Australian Laureate Fellowships - Grant ID: FL120100125
Funder
Australian Research Council
Funding Amount
$1,796,966.00
Summary
Advances in the analysis of random structures and their applications. This project will provide new approaches, insights and results for probabilistic combinatorics. This area has contributed in exciting ways elsewhere in mathematics and provides versatile tools of widespread use in algorithmic computer science, with other applications in physics, coding theory for communications, and genetics.
Australian Laureate Fellowships - Grant ID: FL130100118
Funder
Australian Research Council
Funding Amount
$2,033,722.00
Summary
Nonlinear partial differential equations and applications. This project aims to confirm and enhance Australia as a world leader in this very active and highly significant area of nonlinear partial differential equations. We will develop new methods and techniques to solve challenging problems of immense international interest and continue building expertise and training in the area.
Australian Laureate Fellowships - Grant ID: FL150100126
Funder
Australian Research Council
Funding Amount
$2,080,100.00
Summary
Geometric analysis of eigenvalues and heat flows. Geometric analysis of eigenvalues and heat flows: This fellowship project aims to build on Australia's leading position in the areas of nonlinear partial differential equations and geometric analysis to exploit new and highly innovative mathematical methods. It is expected that the methods will affect a range of related fields including stochastic modelling and finance, image processing, and the basic sciences. The project seeks to serve as a foc ....Geometric analysis of eigenvalues and heat flows. Geometric analysis of eigenvalues and heat flows: This fellowship project aims to build on Australia's leading position in the areas of nonlinear partial differential equations and geometric analysis to exploit new and highly innovative mathematical methods. It is expected that the methods will affect a range of related fields including stochastic modelling and finance, image processing, and the basic sciences. The project seeks to serve as a focal point for a developing community of Australian researchers in this field, providing a training ground for young researchers and students at the forefront of a vigorous and internationally active area of research, and bringing top international researchers to Australia to interact with the local research community.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL220100072
Funder
Australian Research Council
Funding Amount
$2,490,704.00
Summary
Mathematical Breakthroughs in Wave Propagation. This Fellowship proposal in theoretical mathematics aims to solve three major open problems in wave propagation. These are the long-time behaviour of nonlinear waves, including the behaviour and interaction of solitary waves; the propagation of waves in rough media; and the small-scale behaviour of interacting waves under the assumption of chaotic ray dynamics. The research aims to analyse wave equations that model problems in optical media and wav ....Mathematical Breakthroughs in Wave Propagation. This Fellowship proposal in theoretical mathematics aims to solve three major open problems in wave propagation. These are the long-time behaviour of nonlinear waves, including the behaviour and interaction of solitary waves; the propagation of waves in rough media; and the small-scale behaviour of interacting waves under the assumption of chaotic ray dynamics. The research aims to analyse wave equations that model problems in optical media and waveguides, medical and seismic imaging, and nano-electronic devices. Outcomes and benefits are expected in new mathematical theory, Australian research capability, better algorithms for numerically computing waves, and technological advances in communications, medical imaging, and seismic imaging.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100032
Funder
Australian Research Council
Funding Amount
$2,837,520.00
Summary
Zero-dimensional symmetry and its ramifications. This project aims to investigate algebraic objects known as 0-dimensional groups, which are a mathematical tool for analysing the symmetry of infinite networks. Group theory has been used to classify possible types of symmetry in various contexts for nearly two centuries now, and 0-dimensional groups are the current frontier of knowledge. The expected outcome of the project is that the understanding of the abstract groups will be substantially adv ....Zero-dimensional symmetry and its ramifications. This project aims to investigate algebraic objects known as 0-dimensional groups, which are a mathematical tool for analysing the symmetry of infinite networks. Group theory has been used to classify possible types of symmetry in various contexts for nearly two centuries now, and 0-dimensional groups are the current frontier of knowledge. The expected outcome of the project is that the understanding of the abstract groups will be substantially advanced, and that this understanding will shed light on structures possessing 0-dimensional symmetry. In addition to being cultural achievements in their own right, advances in group theory such as this also often have significant translational benefits. This will provide benefits such as the creation of tools relevant to information science and researchers trained in the use of these tools.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL100100137
