Discovery Early Career Researcher Award - Grant ID: DE160100958
Funder
Australian Research Council
Funding Amount
$307,536.00
Summary
Quantum integrability and symmetric functions. This project aims to develop new connections between quantum integrability and a central area of pure mathematics, symmetric function theory. Quantum integrability is one of the most important areas of mathematical physics, in view of its application to modern physical theories and its mathematical richness. The project intends to use advanced symmetric function techniques to calculate quantum mechanical quantities without any approximation, and to ....Quantum integrability and symmetric functions. This project aims to develop new connections between quantum integrability and a central area of pure mathematics, symmetric function theory. Quantum integrability is one of the most important areas of mathematical physics, in view of its application to modern physical theories and its mathematical richness. The project intends to use advanced symmetric function techniques to calculate quantum mechanical quantities without any approximation, and to use the framework of quantum integrability to provide new results in symmetric function theory. The intended outcomes of the project will be new asymptotic expressions for correlation functions and more efficient computer algorithms for the calculation of a variety of symmetric functions.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101264
Funder
Australian Research Council
Funding Amount
$342,346.00
Summary
Toroidal quantum groups, integrable models and applications. Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exci ....Toroidal quantum groups, integrable models and applications. Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exciting developments in toroidal quantum groups. The anticipated outcomes include constructions of new models, developing analytic methods and computer algebra packages. These results are expected to facilitate challenging computational problems in modelling of quantum and classical systems.Read moreRead less
Solvability and universality in stochastic processes. Exactly solvable stochastic processes are an important area of mathematical research, with cross-disciplinary links to quantum physics, quantum algebras and probability theory. These processes can be used to model a variety of real-world phenomena such as crystal growth and polymers in random media. This project aims to significantly expand our knowledge of exactly solvable stochastic processes by extending them to new algebraic frameworks. A ....Solvability and universality in stochastic processes. Exactly solvable stochastic processes are an important area of mathematical research, with cross-disciplinary links to quantum physics, quantum algebras and probability theory. These processes can be used to model a variety of real-world phenomena such as crystal growth and polymers in random media. This project aims to significantly expand our knowledge of exactly solvable stochastic processes by extending them to new algebraic frameworks. Among the outcomes of the project, we expect to identify new probabilistic structures which go beyond the famous Gaussian universality class. These theoretical developments allow better prediction of randomly growing interfaces, which encompass a range of phenomena from tumour growth to forest fires.Read moreRead less
Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and no ....Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and non-symmetric polynomials in symbolic algebra packages by developing completely new algorithms. New understanding from the project is expected to facilitate challenging computational problems of measurable quantities in quantum systems.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101581
Funder
Australian Research Council
Funding Amount
$411,000.00
Summary
Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project includ ....Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems. Read moreRead less
Discrete integrable systems. Discrete integrable systems are a fundamental generalisation of traditional integrable systems. This project, combining 5 world experts from 3 countries and 2 early career researchers, will expand and systematise this new interdisciplinary field, and will place Australia at the forefront of this intensive international activity.
High Resolution Imaging and Analysis of Embedded Interfaces and Interface Phase Transitions in Interface-Dominated Nanomaterials. Heterogeneous nanostructured materials and assemblies offer unique structure-property relationships, dominated by the internal interfaces they contain. This interdisciplinary research project will combine novel techniques based on high-resolution phase-retrieval x-ray diffraction and imaging, with complementary analytical electron microscopy and atom probe analysis, i ....High Resolution Imaging and Analysis of Embedded Interfaces and Interface Phase Transitions in Interface-Dominated Nanomaterials. Heterogeneous nanostructured materials and assemblies offer unique structure-property relationships, dominated by the internal interfaces they contain. This interdisciplinary research project will combine novel techniques based on high-resolution phase-retrieval x-ray diffraction and imaging, with complementary analytical electron microscopy and atom probe analysis, in a coordinated study of the structure and properties of embedded interfaces in strategic bi-crystals and nanostructures. It promises new techniques for the study of such defects, and a breakthrough in the understanding of the structural transitions that occur in embedded interfaces as a function of local changes in composition and temperature.Read moreRead less
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.
Imaging surface topography using Lloyd's Mirror in photo-emission electron microscopy. The wide-ranging and innovative nature of the proposal will significantly raise Australia's international profile in condensed matter physics through high impact publications and invited presentations at major international conferences. Researchers will be trained in cutting-edge electron microscopy and synchrotron science. A spin-off company will be formed to commercialise software for reconstructing surface ....Imaging surface topography using Lloyd's Mirror in photo-emission electron microscopy. The wide-ranging and innovative nature of the proposal will significantly raise Australia's international profile in condensed matter physics through high impact publications and invited presentations at major international conferences. Researchers will be trained in cutting-edge electron microscopy and synchrotron science. A spin-off company will be formed to commercialise software for reconstructing surface topography and generating movies of dynamic events. The development of new synchrotron based electron microscopy techniques will establish the expertise for the future creation of a dedicated nanotechnology beamline equipped with photo-emission electron microscopy which will have far reaching national benefit in the physical sciences.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0347797
Funder
Australian Research Council
Funding Amount
$263,000.00
Summary
A Versatile High-resolution X-ray Diffractometer for Materials Research. The aim of this project is to establish a state-of-the-art triple-axis x-ray diffraction facility capable of non-destructively analysing complex semiconductor materials and structures investigated by all Australian semiconductor-growing groups. Growers and device engineers will be able to control growth processes accurately and correlate device performance with structural analysis. Modern triple-axis instruments can also b ....A Versatile High-resolution X-ray Diffractometer for Materials Research. The aim of this project is to establish a state-of-the-art triple-axis x-ray diffraction facility capable of non-destructively analysing complex semiconductor materials and structures investigated by all Australian semiconductor-growing groups. Growers and device engineers will be able to control growth processes accurately and correlate device performance with structural analysis. Modern triple-axis instruments can also be used for high-resolution texture analysis and surface reflectivity measurements on numerous types of materials. Thus chemists, geologists, and materials scientists with interests outside of the semiconductor growth community will gain substantial benefit from this instrument for the investigation of materials of technological and economic importance.Read moreRead less