Graded semisimple deformations. Recent advances in representation theory have revealed beautiful new structures in the classical representation theory of the symmetric groups and Hecke algebras. These discoveries have provided us with new algebras, the cyclotomic KLR algebras, that encode deep properties of fundamental objects in algebraic combinatorics and geometric representation theory. The cyclotomic quiver Hecke algebras are central to several open problems in mathematics but they are still ....Graded semisimple deformations. Recent advances in representation theory have revealed beautiful new structures in the classical representation theory of the symmetric groups and Hecke algebras. These discoveries have provided us with new algebras, the cyclotomic KLR algebras, that encode deep properties of fundamental objects in algebraic combinatorics and geometric representation theory. The cyclotomic quiver Hecke algebras are central to several open problems in mathematics but they are still poorly understood, with even basic properties like their dimensions being unknown. This project will establish a new framework for studying these algebras that will remove the current obstacles in this field and alllow us to prove substantial new results that advance the theory.Read moreRead less
Computing with Lie groups and algebras: nilpotent orbits and applications. This project aims to advance knowledge of an important class of Lie algebras, for which recent work has shown that a deeper mathematical theory, and better computational tools are required. Lie theory is a mathematical area with rich applications in the physical sciences. Expected outcomes from this project include the first systematic treatment of these algebras, new powerful algorithms to compute with them, and explicit ....Computing with Lie groups and algebras: nilpotent orbits and applications. This project aims to advance knowledge of an important class of Lie algebras, for which recent work has shown that a deeper mathematical theory, and better computational tools are required. Lie theory is a mathematical area with rich applications in the physical sciences. Expected outcomes from this project include the first systematic treatment of these algebras, new powerful algorithms to compute with them, and explicit nilpotent orbit classifications that will solve open problems in black hole theory. This should significantly enhance fundamental mathematical research and the Lie functionality of leading computer algebra systems, and is expected to strengthen international linkages.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210100180
Funder
Australian Research Council
Funding Amount
$400,475.00
Summary
Effective classification of closed vertex-transitive groups acting on trees. Symmetry is a fundamental organising principle in mathematics and human endeavour. This project aims to advance our knowledge of zero-dimensional symmetry, a frontier in symmetry research. In the longer term, advancements in fundamental knowledge in this area have the potential to inform the usage and development of digital structures in more practical contexts, such as data networks and information processing. The proj ....Effective classification of closed vertex-transitive groups acting on trees. Symmetry is a fundamental organising principle in mathematics and human endeavour. This project aims to advance our knowledge of zero-dimensional symmetry, a frontier in symmetry research. In the longer term, advancements in fundamental knowledge in this area have the potential to inform the usage and development of digital structures in more practical contexts, such as data networks and information processing. The project is expected to develop new tools of both theoretical and computational nature that will accelerate ongoing research across the field and enable new approaches. This will cement Australia's position at the forefront of research in symmetry and its use in the digital age.Read moreRead less
Immersive Technologies for Rapid Metallic Tank Inspection and Repairs. Metal tank silos house some of the most dangerous chemicals, which erode the internal structure of the tank over time. It is critical to check the integrity of the tank to prevent disasters from occurring. NDE solutions uses a rapid motion scanner (RMS) to scan the interior surface of the container while it is still full of its storage material. It is the aim of this project to use Augmented Reality, to overlay the scan provi ....Immersive Technologies for Rapid Metallic Tank Inspection and Repairs. Metal tank silos house some of the most dangerous chemicals, which erode the internal structure of the tank over time. It is critical to check the integrity of the tank to prevent disasters from occurring. NDE solutions uses a rapid motion scanner (RMS) to scan the interior surface of the container while it is still full of its storage material. It is the aim of this project to use Augmented Reality, to overlay the scan provided by the RMS, onto the worker's view of the tank, control the robot via. hand gestures, and facilitate remote training/guidance. The result will allow for inspection workers to quickly and accurately the location of critical failures, without performing the hazardous procedures of internal tank inspection. Read moreRead less