Funder
Australian Research Council
Funding Amount
$1,868,132.00
Summary
Derived categories and applications. This project will deepen our understanding of homological algebra, a mathematical tool that has proved useful in areas ranging from physics to the coding of information for computer transmission. Also, having a thriving research presence in Australia, of this vibrant, modern field, should inspire more students to seek a career in mathematics; this would help relieve the acute, well-documented shortage of mathematicians in Australia. It has been established th ....Derived categories and applications. This project will deepen our understanding of homological algebra, a mathematical tool that has proved useful in areas ranging from physics to the coding of information for computer transmission. Also, having a thriving research presence in Australia, of this vibrant, modern field, should inspire more students to seek a career in mathematics; this would help relieve the acute, well-documented shortage of mathematicians in Australia. It has been established that Australia is not producing enough mathematicians to meet the needs of industry; a lively centre, full of young, productive mathematicians, will go a long way towards correcting this problem.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100052
Funder
Australian Research Council
Funding Amount
$2,107,500.00
Summary
Breakthrough methods for noncommutative calculus. This project aims to solve hard, outstanding problems which have impeded our ability to progress in the area of quantum or noncommutative calculus. Calculus has provided an invaluable tool to science, enabling scientific and technological revolutions throughout the past two centuries. The project will initiate a program of collaboration among top mathematical researchers from around the world and bring together two separate mathematical areas int ....Breakthrough methods for noncommutative calculus. This project aims to solve hard, outstanding problems which have impeded our ability to progress in the area of quantum or noncommutative calculus. Calculus has provided an invaluable tool to science, enabling scientific and technological revolutions throughout the past two centuries. The project will initiate a program of collaboration among top mathematical researchers from around the world and bring together two separate mathematical areas into a powerful new set of tools. The outcomes from the project will impact research at the forefront of mathematical physics and other sciences and enhance Australia’s reputation and standing.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100020
Funder
Australian Research Council
Funding Amount
$1,638,060.00
Summary
Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to e ....Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to enhance Australia’s position at the forefront of international research in Geometric Analysis. Ultimately, the project will enhance Australia's leading position in the area of Index Theory by developing novel techniques to solve challenging conjectures, and mentoring HDR students and ECRs.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL200100141
Funder
Australian Research Council
Funding Amount
$3,077,547.00
Summary
Real groups and the Langlands program. This program aims to address deep longstanding questions about real groups, algebraic objects which describe the basic symmetries occurring in nature. The study of these basic symmetries is central in all areas of mathematics and they come up in many applications. The expected outcomes include solving a central 50 year old problem of unitarity as well as making major progress in the Langlands program, a grand unification scheme of mathematics. The benefits ....Real groups and the Langlands program. This program aims to address deep longstanding questions about real groups, algebraic objects which describe the basic symmetries occurring in nature. The study of these basic symmetries is central in all areas of mathematics and they come up in many applications. The expected outcomes include solving a central 50 year old problem of unitarity as well as making major progress in the Langlands program, a grand unification scheme of mathematics. The benefits include raising Australia's international research profile, building a large network of international collaboration with top institutions in the world, and increasing capacity in number theory and algebraic geometry, which are playing an ever more important role in technology. Read moreRead less
Australian Laureate Fellowships - Grant ID: FL230100256
Funder
Australian Research Council
Funding Amount
$3,359,669.00
Summary
Unlocking the secrets of modular representations. This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently p ....Unlocking the secrets of modular representations. This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently possible and a new understanding of the arithmetic difficulties present. Key benefits will be seen in the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in sophisticated theory and large-scale computation in concert.Read moreRead less