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
The Consistency of Price Regulation of Infrastructure Businesses across Australian Jurisdictions. The spread of regulation across the majority of the economy necessitates that regulatory policy should be consistent across jurisdictions and industries. This project would offer policy and regulatory institutions quantitative analysis of the consistency of regulatory decisions across Australia. This research would develop a new database that would maintain and supply details on regulatory decision ....The Consistency of Price Regulation of Infrastructure Businesses across Australian Jurisdictions. The spread of regulation across the majority of the economy necessitates that regulatory policy should be consistent across jurisdictions and industries. This project would offer policy and regulatory institutions quantitative analysis of the consistency of regulatory decisions across Australia. This research would develop a new database that would maintain and supply details on regulatory decisions across jurisdictions and industries. This project would enable the new Australian Centre of Regulatory Economics (ACORE) to supply independent database and quantitative analysis from an open, fully documented, scholarly environment to Australia's policy and regulatory agencies and its regulated firms.Read moreRead less
What makes for successful numeracy education in remote Indigenous contexts: an ethnographic case study approach. There are many successful teachers and schools who have enabled remote Indigenous learners to engage with, and learn, school mathematics. But what do they do? How do they do it? This project investigates and documents successful practices in 32 schools located in remote communities. The project includes the many aspects of teaching practice.
Social and geographical location and its impact on mathematics teaching and learning. Too many students from poor urban backgrounds or from rural communities are at risk of underperforming in school mathematics. This project identifies the critical factors that contribute to this failure and seeks to develop improved practices to enable greater access to school mathematics.
Honesty and efficiency in the provision of expert services: doctors and other experts as participants in economic experiments. Experts serve us when we see the doctor, the financial planner or the car mechanic. In all these case the expert can take advantage of his superior knowledge and sell us something we do not need. This research will inform policy makers about the underlying motives of real world experts and allow them to design better institutions.
Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
The demographic consequences of migration to, from and within Australia. The long-term demographic consequences of migration to, from and within Australia, and the dynamic pathways that produced them, will be studied. This will involve the identification of the specific contributions made by international and internal migration to the age and sex population compositions of nine birthplace-specific populations from 1981 to 2011. To do this, publically available data will be collected and augmente ....The demographic consequences of migration to, from and within Australia. The long-term demographic consequences of migration to, from and within Australia, and the dynamic pathways that produced them, will be studied. This will involve the identification of the specific contributions made by international and internal migration to the age and sex population compositions of nine birthplace-specific populations from 1981 to 2011. To do this, publically available data will be collected and augmented with statistical methods to provide a complete, consistent account of population change for around 60 subnational areas. As migration and population change underpins many aspects of societal change in Australia, this research aims to provide an invaluable resource to other scientists and policy makers.Read moreRead less
Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less
The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interpla ....The Ricci curvature of homogeneous spaces. The geometry of homogeneous spaces is an area of research with applications in numerous fields, including topology, harmonic analysis, relativity and quantum theory. This project aims to resolve a fundamental problem in this area, known as the prescribed Ricci curvature problem for homogeneous metrics, and to settle the important and closely related question of Ricci iteration existence and convergence. Moreover, the project aims to exploit the interplay between geometry and algebra to provide new insight into the physically significant problem of classifying unitary Lie algebra representations. This project is expected to facilitate interdisciplinary interaction leading to exciting developments across a range of fields.Read moreRead less
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