Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify ....Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify the Riemann hypothesis several orders of magnitude further than what is currently known. A secondary aim is to apply this new verification to a multitude of results in analytic number theory: this would provide future researchers with vastly superior results.Read moreRead less
Stabilisation of nonlinear quantum feedback control systems. One of the most exciting technological developments of this century promises to be the development of quantum technology. Quantum feedback systems will play a key part of this technology and this project will develop the underlying fundamental theory which will be crucial to the systematic design of quantum feedback control systems.
Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their ....Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their operation. Standard control system methods do not take into account the special features of quantum systems and there is a need for new control theories that deal with stabilisation and synchronisation as quantum technologies become more advanced. Read moreRead less
Singular phenomena for nonlinear partial differential equations arising in applications. The development of nonlinear Partial Differential Equations (PDEs) in Australia is recognized worldwide through the outstanding contributions of mathematicians from the ANU, University of Sydney and other top Australian Universities. This project undertakes research in the PDEs field and follows directions of very current interest at an international level. Beyond the ANU, the project will enhance expertise ....Singular phenomena for nonlinear partial differential equations arising in applications. The development of nonlinear Partial Differential Equations (PDEs) in Australia is recognized worldwide through the outstanding contributions of mathematicians from the ANU, University of Sydney and other top Australian Universities. This project undertakes research in the PDEs field and follows directions of very current interest at an international level. Beyond the ANU, the project will enhance expertise in Australia in very active areas of mathematics research related to applications in physics, biology and other applied disciplines. Moreover, it will foster collaboration with mathematicians of international standing from Australia and abroad. Read moreRead less
Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere ....Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere type equation arising in applied sciences, by introducing new ideas and developing innovative cutting-edge techniques. Expected outcomes include resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.
Read moreRead less
Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive ....Explicit methods in number theory: Computation, theory and application. This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive roots to signal processing, cryptography and cybersecurity.Read moreRead less
Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater moni ....Control and learning for enhancing capabilities of quantum sensors. This project aims to develop new theories and algorithms to enhance capabilities in engineering quantum sensors from the perspective of systems and control. The project is significant because it is anticipated to advance key knowledge and provide systematic methods to enable achievement of high-precision sensing for wide applications, e.g., early disease detection, medical research, discovery of ore deposits and groundwater monitoring. The intended outcomes are fundamental theories, effective control and learning algorithms for achieving highly-sensitive sensors. These outcomes should make important contributions to and deliver new knowledge and skills for Australia's sensing industries, which could benefit Australia's economic growth.Read moreRead less
Control of network systems with signed dynamical interconnections. New technologies such as online recommendations, smart grids, and cyber-physical systems are becoming backbone infrastructure. Such systems are operated as network systems with interconnected functioning units (agents) where cooperative and adversarial agent relations often coexist. This project aims to develop the theories and tools for designing and building dynamic networks with signed interactions that arise from a variety of ....Control of network systems with signed dynamical interconnections. New technologies such as online recommendations, smart grids, and cyber-physical systems are becoming backbone infrastructure. Such systems are operated as network systems with interconnected functioning units (agents) where cooperative and adversarial agent relations often coexist. This project aims to develop the theories and tools for designing and building dynamic networks with signed interactions that arise from a variety of applications where both cooperative and adversarial agent interactions coexist. By developing theories and algorithms for control and identification over such systems, this project will contribute directly to their safe and robust operation. The resulting theories will provide deeper understanding of network control systems and the resulting algorithms will enable the elimination of attackers and malicious users for online review systems and smart grids. This project will contribute to increased cybersecurity for all Australians.Read moreRead less
Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in e ....Generalised Energy Based Robust and Nonlinear Control Systems. This project aims to develop new energy-based theories of robust stability analysis and controller design for both linear and nonlinear systems, building on passivity and negative imaginary system theories and their physical interpretations along with stochastic optimal control theory. These control theories would allow for a wide range of plant dynamics in the design of high-performance robust control systems, enabling advances in emerging technologies including nanopositioning, micro-electromechanical systems and opto-mechatronics. The project plans to combine these theoretical advances with numerical methods involving advanced optimisation tools and the experimental implementation of nanopositioning control systems in atomic force microscopy.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120102873
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Securing networked control and estimation systems and safeguarding critical infrastructure. The purpose of this project is to reduce the likelihood of success, and the severity of impact, of a cyber-attack against networked control and estimation systems operating within critical infrastructure. The outcome will be a suite of algorithms, tools and design considerations for networked, industrial, control systems that satisfy this purpose.