**Harish Seshardi, Indian Institute of Science, Bangalore**

**Title:** Limits of Positive Einstein metrics on the 4-sphere.

**Abstract:** I will talk about a compactness theorem for positive
Einstein metrics on S^{4}. For general 4-manifolds, it is
known that a limit of such metrics is an orbifold Einstein metric. In
the case of S^{4}, it turns out that the limit is always a
smooth Einstein metric.

This is joint work with Kazuo Akutagawa and Hisaaki Endo.