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New Boron and Gadolinium Agents for Neutron Capture Therapy. The development of new drugs and treatments for cancer is highly important for improved health outcomes and the well-being of the community. This research has the potential to result in the development of new anticancer pharmaceuticals that will dramatically expand the clinical efficacy of a promising treatment for highly aggressive tumours. The innovative nature of this research will also contribute to Australia's science knowledge ....New Boron and Gadolinium Agents for Neutron Capture Therapy. The development of new drugs and treatments for cancer is highly important for improved health outcomes and the well-being of the community. This research has the potential to result in the development of new anticancer pharmaceuticals that will dramatically expand the clinical efficacy of a promising treatment for highly aggressive tumours. The innovative nature of this research will also contribute to Australia's science knowledge base, a key element in its future economic prosperity, and it will provide excellent training of young researchers for employment in the rapidly expanding field of drug design and development.Read moreRead less
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
Algorithmic approaches to braids and their generalisations. This project combines theoretical methods from pure mathematics with computational experiments in order to gain new knowledge. The objects of interest, so-called braid groups and generalisations, are important for many fields of mathematics, but also have applications for data security. Both the theoretical outcomes of this project and the algorithms developed will strengthen Australia as a centre of cutting-edge research in computatio ....Algorithmic approaches to braids and their generalisations. This project combines theoretical methods from pure mathematics with computational experiments in order to gain new knowledge. The objects of interest, so-called braid groups and generalisations, are important for many fields of mathematics, but also have applications for data security. Both the theoretical outcomes of this project and the algorithms developed will strengthen Australia as a centre of cutting-edge research in computational algebra. Moreover, the results can lead to new technologies for protecting confidential data, which are more efficient and hence cheaper to implement than existing alternatives. Secure identification of legitimate users in the context of online banking is one possible field of application.Read moreRead less
Scale-Multiplicative Semigroups and Geometry. Symmetry is treated mathematically through the algebraic concept of a group. Conversely, geometric representations play a crucial role in group theory. Many classes of groups, such as the connected groups that arise in physics, have useful geometric representations, but such a representation is lacking in the case of general disconnected groups. Certain disconnected groups, closely related in algebraic terms to the connected ones, do have a geometric ....Scale-Multiplicative Semigroups and Geometry. Symmetry is treated mathematically through the algebraic concept of a group. Conversely, geometric representations play a crucial role in group theory. Many classes of groups, such as the connected groups that arise in physics, have useful geometric representations, but such a representation is lacking in the case of general disconnected groups. Certain disconnected groups, closely related in algebraic terms to the connected ones, do have a geometric representation called a 'building'. This project aims to address the lack of a representation for general disconnected groups by extending the notion of a building to create combinatorial structures on which these groups act as symmetries.Read moreRead less
Totally disconnected groups and their algebras. Groups are algebraic objects which convey symmetry much as
numbers convey size. For example, the symmetries of a
crystal form a crystallographic group and the classification of
crystallographic groups describes all possible crystal
structures. Totally disconnected groups arise as
symmetries of network structures having nodes and a `neighbour'
relation, as models of crystals do, but which are not rigid like
crystals. Powerful techniques for a ....Totally disconnected groups and their algebras. Groups are algebraic objects which convey symmetry much as
numbers convey size. For example, the symmetries of a
crystal form a crystallographic group and the classification of
crystallographic groups describes all possible crystal
structures. Totally disconnected groups arise as
symmetries of network structures having nodes and a `neighbour'
relation, as models of crystals do, but which are not rigid like
crystals. Powerful techniques for analysing totally
disconnected groups have recently been discovered and this
project aims to develop those techniques. The resulting
significant advances in the understanding of symmetry will
extend the range of applications of
group theory.
Read moreRead less
Totally disconnected groups in algebra and geometry. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have made significant breakthroughs in the study of sym ....Totally disconnected groups in algebra and geometry. Mathematics research creates and develops new concepts for understanding the world. Group theory is a branch of mathematics based on our innate sense of symmetry. It was invented 200 hundred years ago and has grown into a language for analysing and classifying things ranging from wallpaper patterns to crystals, the fundamental particles of physics and Rubik's cube. The chief investigators have made significant breakthroughs in the study of symmetry groups of networks, giving Australia an international lead in this research area. The project will develop the insights gained to make Australia a centre of expertise on these symmetry groups, which have applications to many areas including information and communication technology.Read moreRead less
The mathematics and language of engineering uncertainty, preference and utility. Australian engineering firms are principals in many high-profile projects. To defend their position, they must demonstrate both sound engineering and quality processes, which by international standards includes the traceability of decisions. Yet, there are few tools to vet the multitude of decisions that go into large-scale engineering works. This project aims to form mathematical models of decision-making based on ....The mathematics and language of engineering uncertainty, preference and utility. Australian engineering firms are principals in many high-profile projects. To defend their position, they must demonstrate both sound engineering and quality processes, which by international standards includes the traceability of decisions. Yet, there are few tools to vet the multitude of decisions that go into large-scale engineering works. This project aims to form mathematical models of decision-making based on the language modelling of what is written in engineering documentation about the bases of decisions. The new methods will help decision makers to pinpoint irrationalities in decisions and notify them of possible errors. The research can therefore be applied to important problems in the engineering sector such as risk management.Read moreRead less
Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools fo ....Constructive Representation Theory and its Applications. The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools for linear algebra developed will also find application in cryptography and coding theory. This work represents the latest stage in a long-term project to discover practical algorithms for elucidating the properties of complex algebraic structures - an area where Australia is a world-leader.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
New frontiers in the therapeutic application of gadolinium. This research involves the design and development of new anticancer agents that will dramatically expand the clinical efficacy of a promising treatment for highly aggressive tumours. The innovative nature of this research will also contribute to Australia's science knowledge base and provide excellent training in the area of drug discovery.