Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we ....Optimal shapes in geometry and physics: Isoperimetry in modern analysis. This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we will forge connections between the geometry of curved spaces, and the physics of operators therein. The significant benefits of this project include increasing fundamental mathematical knowledge, building capacity in Australia’s world-class geometric analysis community, and strong links with international partners.Read moreRead less
Improving the efficiency of CRISPR gene editing in cells. Human red blood cells are well-characterised and the globin gene locus is a model system for the study of gene regulation. Gene editing technologies and delivery tools are evolving rapidly and the globin gene locus is the perfect model for gene editing optimisation. This collaboration between UNSW Sydney and CSL aims to bring together our combined expertise and new technologies to develop an optimal platform for genetic modification in a ....Improving the efficiency of CRISPR gene editing in cells. Human red blood cells are well-characterised and the globin gene locus is a model system for the study of gene regulation. Gene editing technologies and delivery tools are evolving rapidly and the globin gene locus is the perfect model for gene editing optimisation. This collaboration between UNSW Sydney and CSL aims to bring together our combined expertise and new technologies to develop an optimal platform for genetic modification in a red blood cell line. Simultaneously, this project aims to generate fundamental insights into mechanisms of human gene regulation. The technological and biological outcomes of this project will be of benefit for future gene editing applications.Read moreRead less
Transcription factors find their targets by reading the epigenetic code. This project aims to elucidate how transcription factors, proteins that regulate gene expression, find their target genes. The hypothesis is that non-DNA binding domains play an essential role in this process. This project expects to transform our understanding of transcription factor families, and how factors in families with the same DNA-binding domain manage to regulate different genes. Expected outcomes of this project ....Transcription factors find their targets by reading the epigenetic code. This project aims to elucidate how transcription factors, proteins that regulate gene expression, find their target genes. The hypothesis is that non-DNA binding domains play an essential role in this process. This project expects to transform our understanding of transcription factor families, and how factors in families with the same DNA-binding domain manage to regulate different genes. Expected outcomes of this project include revealing how accessory proteins help transcription factors identify their targets in the genome by reading epigenetic marks. This should provide significant benefits including improved design of artificial transcription factors to up- or down-regulate specific genes in research and agriculture.Read moreRead less
Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that ....Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that can destroy stored information. This project aims to revolutionise mathematical modelling of magnetic memories and put Australia at the forefront of international research. Technological advances to create much smaller and faster memory devices are expected to enable groundbreaking ways of managing and mining big data.Read moreRead less
Genetic, Cellular and Molecular Analysis of Cardiac Ventricular Septation. The project aims to define the blueprint for ventricular septation in the mammalian heart – how, during heart development, a single ventricle becomes divided in two by a muscular wall, thus creating left and right pumps and electrical circuits serving the body and lung circulations separately. A proprietary mouse genetic model was created and will be used to probe the cellular and molecular mechanisms of septation using n ....Genetic, Cellular and Molecular Analysis of Cardiac Ventricular Septation. The project aims to define the blueprint for ventricular septation in the mammalian heart – how, during heart development, a single ventricle becomes divided in two by a muscular wall, thus creating left and right pumps and electrical circuits serving the body and lung circulations separately. A proprietary mouse genetic model was created and will be used to probe the cellular and molecular mechanisms of septation using new technologies able to resolve biology at a single-cell level. Outcomes may include new knowledge on heart development and evolution, including how the cardiac electrical system is formed, and how cell boundaries and tissue complexity are generated. The project may advance new technologies and create new data resources.Read moreRead less
The shape of chaos: geometric advances in partially hyperbolic dynamics. This project aims to use recent advances in geometry and topology to discover new forms of chaotic dynamical systems and further classify the forms of chaos which are possible. Many systems in nature exhibit chaotic dynamics as they change in time. Not all systems are chaotic in the same way, and identifying the form of chaos and its qualitative properties is crucial to truly understanding the system. Chaotic dynamics aris ....The shape of chaos: geometric advances in partially hyperbolic dynamics. This project aims to use recent advances in geometry and topology to discover new forms of chaotic dynamical systems and further classify the forms of chaos which are possible. Many systems in nature exhibit chaotic dynamics as they change in time. Not all systems are chaotic in the same way, and identifying the form of chaos and its qualitative properties is crucial to truly understanding the system. Chaotic dynamics arise in chemical reactions, celestial mechanics, industrial mixing processes, fusion reactors, and many other processes. This project will aid in predicting the possible long-term behaviours of these systems.Read moreRead less
Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications in ....Nonlinear harmonic analysis and dispersive partial differential equations. This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications include medical imaging, fluid dynamics and subatomic modelling using quantum interpretation.
It will solve several important open problems in spectral analysis of partial differential operators and develop new cutting-edge techniques in harmonic analysis with application to nonlinear partial differential equations.Read moreRead less
Trisections, triangulations and the complexity of manifolds. This project aims at practical representations of 3-dimensional and 4-dimensional spaces as needed in applications. Topology is the mathematical study of the shapes of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Special combinatorial structures, such as minimal triangulations, are often closely connected to geometric structures or topological properties. This project aims to construct ....Trisections, triangulations and the complexity of manifolds. This project aims at practical representations of 3-dimensional and 4-dimensional spaces as needed in applications. Topology is the mathematical study of the shapes of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Special combinatorial structures, such as minimal triangulations, are often closely connected to geometric structures or topological properties. This project aims to construct computable invariants, connectivity results for triangulations, and algorithms to recognise fundamental topological properties and structures such as trisections and bundles.Read moreRead less
Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multileve ....Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multilevel methods, transport maps, and dimension reduction, this project's anticipated outcomes are highly accurate and cost-efficient numerical schemes, certified by rigorous mathematical analysis. This should provide data-centric simulation tools with enhanced reliability, for engineering and scientific applications.Read moreRead less
Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable s ....Finite dimensional integrable systems and differential geometry. Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.Read moreRead less