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
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
Discovery Early Career Researcher Award - Grant ID: DE150100308
Funder
Australian Research Council
Funding Amount
$283,536.00
Summary
Branching and self-similarity in group actions. This project aims to develop the theory of groups of symmetries that have self-similarity (part of the object has the same structure as the whole) and branching (transformations may be performed on parts of the object independently of one another while preserving the overall structure). The focus will be on a class of topological groups in which these properties frequently occur, building on methods recently developed and their actions on trees and ....Branching and self-similarity in group actions. This project aims to develop the theory of groups of symmetries that have self-similarity (part of the object has the same structure as the whole) and branching (transformations may be performed on parts of the object independently of one another while preserving the overall structure). The focus will be on a class of topological groups in which these properties frequently occur, building on methods recently developed and their actions on trees and on the Cantor set. The project aims to significantly advance the theory of locally compact groups, as well as giving insights into the phenomena of self-similarity and branching as they occur in group theory and dynamical systems.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.
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Lie-type methods for totally disconnected groups. Groups are algebraic objects which convey symmetry, much as numbers convey size. For example, the rotations of a sphere form a group. This rotation group is one of a class known as the Lie groups that is well understood and has important applications. Totally disconnected groups arise as symmetries of network structures having nodes and a `neighbour' relation between nodes. The Australian investigator has discovered powerful methods for analysing ....Lie-type methods for totally disconnected groups. Groups are algebraic objects which convey symmetry, much as numbers convey size. For example, the rotations of a sphere form a group. This rotation group is one of a class known as the Lie groups that is well understood and has important applications. Totally disconnected groups arise as symmetries of network structures having nodes and a `neighbour' relation between nodes. The Australian investigator has discovered powerful methods for analysing totally disconnected groups which have parallels with Lie group techniques. This project will develop these parallels and establish links with international researchers on Lie groups.Read moreRead less
A New Model For The Pathogenesis Of Rheumatic Fever: Superantigen Priming Of The Immune Response To Group A Streptococci
Funder
National Health and Medical Research Council
Funding Amount
$248,820.00
Summary
Acute rheumatic fever (ARF) is now rare in developed countries. However, it remains a major problem in Aboriginal Australians in the NT where the rate of ARF is the highest in the world. This leads to high rates of rheumatic heart disease (up to 3% of individuals in some communities) and a premature mortality of over four times that for developing countries. Immunisation and improved living conditions offer a long-term solution but these remain a distant prospect. In the short and medium term, c ....Acute rheumatic fever (ARF) is now rare in developed countries. However, it remains a major problem in Aboriginal Australians in the NT where the rate of ARF is the highest in the world. This leads to high rates of rheumatic heart disease (up to 3% of individuals in some communities) and a premature mortality of over four times that for developing countries. Immunisation and improved living conditions offer a long-term solution but these remain a distant prospect. In the short and medium term, control of this ARF will partly depend on new and better treatment and prevention strategies. To achieve these goals a deeper understanding of the immune mechanisms underlying this disease is urgently needed. It is known that ARF is caused by an abnormal immune response following streptococcal infection. This leads to the production of cells called T cells that attack the body s own tissues rather than the bacteria itself. This autoimmune disease is responsible for the heart damage that underlies ARF. It is believed that this proces only occurs when susceptible individuals are infected with specific rheumatogenic strains of streptococci. However there are a number of deficiencies in this model and it is proposed that there is an additional factor responsible for the abnormal immune response in ARF. This project will explore the possibility that bacterial toxins called superantigens are the critical missing factor , by studying the immune response in ARF. Superantigens are produced by certain streptococci and staphylococci, and are potent in minute quantities causing widespread activation of the immune system. They have been found to play an important role in a number of autoimmune diseases and the type of immune response found in ARF fits well with that expected if superantigens were involved. If superantigens play an important role in causing the abnormal immune response in ARF then a number of new avenues would open for the treatment and prevention of this disease.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