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
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.
Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems des ....Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems described by logarithmic conformal field theory.
Expected Outcomes: Novel representations of fundamental importance in logarithmic conformal field theory.
Benefit: Resolution of open problems in logarithmic conformal field theory, thus continuing the strong tradition in the field in Australia.
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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.
Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less
Understanding cohesive forces in nanosystems. This theory project will provide basic scientific and modelling/computational support for a number of emerging technologies such as clean energy, and advanced materials and textiles (both CSIRO research areas). Other possible application areas are assembly of arrays of nanotube-based mechanical or electronic devices (e.g. single electron transistor arrays for quantum computer readout), and medical imaging and drug delivery via nano-sized magnetic pa ....Understanding cohesive forces in nanosystems. This theory project will provide basic scientific and modelling/computational support for a number of emerging technologies such as clean energy, and advanced materials and textiles (both CSIRO research areas). Other possible application areas are assembly of arrays of nanotube-based mechanical or electronic devices (e.g. single electron transistor arrays for quantum computer readout), and medical imaging and drug delivery via nano-sized magnetic particles. This last application is a strong growth area worldwide, with several Australian groups already participating. The project will train postgraduate students and a postdoctoral researcher. It will connect Australian scientists with a European Network of Excellence.Read moreRead less
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
Algebraic approach to exactly soluble models for disordered systems. In nanoscience there are a diverse range of systems in which disorder, randomness, or noise can play a significant role. Examples range from quantum wires to qubits to unzipping DNA.
Even the simplest mathematical models for systems in the presence of disorder have a rich mathematical structure because they can be formulated in terms of Lie algrebras or diffusion on a curved surface.
The complementary physical and mathem ....Algebraic approach to exactly soluble models for disordered systems. In nanoscience there are a diverse range of systems in which disorder, randomness, or noise can play a significant role. Examples range from quantum wires to qubits to unzipping DNA.
Even the simplest mathematical models for systems in the presence of disorder have a rich mathematical structure because they can be formulated in terms of Lie algrebras or diffusion on a curved surface.
The complementary physical and mathematical expertise of the two Chief Investigators is crucial to this project.Read moreRead less
From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models ....From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models such as superintegrable systems, quantum spin chains, and spin-boson models. Anticipated applications of the proposed research include the accurate prediction of physical phenomena, from energy spectra to quantum correlations. Such advances should have significant ramifications, and provide benefits, well beyond the mathematical discipline itself.Read moreRead less