Differential Geometry Seminar: The Holonomy Groups of Symmetric Spaces

Speaker: Thorsten Hertl (University of Melbourne)

Title: TBA

Date: Thursday 1 May 2025, 11:10pm in Lower Napier LG28

Abstract: The Holonomy group of a Riemannian manifold is a global differential geometric invariant of the Riemannian manifold that provides information about the addition structures of the Riemannian manifold. In general, it is hard to compute. However, in case of symmetric spaces, the global computation reduce to local ones, which simplifies the problem significantly.

Starting from the holonomy and some of its properties, I will define what a symmetric space is, explain some of their properties and introduce the notion of a symmetric pair and its isotropy representation, which will be indispensable in the determination of the holonomy groups. If time permits, I will also say something about the classification of simply connected symmetric spaces, which gives a list which Lie groups can appear as holonomy groups of Riemannian manifolds.