Limits of Positive Einstein metrics on the 4-sphere.
Abstract: I will talk about a compactness theorem for positive Einstein metrics on S4. For general 4-manifolds, it is known that a limit of such metrics is an orbifold Einstein metric. In the case of S4, it turns out that the limit is always a smooth Einstein metric.
This is joint work with Kazuo Akutagawa and Hisaaki Endo.