Department of Mathematics
Title : Compactification, projective geometry, and Einstein metrics
| Speaker: Rod Gover Affiliation: University of Auckland Time: 9am Wednesday, 6 March, 2013 Location: 303-412 |
Abstract
| Conformal compactification, as originally defined by Penrose, has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories ``at infinity'', to the asymptotic phenomena of an interior (pseudo-)-Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. For many of these applications it should be profitable to consider other notions of geometric compactification. For manifolds $M$ with a complete affine connection $\nabla$, I will define a class of compactifications based around projective geometry (that is the geodesic path structure of $\nabla$). This applies to pseudo-Riemannian geometry via the Levi-Civita connection and provides an effective alternative to conformal compactification. The construction is linked to the solutions of overdetermined PDE known as BGG equations and via this is seen to a part of a very general picture. |
-
Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
