Discovery Early Career Researcher Award - Grant ID: DE160100473
Funder
Australian Research Council
Funding Amount
$346,434.00
Summary
The invention of collateral damage and the changing moral economy of war. This project aims to provide a novel philosophical account of the invention of the concept of collateral damage in war. It seeks to understand the historical and institutional processes that have produced a moral distinction between deliberate harm inflicted on non-combatants, and the non-intentional harm that is seen as an inevitable side effect of modern warfare. Drawing on archival material and military manuals, and com ....The invention of collateral damage and the changing moral economy of war. This project aims to provide a novel philosophical account of the invention of the concept of collateral damage in war. It seeks to understand the historical and institutional processes that have produced a moral distinction between deliberate harm inflicted on non-combatants, and the non-intentional harm that is seen as an inevitable side effect of modern warfare. Drawing on archival material and military manuals, and combining insights from the history of human rights and contemporary European political philosophy, the project aims to produce a sophisticated philosophical framework for understanding the social and political implications of conceiving civilian deaths as collateral damage to contribute to public debate about the human costs of war.Read moreRead less
The quest for the 'I': reaching a better understanding of the self through Hegel and Heidegger. The conception of the 'I' is central to our lives. The more multicultural a country is, the more pressing becomes the question of the conception of the self. Focusing on the thought of Hegel and Heidegger, this project aims to offer a richer account that avoids individualism and allows thinking of the formation of the self as a collective enterprise.
The God of Hegel's Post-Kantian Idealism. Recently both philosophical and popular debates over the role of religion in modern society have, like earlier debates from the 18th century, been marked by a commitment to philosophical realism. In the largely neglected "idealist" tradition of the nineteenth century, such disputes were cast in a different light. By developing an idealist conception of God, using contemporary philosophical resources, this project aims to offer a way of thinking about the ....The God of Hegel's Post-Kantian Idealism. Recently both philosophical and popular debates over the role of religion in modern society have, like earlier debates from the 18th century, been marked by a commitment to philosophical realism. In the largely neglected "idealist" tradition of the nineteenth century, such disputes were cast in a different light. By developing an idealist conception of God, using contemporary philosophical resources, this project aims to offer a way of thinking about the role of religion in human life that avoids the primacy of the question of belief in God as well as antagonistic conceptions of religious differences.Read moreRead less
Broadening Choice and Increasing Diversity in Public Schools. Currently, most families are limited to the public school in their catchment area, meaning the area in which they can afford to live. This leads to socio-economically and ethnically homogenous schools and entrenches disadvantage, as well as denying students the crucial life lessons that flow from being part of a diverse student body. This project aims to investigate a model for allocating public school places that integrates catchment ....Broadening Choice and Increasing Diversity in Public Schools. Currently, most families are limited to the public school in their catchment area, meaning the area in which they can afford to live. This leads to socio-economically and ethnically homogenous schools and entrenches disadvantage, as well as denying students the crucial life lessons that flow from being part of a diverse student body. This project aims to investigate a model for allocating public school places that integrates catchment areas. The expected outcome would be a system that gives families a wider choice, enabling them to enrol in out-of-area schools, while ensuring that allocations remain fair, equitable and balanced, and also delivering benefits such as achieving a desired level of diversity in student populations within schoolsRead moreRead less
Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
Read moreRead less
New constructions and techniques for tensor categories. The goal of this project is to make fundamental advances in the structure theory of tensor categories. Such categories play crucial roles in numerous fields of mathematics, physics and beyond. New methods, theory and examples will be developed, inspired by algebra, representation theory and geometry. These will then be applied in the foundational study of tensor categories for (dis)proving several of the most important open conjectures in t ....New constructions and techniques for tensor categories. The goal of this project is to make fundamental advances in the structure theory of tensor categories. Such categories play crucial roles in numerous fields of mathematics, physics and beyond. New methods, theory and examples will be developed, inspired by algebra, representation theory and geometry. These will then be applied in the foundational study of tensor categories for (dis)proving several of the most important open conjectures in the field. This will open new perspectives for applications in other areas, most notably in representation theory. Other benefits include enhanced international collaboration and scientific capacity in Australia.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150101161
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Quantum Groups and Categorification in Geometric Representation Theory. Representation theory, the mathematical study of symmetry, has applications in diverse areas such as particle physics, computer science, and molecular biology. This project aims to use a new family of quantum groups to prove a network of conjectures about categorical and geometric representation theory. The project aims to answer a long-standing open question in geometric representation theory concerning two families of geom ....Quantum Groups and Categorification in Geometric Representation Theory. Representation theory, the mathematical study of symmetry, has applications in diverse areas such as particle physics, computer science, and molecular biology. This project aims to use a new family of quantum groups to prove a network of conjectures about categorical and geometric representation theory. The project aims to answer a long-standing open question in geometric representation theory concerning two families of geometric spaces underlying the theory of Lie groups. Representation theory is a strength of Australian mathematics, and this project aims to undertake pressing research at the forefront of this dynamic field.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE190101099
Funder
Australian Research Council
Funding Amount
$420,256.00
Summary
Representation theory: studies of symmetry shadows. This project aims to solve fundamental problems in representation theory by combining cutting-edge techniques and developing novel higher level structures. Representation theory is the mathematical study of symmetry, an essential concept in science. Since the 1990s, mathematicians have been observing shadows of a more general notion of symmetry but so far have failed to explain it. Expected outcomes include a structural explanation of these sh ....Representation theory: studies of symmetry shadows. This project aims to solve fundamental problems in representation theory by combining cutting-edge techniques and developing novel higher level structures. Representation theory is the mathematical study of symmetry, an essential concept in science. Since the 1990s, mathematicians have been observing shadows of a more general notion of symmetry but so far have failed to explain it. Expected outcomes include a structural explanation of these shadows, new mathematical software to understand them and solutions to important conjectures. This project will make a significant contribution to the field of representation theory, with ramifications in mathematical physics and computer science.Read moreRead less
New dualities in modular representation theory. This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepes ....New dualities in modular representation theory. This project aims to introduce new geometric techniques in the modular representation theory of the general linear group, and resolve fundamental questions about modular representations of orthogonal and symplectic groups. Representation theory, the mathematical study of symmetry, has applications in many areas ranging from physics to computer science. The modular setting, where the characteristic of the field is positive, is a source of the deepest conjectures in this subject. Recent breakthroughs have provided approaches to some problems in modular representation theory that were previously inaccessible. This project will promote research at the forefront of the field, and help maintain Australia's international standing. It will train Australian postgraduates, who will be able to apply their research skills in industry, and strengthen the country's ties to a vibrant international community.Read moreRead less
Asymptotic Expansions and Large Deviations in Probability and Statistics: Theory and Applications. Statistics is the major enabling science in a number of disciplines. This is fundamental research in probability and statistics but it has wide applications in Biology and Social Sciences which will ultimately be of national benefit. The behaviour of self normalized sums is an exciting new area of fundamental research that has implications for the application of statistics in many areas. U-statist ....Asymptotic Expansions and Large Deviations in Probability and Statistics: Theory and Applications. Statistics is the major enabling science in a number of disciplines. This is fundamental research in probability and statistics but it has wide applications in Biology and Social Sciences which will ultimately be of national benefit. The behaviour of self normalized sums is an exciting new area of fundamental research that has implications for the application of statistics in many areas. U-statistics for dependent situations has direct application to understanding financial time series and the analysis of sample survey data. Saddlepoint methods provide extremely accurate approximations in a number of important applications.
Read moreRead less