Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathe ....Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathematics. Expected outcomes include a completely new understanding of the mathematical structure of these theories which will, in turn, facilitate applications in 4D gauge theory. This will boost research capacity and further cement Australia's reputation as an international leader in mathematical physics research.Read moreRead less
Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systemati ....Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systematically and rigorously analysing a wide variety of logarithmic conformal field theories so as to facilitate applications.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