Gravity Changes, Soil Moisture and Data Assimilation. This project will assess the utility of space and ground based gravity measurements for monitoring changes in the hydrological cycle at regional scales. At present there are no methods available for monitoring changes in terrestrial water storage over the globe, despite their importance for assessing the effects of large-scale changes in land use and climate change. The launch of NASA's Gravity Recovery and Climate Experiment satellites later ....Gravity Changes, Soil Moisture and Data Assimilation. This project will assess the utility of space and ground based gravity measurements for monitoring changes in the hydrological cycle at regional scales. At present there are no methods available for monitoring changes in terrestrial water storage over the globe, despite their importance for assessing the effects of large-scale changes in land use and climate change. The launch of NASA's Gravity Recovery and Climate Experiment satellites later this year provides a 5-year window of opportunity to undertake ground-based research to test this innovative technique for monitoring terrestrial water storage from gravity measurements - something that has been shown to be possible theoretically, but has not been testable until now.Read moreRead less
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
Quantum invariants and hyperbolic manifolds in three-dimensional topology. The project aims to broaden our understanding of three-dimensional (3-D) spaces, including spaces that arise in engineering, microbiology and physics. It is known that all 3-D spaces can be decomposed into geometric pieces. The most common type of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum physics, known as quantum invariants. Several important conjectures, bas ....Quantum invariants and hyperbolic manifolds in three-dimensional topology. The project aims to broaden our understanding of three-dimensional (3-D) spaces, including spaces that arise in engineering, microbiology and physics. It is known that all 3-D spaces can be decomposed into geometric pieces. The most common type of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum physics, known as quantum invariants. Several important conjectures, based on developments in physics, assert that hyperbolic geometry and quantum invariants are deeply related, but they remain unproved. The project aims to find new relationships between hyperbolic geometry and quantum invariants, advancing our understanding of both areas.Read moreRead less
Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as we ....Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as well as to viable paths towards the unknown theory that interpolates them. This project contributes to these developments by adapting and developing sophisticated technical tools and insights from integrable models to shed light on that unknown theory that transcends the gauge/string gap. Read moreRead less
Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation ....Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation functions, advances in the theory of topological vertices and the related representation theory, and new solutions of the Yang-Baxter equations. This should provide benefits that include a better understanding of two-dimensional integrable models and their deep connections with topological strings.Read moreRead less
Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140100633
Funder
Australian Research Council
Funding Amount
$395,169.00
Summary
Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations ....Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations of affine Kac-Moody algebras at the critical level.Read moreRead less
Mathematical models for disordered critical point theories. This project sets up a team to develop innovative techniques for fundamental advances in critical behaviour of disordered systems including the Nobel Prize winning integer quantum Hall effect. It will yield new mathematical models for disordered critical point theories, essential for the theoretical analysis of associated emerging technologies.
Novel Conformal Techniques in Quantum Field Theory, Gravity and Supergravity. Conformal symmetry is the maximal spacetime symmetry in relativistic quantum theory. This project will explore the dynamics of those quantum field theories and matter-coupled gravity theories that possess conformal symmetry and have recently been the focus of enormous interest worldwide. Its scientific outcomes will include a deeper understanding of Wilson loops in Yang-Mills theories, scattering amplitudes in conforma ....Novel Conformal Techniques in Quantum Field Theory, Gravity and Supergravity. Conformal symmetry is the maximal spacetime symmetry in relativistic quantum theory. This project will explore the dynamics of those quantum field theories and matter-coupled gravity theories that possess conformal symmetry and have recently been the focus of enormous interest worldwide. Its scientific outcomes will include a deeper understanding of Wilson loops in Yang-Mills theories, scattering amplitudes in conformal gravity and supergravity as well as other conceptual results of major importance to modern mathematical physics, thus placing Australia at the forefront of this research. A rich intellectual environment will be provided for training of Australian PhD students by internationally recognised experts. Read moreRead less
Advances in HIgher Spin Gauge Theory. This project aims to explore the dynamical and geometrical aspects of higher spin gauge theory that have recently become the focus of enormous interest worldwide. Higher spin gauge theory is a unique generalisation of Einstein’s gravitation theory, which possesses maximal gauge symmetry and is a novel candidate for quantum gravity. Expected project outcomes include a better understanding of higher-spin interaction vertices, correlation functions, and other c ....Advances in HIgher Spin Gauge Theory. This project aims to explore the dynamical and geometrical aspects of higher spin gauge theory that have recently become the focus of enormous interest worldwide. Higher spin gauge theory is a unique generalisation of Einstein’s gravitation theory, which possesses maximal gauge symmetry and is a novel candidate for quantum gravity. Expected project outcomes include a better understanding of higher-spin interaction vertices, correlation functions, and other conceptual results of major importance to mathematical physics.Read moreRead less