Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathe ....Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathematical physics experts in Australia. The research in these exciting areas of mathematics will contribute to maintaining Australia's position as a research leader in pure mathematics.
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Social Network Analysis: Social Media, Peer Effects and the Environment. The aims of this proposal are to better understand the role of networks in different activities such as social media, education, crime and environment-friendly behaviour. The project expects to help inform the design and practice of policies for education and environmental authorities, police and media markets. Social networks are pervasive in Australia. The project tackles issues of criminal gangs in Australian cities, the ....Social Network Analysis: Social Media, Peer Effects and the Environment. The aims of this proposal are to better understand the role of networks in different activities such as social media, education, crime and environment-friendly behaviour. The project expects to help inform the design and practice of policies for education and environmental authorities, police and media markets. Social networks are pervasive in Australia. The project tackles issues of criminal gangs in Australian cities, the political system and environment-friendly behaviours. This project is at the frontier of work in the economics of networks, with expected outcomes to include new models and methods to better understand the impact of social networks. Benefits include clear policy recommendations to improve welfare in Australian society.Read moreRead less
New methods in network economics to study environment-friendly behaviours. This project aims to develop two new methodologies for measuring how people interact with each other and how one’s peers affect their outcomes. The project expects to test these new ground-breaking models for investigating the effect of peers and networks on environmental issues, such as recycling behaviours. The anticipated outcomes of this project include new theoretical and empirical advancements for studying the econo ....New methods in network economics to study environment-friendly behaviours. This project aims to develop two new methodologies for measuring how people interact with each other and how one’s peers affect their outcomes. The project expects to test these new ground-breaking models for investigating the effect of peers and networks on environmental issues, such as recycling behaviours. The anticipated outcomes of this project include new theoretical and empirical advancements for studying the economics of networks and peers for better policy design. Benefits include clear policy recommendations to motivate environment-friendly behaviours. Read moreRead less
The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to com ....The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to computational mathematics, particularly elliptic curve cryptosystems; - a huge boost to the development of number theory Australia-wide.
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Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their bud ....Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their budget constraints. It also aims to uncover the relationship between the innate abilities of workers and their education choices - and the consequences for macro economies and public policy.Read moreRead less
Reading the Social Future of the Australian Red Cross Blood Service. This project investigates how and if the Australian Red Cross Blood Service (ARCBS) is building social capital. It does this by interrogating existing practices and operations at the ARCBS and by surveying donors and non-donors. This project aims to develop a Deleuzian critique of the notion of social capital.
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
Subtle Symmetries and the Refined Monster. The project plans to develop a new conceptual framework for the representations and characters of categorical groups. The field of representation theory exploits the symmetries of an object (eg a molecule) in order to facilitate its study. This project aims to investigate the case where the symmetries themselves are related by symmetries. Traditionally often ignored, this subtle but powerful information turns out to be at the heart of various deep pheno ....Subtle Symmetries and the Refined Monster. The project plans to develop a new conceptual framework for the representations and characters of categorical groups. The field of representation theory exploits the symmetries of an object (eg a molecule) in order to facilitate its study. This project aims to investigate the case where the symmetries themselves are related by symmetries. Traditionally often ignored, this subtle but powerful information turns out to be at the heart of various deep phenomena. It is anticipated that the project’s approach recasts and simplifies some important and difficult mathematics, providing a new approach to affine representation theory, to the foundations and symmetries of string theory, and the Refined Monster Conjecture.Read moreRead less
Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived ....Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived categories of algebraic stacks via the
Fourier-Mukai transform.
The benefit will be to enhance the international stature of Australian
science.Read moreRead less
Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relat ....Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relationship between algebraic and other geometries.
The benefit will be to enhance the international stature of Australian science.Read moreRead less