Gravitating relativistic material bodies: A mathematical analysis. This project aims to establish the local-in-time existence and geometric uniqueness of solutions to the Einstein-Elastic equations representing systems of gravitating relativistic material bodies, and to understand the long-time behaviour of these solutions. In spite of their importance to astrophysics, almost nothing is known about the mathematical properties of solutions to the equations of motion governing gravitating systems ....Gravitating relativistic material bodies: A mathematical analysis. This project aims to establish the local-in-time existence and geometric uniqueness of solutions to the Einstein-Elastic equations representing systems of gravitating relativistic material bodies, and to understand the long-time behaviour of these solutions. In spite of their importance to astrophysics, almost nothing is known about the mathematical properties of solutions to the equations of motion governing gravitating systems of relativistic material bodies. This project would provide mathematical tools for the study of gravitating relativistic material bodies and provide guidance on developing stable numerical schemes for simulations that are essential for comparing theory with experiment. This would significantly improve current understanding of the behaviour of matter and gravitational fields near the matter-vacuum boundary of bodies and help understanding of the physics of these boundaries.Read moreRead less
A mathematical analysis of the influence of small scale inhomogeneities on the evolution of the universe. A fundamental unresolved problem in modern cosmology is to quantify the influence of small-scale inhomogeneities on the evolution of the universe. This project will develop the mathematical techniques required to resolve this question. In addition, these techniques will have important applications to the analysis of astronomical data.