Scalar Invariants for Even Dimensional Conformal Structures

GEOMETRIC PDE SEMINAR
Topic:Scalar Invariants for Even Dimensional Conformal Structures
Speaker:Kengo Hirachi
Affiliation:University of Tokyo and Member, School of Mathematics
Date:Tuesday, February 3
Time/Room:2:00pm - 3:00pm/S-101

The first aim of Fefferman-Graham ambient metric construction was to write down all scalar invariants of conformal structures. For odd dimensions, the aim was achieved with the aid of the parabolic invariant theory by Bailey, Eastwood and Graham. In this talk I will explain how far we can extend the result for even dimension.The main tool is the inhomogensous ambient metric and the jet isomorphism theorem. In particular, I give a construction of all conformal invariants in dimensions 4, 6 and 8. This is a joint work with Robin Graham.