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Conformal geometry and holography

Rod Gover
(Auckland)
Analyseseminar
Torsdag, 28 juni, 2012, at 15:15, in Aud. G2 (1532-122)
Abstrakt:
The Poincaré model realises hyperbolic $(n+1)$-space $\mathbb{H}^{n+1}$ as the interior of a unit Euclidean ball, but equipped with a metric conformally related to the Euclidean metric in a way that places the boundary $n$-sphere $S^n$ at infinity. This provides a concrete setting for identifying the isometry group of $\mathbb{H}^{n+1}$ with the conformal group of $S^n$ and so a geometric foundation for Poisson transforms linking $G=SO(n+1,1)$ representations of $G=SO(n+1,1)$, as induced by its maximal parabolic, to those induced by its maximal compact subgroup. Generalising "curved analogues" of this picture form the basis of striking new developments in mathematics and physics. I will describe some new mathematics that enables solving to all orders the asymptotics of linear boundary problems problems with boundary data along the conformal infinity. Generalisations of the GJMS operators arise from the coefficients of log terms in suitable cases. The problems considered form a class of problem of interest in the conjectural AdS/CFT correspondence of quantum gravity. 

This is joint work with Andrew Waldron and Emanuele Latini.
Kontaktperson: Bent Ørsted