Infinite-dimensional Lie groups and algebras in mathematical physics.
Infinitesimal holonomy group structure and geometrization
Initial data for numerical relativity.
Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of the curvature, our method requires only a sup-norm bound on the curvature near the given observer.
Instantons, topological strings, and enumerative geometry.
Integrability and Einstein's equations
1. Introduction. In recent years, there has been considerable interest in Oxford and elsewhere in the connections between Einstein's equations, the (anti-) self-dual Yang-Mills (SDYM) equations, and the theory of integrable systems. The common theme running through this work is that, to a greater or lesser extent, all three areas involve questions that can be addressed by twistor methods. In this paper, I shall review progress, with particular emphasis on the known and potential applications in...
Interferometer techniques for gravitational-wave detection.
Inverse problem for networks of laser interferometers
Estimation of the parameters of the gravitational-wave signal from a coalescing binary by a network of laser interferometers is considered. A generalization of the solution of the inverse problem found previously for the network of 3 detectors to the network of N detectors is given. Maximum likelihood and least squares estimators are applied to obtain the solution. Accuracy of the estimation of the parameters is assessed from the inverse of the Fisher information matrix. The results of the Monte...
Is the geodesic hypothesis in general relativity falsifiable?
Isolated and dynamical horizons and their applications.