### 12/03/2019, 12:00 — 13:00 — Room P3.10, Mathematics Building

Claude LeBrun, *Stonybrook*

### Einstein Metrics, Harmonic Forms, and Conformally Kaehler Geometry

There are certain compact 4-manifolds, such as real and complex hyperbolic 4-manifolds, 4-tori, and K3, where we completely understand the moduli space of Einstein metrics. But there are vast numbers of other 4-manifolds where we know that Einstein metrics exist, but cannot currently determine whether or not there are other Einstein metrics on them that are quite different from the currently-known ones. In this lecture, I will first present a characterization of the known Einstein metrics on Del Pezzo surfaces which I proved several years ago, and then describe an improved version which I obtained only quite recently.