New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distin ....New techniques and invariants in low-dimensional topology. The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distinguishing families of spaces, measuring their complexity and new obstructions for their existence. The new invariants and techniques will lead to the resolution of some open problems in low-dimensional topology and enhance Australia's reputation as a world leader in this field.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100020
Funder
Australian Research Council
Funding Amount
$1,638,060.00
Summary
Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to e ....Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to enhance Australia’s position at the forefront of international research in Geometric Analysis. Ultimately, the project will enhance Australia's leading position in the area of Index Theory by developing novel techniques to solve challenging conjectures, and mentoring HDR students and ECRs.Read moreRead less
Twisted K-theory, higher geometry and operator algebras. This project aims to develop new theory and techniques linking twisted K-theory, higher-geometry and operator algebras. These are all fundamental areas of mathematics with applications both within mathematics itself and to mathematical physics, particularly in string theory. Anticipated outcomes are fundamental advances in knowledge in mathematics and mathematical physics, enhancement of Australia's international mathematical reputation an ....Twisted K-theory, higher geometry and operator algebras. This project aims to develop new theory and techniques linking twisted K-theory, higher-geometry and operator algebras. These are all fundamental areas of mathematics with applications both within mathematics itself and to mathematical physics, particularly in string theory. Anticipated outcomes are fundamental advances in knowledge in mathematics and mathematical physics, enhancement of Australia's international mathematical reputation and collaborative linkages, and the training of the next generation of Australian mathematicians.Read moreRead less
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less
Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understan ....Unravelling the neutron lifetime puzzle with lattice quantum chromodynamics. This project will perform supercomputer simulations to confront one of the outstanding puzzles of nuclear and particle physics, the neutron lifetime. New knowledge will be generated through the development of novel theoretical and numerical techniques to increase the precision of the leading theoretical inputs required to predict the neutron lifetime. The outcomes will provide crucial theoretical guidance into understanding the neutron; helping to guide the next-generation neutron experiments, from particle physics to applications in advanced materials science. The results will have immediate benefit by resolving the neutron lifetime puzzle, while enabling Australian scientists to take a leadership role in this area of fundamental science.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
A New Approach to the Structure of Atomic Nuclei. Starting at the quark level, we have derived a theory of nuclear structure, that in its initial application appears extremely successful. The aim of this project is to advance this revolutionary new approach to the theory of nuclear structure to the next level by exploring its predictions for a number of outstanding questions in modern nuclear physics. This includes the properties of superheavy nuclei, with atomic number beyond 100, including the ....A New Approach to the Structure of Atomic Nuclei. Starting at the quark level, we have derived a theory of nuclear structure, that in its initial application appears extremely successful. The aim of this project is to advance this revolutionary new approach to the theory of nuclear structure to the next level by exploring its predictions for a number of outstanding questions in modern nuclear physics. This includes the properties of superheavy nuclei, with atomic number beyond 100, including the potential existence of a new region of stability and complementing experimental searches underway internationally to discover the limits of stability with large neutron or proton excess, which is crucial to understanding the origin of the elements and may contribute new energy related technology.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100625
Funder
Australian Research Council
Funding Amount
$446,700.00
Summary
Integrated slab-mode beam engineering for handheld terahertz systems. Current dominant system architectures for terahertz waves are adapted from other ranges, leading to critical bottlenecks. This project will address this with a new integration platform that is tailored to the particular needs of terahertz waves. This requires advances in the emerging field of micro-scale integrated optics, combined with antenna-theory principles, semiconductor science, and advanced microfabrication to incorpor ....Integrated slab-mode beam engineering for handheld terahertz systems. Current dominant system architectures for terahertz waves are adapted from other ranges, leading to critical bottlenecks. This project will address this with a new integration platform that is tailored to the particular needs of terahertz waves. This requires advances in the emerging field of micro-scale integrated optics, combined with antenna-theory principles, semiconductor science, and advanced microfabrication to incorporate active devices. Novel spatially-dependent dispersion engineering techniques will also be pioneered for phased-array-free beamforming. This will enable a broad variety of all-in-one handheld systems for practical applications of terahertz waves such as noninvasive standoff sensing and self-aligning wireless links.Read moreRead less
Positrons in biosystems. This project aims to improve our understanding of the damage processes in Positron Emission Tomography (PET). PET is a widely used medical imaging technique, but there are gaps in our understanding of the underlying interactions, in particular in the case of the radiation damage induced during the process. By using new models incorporating accurate descriptions of interactions processes, verified by experimental measurement, this project will develop a new model of posit ....Positrons in biosystems. This project aims to improve our understanding of the damage processes in Positron Emission Tomography (PET). PET is a widely used medical imaging technique, but there are gaps in our understanding of the underlying interactions, in particular in the case of the radiation damage induced during the process. By using new models incorporating accurate descriptions of interactions processes, verified by experimental measurement, this project will develop a new model of positron transport in PET. The project will allow validation of predictions from the model by undertaking experiments in liquid water.Read moreRead less
New Techniques for New Physics Searches at the CERN Large Hadron Collider. This project aims to break new ground in the quest to discover the existence of new fundamental constituents of nature. In order to achieve this, the team will invent and deploy a suite of advanced machine learning and anomaly detection techniques, developed by the chief investigators, to mine the data processed and collected with the ATLAS experiment at the CERN Large Hadron Collider throughout the entirety of the next d ....New Techniques for New Physics Searches at the CERN Large Hadron Collider. This project aims to break new ground in the quest to discover the existence of new fundamental constituents of nature. In order to achieve this, the team will invent and deploy a suite of advanced machine learning and anomaly detection techniques, developed by the chief investigators, to mine the data processed and collected with the ATLAS experiment at the CERN Large Hadron Collider throughout the entirety of the next data taking run. Expected outcomes of this project include the first application of revolutionary anomaly detection methods to fundamental physics, probing unexplored space in the process, and enhancing the capacity and development of future leaders in Australian science and technology at the forefront of data analytics.Read moreRead less