Claude LeBrun (Stony Brook University) will speak in the geometry seminar on Wednesday 26 of June. Claude’s title is Einstein Metrics, Harmonic Forms, and Conformally Kähler Geometry and his abstract is below.
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 qualitatively different from the currently-known ones. In this lecture, I will first present a characterization of the known Einstein metrics on Del Pezzo surfaces that I discovered several years ago, and then describe a delicate generalization which I obtained only quite recently.