Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
Representation theory in exactly solvable systems. This project aims to develop the representation theory of Lie and generalised Lie algebras related to exactly solvable models. The project will exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realisations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new, exactly solvable models. This w ....Representation theory in exactly solvable systems. This project aims to develop the representation theory of Lie and generalised Lie algebras related to exactly solvable models. The project will exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realisations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new, exactly solvable models. This will have an impact on theoretical physics as exactly solvable models play a central role in our understanding of a plethora of physical phenomena.Read moreRead less
Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing sta ....Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing state of the art analysis in supergravity and holographic dualities, the project will advance our understanding of quantum gravity, black holes, and cosmology placing Australia at the forefront of these important research fields.Read moreRead less
Scalable and Robust Bayesian Inference for Implicit Statistical Models. This project aims to develop the next generation of efficient methods for fitting complex simulation-based statistical models to data. Practitioners and scientists are interested in such implicit models to enable discoveries, produce accurate predictions and inform decisions under uncertainty. However, the associated computational cost has restricted researchers to implicit models that must have a small number of parameters ....Scalable and Robust Bayesian Inference for Implicit Statistical Models. This project aims to develop the next generation of efficient methods for fitting complex simulation-based statistical models to data. Practitioners and scientists are interested in such implicit models to enable discoveries, produce accurate predictions and inform decisions under uncertainty. However, the associated computational cost has restricted researchers to implicit models that must have a small number of parameters and be well specified, impeding scientific progress. This project will develop new computational methods and algorithms for implicit models that scale to high dimensions and are robust to misspecification. Benefits will arise from the more routine use of implicit models in epidemiology, biology, ecology and other fields.Read moreRead less
An evolutionary landscape to better predict our future climate. Soil microbial communities are the most complicated and difficult to study on Earth, but their effects on our climate are profound. This project will examine the evolution of microorganisms and their viruses in soil using novel methods. It will uncover how the evolution of one microbial species influences the evolution of other community members. It will also apply a new model of evolution to the viruses that infect these microorgan ....An evolutionary landscape to better predict our future climate. Soil microbial communities are the most complicated and difficult to study on Earth, but their effects on our climate are profound. This project will examine the evolution of microorganisms and their viruses in soil using novel methods. It will uncover how the evolution of one microbial species influences the evolution of other community members. It will also apply a new model of evolution to the viruses that infect these microorganisms, constructing a viral ‘tree of life’. This improved fundamental understanding of soil communities will be used to study climate feedback from permafrost wetlands, a key and poorly constrained input of global climate models, improving predictions of our future climate.Read moreRead less
Development of population-level algorithms for modelling genomic variation and its impact on cellular function in animals and plants. The purpose of this project is to develop mathematical and computational tools which will enable researchers to model high-throughput biological data at the population level. These models will be used to uncover the effect that genetic variation has on the physiology of the cell and the organism.
The Systems Biochemistry of Adaptation in Cellular Protein Networks. A living cell must process and interpret a host of diverse signals using a complex network of interacting proteins inside the cell. The detailed molecular mechanisms by which cells exhibit adaptation to these signals remains a fundamental question in biology. This project aims to develop a novel mathematical framework for analysing the capacity of intracellular protein interactions to contribute to cellular adaptation, along ....The Systems Biochemistry of Adaptation in Cellular Protein Networks. A living cell must process and interpret a host of diverse signals using a complex network of interacting proteins inside the cell. The detailed molecular mechanisms by which cells exhibit adaptation to these signals remains a fundamental question in biology. This project aims to develop a novel mathematical framework for analysing the capacity of intracellular protein interactions to contribute to cellular adaptation, along with a novel methodology for validating mathematical models against experimental data. These innovations offer a completely fresh approach to identifying and modulating the adaptive capacities of living cells, which may contribute to overcoming the problem of drug resistance in future therapeutic development.
Read moreRead less
Towards the prime power conjecture. This project attacks a famous and long standing conjecture in pure mathematics that has important ramifications in many applied areas. The project aims to determine when it is possible to produce more efficient codes for electronic communication and statistically balanced designs for experiments in areas as diverse as agriculture and psychology.
Mathematical modeling of multicellular organization of epithelial tissues. This project will use mathematical modelling and computer simulations to understand the dynamic organisation of epithelial tissues in close interaction with ongoing laboratory experiments. The key challenge is to develop a multi-scale modelling framework that is capable of bridging the gap between biochemical and biophysical sub-cellular processes, cell-cell interactions and the large scale multicellular properties of tis ....Mathematical modeling of multicellular organization of epithelial tissues. This project will use mathematical modelling and computer simulations to understand the dynamic organisation of epithelial tissues in close interaction with ongoing laboratory experiments. The key challenge is to develop a multi-scale modelling framework that is capable of bridging the gap between biochemical and biophysical sub-cellular processes, cell-cell interactions and the large scale multicellular properties of tissues composed of large cell populations. This will require the design of novel mathematical approximation techniques and application of high performance parallel computing technology specifically adapted for the description of multicellular systems. Read moreRead less
Scalable biocomputing on networks: design and mathematical foundations. This project aims to develop technology with the potential to disrupt computation by providing a way to solve combinatorial mathematical problems in an efficient manner. Electronic computers have revolutionised our lives over the last half-century, but there are tasks they can not do, usually those requiring multi-tasking, much as our brains do. This project aims to overcome some of these problems by physically using molecul ....Scalable biocomputing on networks: design and mathematical foundations. This project aims to develop technology with the potential to disrupt computation by providing a way to solve combinatorial mathematical problems in an efficient manner. Electronic computers have revolutionised our lives over the last half-century, but there are tasks they can not do, usually those requiring multi-tasking, much as our brains do. This project aims to overcome some of these problems by physically using molecular parts of living things moving within specially mathematically designed networks to solve, in parallel, "combinatorial" mathematical problems that vex traditional computers, while using far less energy than electronic devices. This project expects to develop this nascent field into a practically useful, disruptive technology based in Australia.Read moreRead less