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Quantum symmetries: mathematical models for topological matter. This project aims to investigate quantum symmetries, new mathematical objects which allow an algebraic description of topological phases of matter. The project expects to bridge the current gap between our mathematical and physical understandings of these topological phases of matter. The project will develop innovative tools for analysing and constructing new exotic symmetries, and provide an extensive survey of examples. It is exp ....Quantum symmetries: mathematical models for topological matter. This project aims to investigate quantum symmetries, new mathematical objects which allow an algebraic description of topological phases of matter. The project expects to bridge the current gap between our mathematical and physical understandings of these topological phases of matter. The project will develop innovative tools for analysing and constructing new exotic symmetries, and provide an extensive survey of examples. It is expected to build national research capacity in an emerging field and put Australia at the forefront of the mathematics of topological matter.Read moreRead less
Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this pr ....Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this project include resolutions of open problems in the theory of Artin groups and the creation of a new subject, the dynamical theory of two-linear groups.Read moreRead less
Towards a new concrete theory of cohomology: a fundamental concept in geometry. This project will develop a geometric linearisation method related to Witt vectors, an exotic but important number system. This will let us take one more step towards solving a fifty-year-old mystery: to find the elusive universal linearisation in algebraic geometry, which is the linearisation that controls all the others.
Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic beh ....Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic behaviour of the dimensions of the irreducible representations. Second, it will explore the evolution of representations across families of groups under new induction and restriction functors, in analogy with creation and annihilation operators in physics. The project will enhance Australia's capacity in representation theory and group theory, the mathematics that underline symmetry in nature.Read moreRead less
Solving and estimating dynamic models of strategic interaction. This project aims to investigate how firms interact with each other through time and how these interactions drive both the operation of, and value created in, economic markets. While recent theoretical models predominantly capture the complexity of these dynamic interactions, the methods for testing these models’ predictions against observed data do not. Instead, they are based on a range of simplifying assumptions that undermine th ....Solving and estimating dynamic models of strategic interaction. This project aims to investigate how firms interact with each other through time and how these interactions drive both the operation of, and value created in, economic markets. While recent theoretical models predominantly capture the complexity of these dynamic interactions, the methods for testing these models’ predictions against observed data do not. Instead, they are based on a range of simplifying assumptions that undermine the reliability of their analysis. This project will develop statistical and computational methods to better understand observed economic behaviour. By allowing the effects of proposed economic interventions and regulations ex ante, this project will support the development of more efficient and better-targeted policies in every area of the economy.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
Feasibility in politics: Taking account of groups and institutions. This project aims to research feasibility in politics. Normative political discourse is pervaded by the use of claims about what is feasible and infeasible. The project will examine feasibility practices, the functions they serve, what is required to serve the functions effectively, how actual practices stack up, and how to improve them. It will fuse philosophical and empirical analysis; encompass three salient case studies (imm ....Feasibility in politics: Taking account of groups and institutions. This project aims to research feasibility in politics. Normative political discourse is pervaded by the use of claims about what is feasible and infeasible. The project will examine feasibility practices, the functions they serve, what is required to serve the functions effectively, how actual practices stack up, and how to improve them. It will fuse philosophical and empirical analysis; encompass three salient case studies (immigration, poverty and climate change); and engage practitioners, commentators and ordinary citizens. The project intends to inform the development of just and effective immigration, poverty and climate change policy, reflecting a better understanding of the role of feasibility in politics.Read moreRead less
Future fables: literature, evolution and artificial intelligence. The future of AI is a site of considerable philosophical and cultural anxiety in the West. Given the future of AI is currently only available to publics through literary or fictional tropes, it is vital that we investigate the historical evolution of these literary or fictional tropes of AI to understand its future direction. This project aims to understand (1) how the post-Darwinian literary imagination has shaped our current anx ....Future fables: literature, evolution and artificial intelligence. The future of AI is a site of considerable philosophical and cultural anxiety in the West. Given the future of AI is currently only available to publics through literary or fictional tropes, it is vital that we investigate the historical evolution of these literary or fictional tropes of AI to understand its future direction. This project aims to understand (1) how the post-Darwinian literary imagination has shaped our current anxieties about AI and (2) how literary and scientific writers after Darwin rethink the future of the human species by imagining the co-evolution of humans, animals and machines. Expected outcomes of the project include conceptual resources to understand the human-nonhuman relation and the future of AI.Read moreRead less
Automatic Authorities: Charting a Course for Legitimate AI. Public and private actors are increasingly using Artificial Intelligence (AI) to exercise power over citizens, who are increasingly unsure whether to accept that power. AI faces a crisis of legitimacy. This project aims to use technically- and empirically-grounded philosophy to make Australia a global leader in the study and design of legitimate AI. The project expects to launch and make fundamental progress in a new field: the Politica ....Automatic Authorities: Charting a Course for Legitimate AI. Public and private actors are increasingly using Artificial Intelligence (AI) to exercise power over citizens, who are increasingly unsure whether to accept that power. AI faces a crisis of legitimacy. This project aims to use technically- and empirically-grounded philosophy to make Australia a global leader in the study and design of legitimate AI. The project expects to launch and make fundamental progress in a new field: the Political Philosophy of AI. Expected outcomes include new strategies shared with industry and government partners for designing and deploying legitimate AI systems. Expected benefits include the opportunity to enjoy the public and private efficiencies enabled by AI, without compromising our freedom and equality.Read moreRead less