Coupled Kaehler-Einstein metrics consist of Kaehler metrics on Fano manifolds satisfying a system of Monge-Amepere equations extending the Kaehler-Einstein equation. There are obstructions naturally extending those for Kaehler-Einstein metrics. We show a residue formula for one of the obstructions and a concrete example of the computation. This talk is based on joint works with Yingying Zhang.
In the colloquium talk, I will start from the classical results of Yau and Aubin, so it should be understandable for general audience.