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.
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.