Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. ....Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. The project will also apply diagrammatic methods to address a long-standing challenge in solving a particular model. The project aims to contribute to training researchers in an area of the mathematical sciences of benefit to the future development of new concepts for next-generation electronic devices and smart materials.Read moreRead less