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A gauge theoretic approach to Einstein 4-manifolds.

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If you have a question about this talk, please contact Professor Maciej Dunajski.

I will describe a new way to formulate Einsteinâs equations on 4-manifolds, so that the independent variable is not a Riemannian metric, but instead an SO(3) connection on an auxiliary bundle. The metric is then determined algebraically from the curvature of the connection. (This is reminiscent of the way that Maxwellâs equations can be thought of as equations for a U(1)-connection, whose curvature then gives the electro-magnetic field.) This point of view gives a new action principle for Einstein metrics, discovered by Krasnov, which is seemingly less problematic than the Einstein-Hilber action. It also reveals a link between Einstein 4-manifolds and symplectic manifolds in dimension 6. Finally it leads to some interesting open questions which I hope to have time to discuss.

This talk is part of the Mathematical Physics Seminar series.

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