Environmental geodesy: variations of sea level and water storage in the Australian region. It is essential for Australia's long-term planning and security that the effects of global warming on our nation's water resources and coastlines are quantified. Sea level variations projected into the future vary around Australia and have large uncertainties, yet the impacts have substantial social and financial ramifications for our community. Australia hasn't yet quantified accurately its critical water ....Environmental geodesy: variations of sea level and water storage in the Australian region. It is essential for Australia's long-term planning and security that the effects of global warming on our nation's water resources and coastlines are quantified. Sea level variations projected into the future vary around Australia and have large uncertainties, yet the impacts have substantial social and financial ramifications for our community. Australia hasn't yet quantified accurately its critical water resources nor how they are changing. This proposal will address both these issues, providing for the first time valuable and accurate information for planning appropriate strategies to mitigate the impact of sea level rise and water storage on the Australian society.Read moreRead less
Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the clas ....Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the classification of topological phases in strongly interacting systems. This project involves postgraduate training as a crucial tool in achieving its aims and enhances Australia's position at the forefront of international research.Read moreRead less
Applications of generalised geometry to duality in quantum theory. This project will undertake research into mathematics at the forefront of modern physics. The aim of the project is to develop a mathematical theory of T-duality, a phenomenon in quantum physics, using generalised geometry.
Discovery Early Career Researcher Award - Grant ID: DE200100407
Funder
Australian Research Council
Funding Amount
$427,066.00
Summary
Homology theories in quantum topology. This project aims to resolve a major 25-year-old open problem relating the quantum topology of knots, 3- and 4-dimensional spaces to higher representation theory, the study of hidden symmetries of algebraic structures. The project expects to use homological invariants of knots and the higher representation theory of quantum groups to construct highly anticipated invariants of 3- and 4-dimensional manifolds and tools to compute these invariants by reduction ....Homology theories in quantum topology. This project aims to resolve a major 25-year-old open problem relating the quantum topology of knots, 3- and 4-dimensional spaces to higher representation theory, the study of hidden symmetries of algebraic structures. The project expects to use homological invariants of knots and the higher representation theory of quantum groups to construct highly anticipated invariants of 3- and 4-dimensional manifolds and tools to compute these invariants by reduction to basic building blocks. Expected outcomes also include new connections to diverse areas in mathematics. This is expected to benefit Australian science by invigorating collaboration in mathematics and theoretical physics and by attracting students and distinguished research visitors. Read moreRead less
Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systemati ....Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systematically and rigorously analysing a wide variety of logarithmic conformal field theories so as to facilitate applications.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101825
Funder
Australian Research Council
Funding Amount
$334,710.00
Summary
The Algebraic Structure of Logarithmic Conformal Field Theory. Conformal field theory has given rise to a myriad of deep connections between physics and mathematics. Recently a generalisation of conformal field theory, called logarithmic conformal field theory, has garnered a lot of interest. These theories are necessary for understanding condensed matter systems with non-local observables such as percolation or polymers and for string theory on super group manifolds. This project will explore t ....The Algebraic Structure of Logarithmic Conformal Field Theory. Conformal field theory has given rise to a myriad of deep connections between physics and mathematics. Recently a generalisation of conformal field theory, called logarithmic conformal field theory, has garnered a lot of interest. These theories are necessary for understanding condensed matter systems with non-local observables such as percolation or polymers and for string theory on super group manifolds. This project will explore the algebraic structure of logarithmic conformal field theory. Expected outcomes include an improved understanding of how to systematically construct and solve logarithmic theories and will further consolidate Australia's reputation as an international centre for logarithmic conformal field theory.Read moreRead less
Supersymmetric quantum field theory, topology and duality. Supersymmetry is universally considered as one of the most fundamental concepts in physics, playing an increasingly central role in recent studies of quantum field theory and string theory. There is a corresponding development of supersymmetry in mathematics and this project will make advances both in 'superphysics' and 'supermathematics'.