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.
Quantum steering, nonlocality and foundations. This project aims at answering foundational questions that will help further our understanding of quantum mechanics---a scientific discipline with proven track record of technological output of great impact in modern society and a huge potential for future developments such as quantum computation and communication. There is a global trend towards interest in quantum foundations, and Australia is already a world leader in the closely related fields o ....Quantum steering, nonlocality and foundations. This project aims at answering foundational questions that will help further our understanding of quantum mechanics---a scientific discipline with proven track record of technological output of great impact in modern society and a huge potential for future developments such as quantum computation and communication. There is a global trend towards interest in quantum foundations, and Australia is already a world leader in the closely related fields of quantum information and quantum-atom optics. Funding of this project will help strengthen and consolidate Australia's position as a world leader in the foundations of quantum mechanics.Read moreRead less
Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Mathematical models for disordered critical point theories. This project sets up a team to develop innovative techniques for fundamental advances in critical behaviour of disordered systems including the Nobel Prize winning integer quantum Hall effect. It will yield new mathematical models for disordered critical point theories, essential for the theoretical analysis of associated emerging technologies.
Decoherence and Quantum Simulations of Spin-Environment systems. The effort to develop quantum technologies relies on our ability to understand and manipulate quantum mechanical objects with great precision. In order to do this, we need to study how such systems interact with their surroundings. Solid-state quantum systems connected to an environment show a rich range of phenomena, such as quantum phase transitions, which are interesting in their own right. This work will better enable experi ....Decoherence and Quantum Simulations of Spin-Environment systems. The effort to develop quantum technologies relies on our ability to understand and manipulate quantum mechanical objects with great precision. In order to do this, we need to study how such systems interact with their surroundings. Solid-state quantum systems connected to an environment show a rich range of phenomena, such as quantum phase transitions, which are interesting in their own right. This work will better enable experimentalists to develop the techniques required for the future of quantum technology.Read moreRead less
Special Research Initiatives - Grant ID: SR0354741
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of t ....Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of the quantum realm will lead to breakthrough science of vital importance to the development of frontier technologies in Australia. This Network will also place a strong emphasis on research training, the mentoring of early career researchers and establishing collaborations with leading international research groups and networks.
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Discovery Early Career Researcher Award - Grant ID: DE130101067
Funder
Australian Research Council
Funding Amount
$302,540.00
Summary
New constructions of superintegrable systems and the connection with Painlevé transcendents. The research of this project will lead to deep discoveries in the field of superintegrability and expand our knowledge of their related algebraic structures, supersymmetric quantum mechanics and Painlevé transcendents. The project will generate new techniques that will be utilised in future applications of mathematical and theoretical physics.
Unified theory of Richardson-Gaudin integrability. Richardson-Gaudin systems form a class of mathematical models of interacting particles that serve as a foundation to understand important phenomena in modern physics. Being integrable, these quantum systems enable deep insights. They are tractable so as to allow for exact analysis, while being elaborate enough to exhibit complex physical properties, notably phase transitions. The international team of researchers aims to merge various approaches ....Unified theory of Richardson-Gaudin integrability. Richardson-Gaudin systems form a class of mathematical models of interacting particles that serve as a foundation to understand important phenomena in modern physics. Being integrable, these quantum systems enable deep insights. They are tractable so as to allow for exact analysis, while being elaborate enough to exhibit complex physical properties, notably phase transitions. The international team of researchers aims to merge various approaches for analysing the integrability of such models. Successful outcomes are expected to produce inventive mathematical techniques, linking a diverse range of fields of current activity and growth. The resulting unified theory is expected to open the door to exciting and innovative pathways in mathematical physics research.Read moreRead less
Quantum states of matter: from spin liquids to superconductors. Condensed matter physics has produced the technologies and materials that fuelled the digital and communications revolution. The scientific importance of condensed matter physics is indicated by the fact that ten Nobel prizes have been awarded for work in this field since 1990. This proposal brings together world leading chemists, experimental physicists and theoretical physicists from Australia, USA and UK to work on highly interdi ....Quantum states of matter: from spin liquids to superconductors. Condensed matter physics has produced the technologies and materials that fuelled the digital and communications revolution. The scientific importance of condensed matter physics is indicated by the fact that ten Nobel prizes have been awarded for work in this field since 1990. This proposal brings together world leading chemists, experimental physicists and theoretical physicists from Australia, USA and UK to work on highly interdisciplinary projects designed to discover how quantum mechanics leads to the novel properties of chemically complex materials. Such materials will be of central importance to the technologies of the future such as computer memories and the superconducting magnets in hospital MRI machines.Read moreRead less
Strongly correlated electron models for organic superconductors. In conventional metals such as copper the interactions between the electrons do not qualitively change the behaviour of the material. However, over the last few decades many materials have been discovered whose behaviours are dominated by the interactions between electrons. These 'strongly correlated' materials include technologically important materials used in power distribution, catalysis and plastic display technologies. This p ....Strongly correlated electron models for organic superconductors. In conventional metals such as copper the interactions between the electrons do not qualitively change the behaviour of the material. However, over the last few decades many materials have been discovered whose behaviours are dominated by the interactions between electrons. These 'strongly correlated' materials include technologically important materials used in power distribution, catalysis and plastic display technologies. This project will combine theoretical and experimental methods from chemistry and physics in an effort to explain the novel behaviours seen in certain classes of organic strongly correlated materials. This understanding has the potential to impact future electronic devices and advanced materials.Read moreRead less