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Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi. [ABSTRACT FROM AUTHOR]

Describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariants objects on their boundaries at infinity; Relation of far field phenomena on a conformally compact Einstein manifold to conformal theories on its boundary at infinity; Proposal of relationship as a means of studying conformal geometry; Progress in understanding the Q-curvature and its geometric meaning in low dimensions and on conformally flat manifolds