In this seminar, Professor Song Sun started with explaining the most basic concepts like, Riemannian metric, curvature in differential geometry. He then introduced one of the most important equations differential geometry, the so-called Einstein equation. After defining the holonomy group of a Riemannian manifold, he explained Berger's classification of holonomy groups of Riemannian manifolds which are not locally symmetric. He then pointed out the importance of studying Riemannian manifolds with special/exceptional holonomy groups, e.g. Calabi-Yau manifolds, hyperkahler manifolds, G2 and Spin(7) manifolds. He concentrated on hyperkahler 4-manifolds and explained their geometry and topology in more details. In the end, he introduced his recent research result on studying Gromov-Hausdorff limit of hyperkahler 4-manifolds.

Reported by Yalong Cao