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
A top-down approach to synthesising high-value fluorocarbons. Fluorocarbons' ability to impart high stability, solubility, and unique reactivity to host molecules renders them invaluable in agrochemicals, pharmaceuticals, polymers and surfactants. Their robustness also renders them environmentally persistent. There are no industrially utilised methods for the re-purposing or recycling of fluorocarbons. This project aims to generate new methods for the selective activation of carbon-fluorine bond ....A top-down approach to synthesising high-value fluorocarbons. Fluorocarbons' ability to impart high stability, solubility, and unique reactivity to host molecules renders them invaluable in agrochemicals, pharmaceuticals, polymers and surfactants. Their robustness also renders them environmentally persistent. There are no industrially utilised methods for the re-purposing or recycling of fluorocarbons. This project aims to generate new methods for the selective activation of carbon-fluorine bonds in polyfluorocarbons, allowing their incorporation or repurposing into high value chemicals and/or easy derivitisation to access a plethora of new fluorocarbon products. Expected outcomes will allow new processing methods to value add to fluorocarbons while preventing their environmental release. Read moreRead less