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
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
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
Teaching Main Group Compounds to Activate Catalytically Relevant Bonds. The project aims to generate novel, earth abundant main group compounds, with the ultimate objective of developing these as sustainable replacements for toxic/expensive late transition metal complexes, that are currently central to numerous stoichiometric and catalytic synthetic transformations. The project expects to generate major fundamental and applied advances in chemistry, using innovative synthetic and computational a ....Teaching Main Group Compounds to Activate Catalytically Relevant Bonds. The project aims to generate novel, earth abundant main group compounds, with the ultimate objective of developing these as sustainable replacements for toxic/expensive late transition metal complexes, that are currently central to numerous stoichiometric and catalytic synthetic transformations. 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 research network, and a highly trained workforce. Success should see substantial economic, environmental and societal benefits flowing to Australia.Read moreRead less
Exceptionally symmetric combinatorial designs. Advances in digital technologies are underpinned by powerful mathematics; use of symmetry greatly simplifies complex problems. This project aims to exploit the mathematical theory of groups to advance our understanding of combinatorial designs with exceptional symmetry. New designs have become prominent through links with networks and error correcting codes. The project expects to generate constructions and classifications in these areas by utilisin ....Exceptionally symmetric combinatorial designs. Advances in digital technologies are underpinned by powerful mathematics; use of symmetry greatly simplifies complex problems. This project aims to exploit the mathematical theory of groups to advance our understanding of combinatorial designs with exceptional symmetry. New designs have become prominent through links with networks and error correcting codes. The project expects to generate constructions and classifications in these areas by utilising powerful group theory. As well as innovative methods for studying designs with symmetry based on group actions, expected outcomes include enhanced international collaboration, and highly trained combinatorial mathematicians to strengthen Australia’s research standing in fundamental science. Read moreRead less
The synchronisation hierarchy of permutation groups. This project aims to make significant advances in understanding finite primitive permutation groups, which are the basic building blocks of the mathematical study of symmetry. A recently-developed perspective, inspired by the notion of a synchronising automaton, has revealed that these groups fall into a natural hierarchy. While the outline of this synchronisation hierarchy is known, many questions remain about exactly which primitive groups l ....The synchronisation hierarchy of permutation groups. This project aims to make significant advances in understanding finite primitive permutation groups, which are the basic building blocks of the mathematical study of symmetry. A recently-developed perspective, inspired by the notion of a synchronising automaton, has revealed that these groups fall into a natural hierarchy. While the outline of this synchronisation hierarchy is known, many questions remain about exactly which primitive groups lie in which layers. Answering these questions using techniques from group theory, graph theory and finite geometry will substantially deepen our understanding. The benefits of this include new knowledge and enhanced insight into this fundamental class of groups and new tools for their analysis.Read moreRead less