Study of complex analysis from a point of view of parabolic geometry

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We have given a complete construction of scalar conformal invariants of dimension less than 9 or degree less than 3 ; this was a unsolved problem for even dimensions and is expected to have application to the construction of CR invariants. This result is a consequence of the jet isomorphism theorem that gives a decomposition of the jet space of conformal structures as irreducible tensor spaces ; the isomorphism is defined via the curvature of the ambient metric, a Ricci-flat Lorentz metric associated to conformal structure. On CR geometry, we have formulated an invariant theory that can be applied to describe the Szego kernel.