Location: Room 383N.
Time: Wednesdays, 3-4pm, or 4-5pm if the geometry seminar does not meet.
Abstract: In this talk I will describe some of the significant properties of three compact manfolds with corners obtained, respectively, as the resolution of a group action (joint work with Pierre Albin), the asymptotic configuration space for a vector space and the compactified moduli space of magnetic monopoles (joint work with Michael Singer). I will not have time to discuss these constructions in any detail but intend instead to emphasize their common, particularly their iterative, features and how these can be expected to appear elsewhere.
Abstract: In this talk I describe the asymptotics of solutions of the wave equation on asymptotically De Sitter and Anti-de Sitter spaces. This is part of a larger program to analyze hyperbolic equations on non-product, non-compact manifolds, similarly to how various types of `ends' have been studied for the Laplacian and other elliptic operators on Riemannian manifolds. The AdS setting is particularly interesting from the point of view of propagation phenomena, since for the conformally related incomplete metric, there are null-geodesics which are tangent to the boundary.