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Geodetic groups: foundational problems in algebra and computer science. The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being geodetic is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations.
The project team's expertise in geodesic properties of groups, the interaction between formal languages and g ....Geodetic groups: foundational problems in algebra and computer science. The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being geodetic is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations.
The project team's expertise in geodesic properties of groups, the interaction between formal languages and groups, and the theory of rewriting systems, together with recent breakthroughs by the team ensures that significant results can be expected.
Benefits include training research students and postdoctoral researchers in cutting-edge techniques, and advancing fundamental knowledge in mathematics and computer science.Read moreRead less
ARC Centre of Excellence for Plant Success in Nature and Agriculture. The ARC CoE for Plant Success in Nature and Agriculture will discover the adaptive strategies underpinning productivity and resilience in diverse plants and deepen knowledge of the genetic and physiological networks driving key traits. Using novel quantitative and computational approaches, the Centre will link gene networks with traits across biological levels, giving breeders an unparalleled predictive capacity. The Centre wi ....ARC Centre of Excellence for Plant Success in Nature and Agriculture. The ARC CoE for Plant Success in Nature and Agriculture will discover the adaptive strategies underpinning productivity and resilience in diverse plants and deepen knowledge of the genetic and physiological networks driving key traits. Using novel quantitative and computational approaches, the Centre will link gene networks with traits across biological levels, giving breeders an unparalleled predictive capacity. The Centre will accelerate technologies to transfer successful networks into crops and build legal frameworks to secure this knowledge. With a uniquely multidisciplinary team, the Centre will deliver new strategies to address the problems of food security and climate change, establishing Australia as a global leader in these areas.Read moreRead less
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. 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
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
Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, ....Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, statistics and different ways of aggregating information. By building a more complete theoretical map it is expected that new machine learning methods will be developed, but more importantly that machine learning will be able to be better integrated into larger socio-technical systems.Read moreRead less
New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are ....New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are at the limit of the range of mathematical techniques. Solving these problems is expected to influence non-commutative analysis.Read moreRead less
Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quanti ....Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quantitative tools within a unifying framework. The anticipated project outcomes will be of mathematical interest and valuable in applications such as finance (predicting Australian stock returns); modelling electroencephalography data; Australian geochemical data, relating to sediments; and Australian X-ray tumour image data. Read moreRead less
Control and Optimization of Distributed Multiagent Formations. The project aims to develop a conceptual framework and algorithms for handling multi-vehicle formation control. Formations of unmanned airborne vehicles are currently used by defence forces and swarms of micro-vehicles are beginning to find increasing use in defence and for civilian emergency response, largely for surveillance purposes. Vehicles must cooperate to achieve a global formation objective, while respecting constraints on s ....Control and Optimization of Distributed Multiagent Formations. The project aims to develop a conceptual framework and algorithms for handling multi-vehicle formation control. Formations of unmanned airborne vehicles are currently used by defence forces and swarms of micro-vehicles are beginning to find increasing use in defence and for civilian emergency response, largely for surveillance purposes. Vehicles must cooperate to achieve a global formation objective, while respecting constraints on sensors, energy, and general mechanical limitations. The project aims to resolve the challenges of deciding what a single vehicle should observe, what and to where it should communicate, and how it should move in relation to what it sees. The conceptual framework developed may also be relevant in guiding future defence acquisitions and civilian applications.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200101834
Funder
Australian Research Council
Funding Amount
$418,410.00
Summary
The structure of singularities in geometric flows. The proposed research aims to develop our understanding of the structure of singularities in mean curvature and related flows, with certain applications in mind.