Theoretical Investigations in Classical and Quantum Gravity

A number of projects will be completed in the areas of general relativistic gravity, unification of general relativity with quantum physics and applications of these theories to cosmology. This research is aimed at deepening our understanding of the dynamics of black holes, physics of the early universe, fundamental issues related to space-time structure such as whether information is lost inside black holes, quantum nature of space-time, the emergence of classical space-times from quantum geometries and the interface of general relativity and the foundations of quantum mechanics.

This research is expected to have a broader impact on related areas because it will provide: i) new tools to extract reliable physical content of the numerical simulations of strongly gravitating systems such as black holes; ii) new inputs into cosmology arising from the quantum nature of space-time near the big-bang; iii) a rigorous basis for analyzing the dynamical and fully non-linear regime of general relativity which is important for astrophysical sources of gravitational waves; iv) foundations of quantum mechanics; and v) contributions to a areas of mathematics such as geometric analysis, theory of quantum groups and applications of holomorphic structures.