Jiasheng Teh, McMaster University
"On moduli spaces of Ricci-flat 4-manifolds"
Einstein metrics have long been considered as the canonical metrics in Riemannian geometry. The moduli space of Einstein metrics constitutes a diffeomorphism invariant of the underlying closed smooth manifold. In dimension four, they exhibit a balance between the rigidity of the constant sectional curvature metrics in low dimensions and the flexibility coming from higher dimensions. In this talk, we will outline the strategies to show that the moduli spaces of Einstein metrics for a certain family of closed 4-manifolds, the ones which admit a locally hyperKähler metric, are all path-connected. We will also present a Torelli theorem for semi-complex structures.