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
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
Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approac ....Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approaches that struggle to rapidly respond to new information. This should provide significant benefits. Specifically, this project aims to facilitate a technological leap that generates smaller, faster, and more powerful embedded systems such as broadband services, mobile phones, medical imagining, radar and avionics.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
Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms dev ....Cooperative control of networked systems with constraints. This project aims to address the challenge of networked systems in deploying teams of robotic agents. Control of the networked system is extremely difficult due to real world constraints imposed on each agent. This project will focus on motion constraints, equipment/capability constraints, and spatial constraints. In addition to theoretical advances, the wider scientific community will benefit directly, because the control algorithms developed are expected to allow straightforward deployment of robotic teams. There are myriad applications for cooperative robotic agents, ranging from surveillance, to environmental monitoring using underwater and aerial drone formations – with an array of benefits and impacts including economic, commercial and societal. The results are intended to ensure and cement Australia’s front-line position in the current technological revolution known as “Industry 4.0”.Read moreRead less
Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the lands ....Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the landscape of topological and conformal field theories, laying the foundation for new technologies based on topological order. This timely project capitalises on the recent arrival of subfactor experts in Australia, and builds capacity in mathematical research and international links in a cutting edge field.Read moreRead less
Reconciliation strategies for continuous variable quantum key distribution. This project aims to advance a novel key distribution method, called quantum key distribution, which distributes secure keys using the quantum state of optical channels. Key distribution is a foundational part of data security, allowing digital keys to be securely exchanged between two or more parties, before they are used to protect and share information. The expected outcome is new rateless error correction codes desi ....Reconciliation strategies for continuous variable quantum key distribution. This project aims to advance a novel key distribution method, called quantum key distribution, which distributes secure keys using the quantum state of optical channels. Key distribution is a foundational part of data security, allowing digital keys to be securely exchanged between two or more parties, before they are used to protect and share information. The expected outcome is new rateless error correction codes designed specifically to implement quantum key distribution over long distances. Quantum key distribution is beneficial for ultra-secure communications as it avoids the vulnerability to weak random numbers and quantum-computing brute force attacks that currently threated the security of data protected by existing methods. Read moreRead less
New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact soluti ....New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.Read moreRead less
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Monetary policy, redistribution and endogenous asset market incompleteness. This project aims to provide a new framework for modelling agent heterogeneity and for evaluating the effects of monetary policy on aggregate welfare and wealth distribution over the business cycle. This project will focus on monetary policy, using new quantitative theories with new efficient computational methods, to understand and quantify links between monetary policy the dynamics of aggregate outcomes (such as inflat ....Monetary policy, redistribution and endogenous asset market incompleteness. This project aims to provide a new framework for modelling agent heterogeneity and for evaluating the effects of monetary policy on aggregate welfare and wealth distribution over the business cycle. This project will focus on monetary policy, using new quantitative theories with new efficient computational methods, to understand and quantify links between monetary policy the dynamics of aggregate outcomes (such as inflation or employment), and the distribution of individual wealth (such as money, capital and housing).Read moreRead less