Earth Abundant Metal Complexes for Nitrogen Activation. This project aims to develop a range of complexes based around earth abundant metals that are capable of activating nitrogen (N2) at ambient pressure and temperature. The project expects to generate new knowledge in the area of organometallic chemistry, specifically with regards to molecular metal-metal bonding and subsequent reactivity towards the activation of nitrogen. The activation of atmospheric nitrogen is performed on a multi-millio ....Earth Abundant Metal Complexes for Nitrogen Activation. This project aims to develop a range of complexes based around earth abundant metals that are capable of activating nitrogen (N2) at ambient pressure and temperature. The project expects to generate new knowledge in the area of organometallic chemistry, specifically with regards to molecular metal-metal bonding and subsequent reactivity towards the activation of nitrogen. The activation of atmospheric nitrogen is performed on a multi-million tonne scale each year and is key to a number of industrial processes. As such, investigations into new and improved catalysts for this process would potentially bring huge financial benefits to industry, as well as benefiting the environment by reducing energy demand and associated climate change.Read moreRead less
Mitochondrial targeting by a new class of gadolinium agents. This research project will lead to the development of new molecular agents containing the element gadolinium which can selectively accumulate within cell mitochondria, with a long-term application in cutting-edge therapies involving X-rays or neutrons. The lanthanoid element gadolinium offers many unique opportunities for medicinal chemistry and this project will generate new knowledge in bioinorganic chemistry and synchrotron science. ....Mitochondrial targeting by a new class of gadolinium agents. This research project will lead to the development of new molecular agents containing the element gadolinium which can selectively accumulate within cell mitochondria, with a long-term application in cutting-edge therapies involving X-rays or neutrons. The lanthanoid element gadolinium offers many unique opportunities for medicinal chemistry and this project will generate new knowledge in bioinorganic chemistry and synchrotron science. The expected outcomes of this research will address many of the unresolved questions regarding mitochondrially-targeted gadolinium complexes, the first such agents specifically designed for potential long-term application in binary therapies and imaging.Read moreRead less
Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic beh ....Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic behaviour of the dimensions of the irreducible representations. Second, it will explore the evolution of representations across families of groups under new induction and restriction functors, in analogy with creation and annihilation operators in physics. The project will enhance Australia's capacity in representation theory and group theory, the mathematics that underline symmetry in nature.Read moreRead less
Advancing the chemistry of rare earths - an Australian resource. This project aims to advance knowledge of the synthesis, structures and reactivity of highly reactive rare earth metal-organic compounds. The project expects to build the knowledge and skills to underpin many developments of Australia's still under utilized rare earth resources to diversify from Chinese domination. The anticipated outcomes will be new synthetic and reaction chemistry including a demonstration of how size and electr ....Advancing the chemistry of rare earths - an Australian resource. This project aims to advance knowledge of the synthesis, structures and reactivity of highly reactive rare earth metal-organic compounds. The project expects to build the knowledge and skills to underpin many developments of Australia's still under utilized rare earth resources to diversify from Chinese domination. The anticipated outcomes will be new synthetic and reaction chemistry including a demonstration of how size and electronic factors can be used to modify and advance rare earth chemistry. This project should provide significant benefit such as are a better knowledge base in rare earth chemistry to underpin future applications in chemical manufacturing, new materials, catalysis and recycling.Read moreRead less
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Reactivity Enhanced Low-Valent Alkaline Earth Metal Compounds. The project aims to develop highly activated low oxidation state alkaline earth metal complexes as cheap and sustainable alternatives to toxic/expensive late transition metal complexes, that currently dominate the transformation of inert small molecule substrates into value-added organic chemicals. The project expects to generate major fundamental and applied advances in chemistry, using innovative synthetic and computational approac ....Reactivity Enhanced Low-Valent Alkaline Earth Metal Compounds. The project aims to develop highly activated low oxidation state alkaline earth metal complexes as cheap and sustainable alternatives to toxic/expensive late transition metal complexes, that currently dominate the transformation of inert small molecule substrates into value-added organic chemicals. The project expects to generate major fundamental and applied advances in chemistry, using innovative synthetic and computational approaches, and a multidisciplinary collaborative team. Expected outcomes include building of academic and, later, industrial research capacity, knowledge, an international network, and a highly trained workforce. Success should see substantial economic, environmental and societal benefits flowing to Australia.Read moreRead less