and physics, but it remains difficult to understand. We propose a new analytic foundation, which will replace the so far non-analytical ad hoc approach, and make accessible many ....A Functional Analysis of the Hypoelliptic Laplacian. Strike a bell, a sphere, or any geometrical object, and it rings. The frequencies of ringing are the mathematical spectrum, which encodes deep secrets about the shape of the object. The spectrum of the hypoelliptic laplacian is known to carry deep truths in mathematics and physics, but it remains difficult to understand. We propose a new analytic foundation, which will replace the so far non-analytical ad hoc approach, and make accessible many new results. It is key to better understanding differential equations which lie at the boundary between quantum mechanics and the classical world. This will pave the way for Australian leadership in a new century of differential equations and geometry, and training of young mathematicians.Read moreRead less
Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable s ....Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.Read moreRead less