Thomas Walpuski

Seminar: Riemannian Convergence Theory (summer semester 2021)

Moodle (key: cheeger), AGNES.

The seminar meets on Wednesdays 13:15–14:45. The Zoom invite can be found on the Moodle page.

What is this about?

In mathematics it is often crucial to understand when a particular sequence of objects has a limit (possibly after passing to a subsequence). In this seminar we study this problem with the objects under considerations being Riemannian manifolds. In particular, we will investigate various notions of convergence of Riemannian manifolds, prove corresponding compactness results (under various geometric hypotheses), derive lots of applications, and finally try to understand how compactness fails in a controlled way.

The history of Riemannian Convergence Theory goes back roughly 60 years, major breakthroughs have been achieved within recent years. The goal of this seminar is to discuss some milestones of this development up to the early 2000s.


The seminar has 14 meetings. Here is a rough plan.


You should have a solid understanding of Differential Geometry and Riemannian Geometry. The two review talks might bring you up to speed if you're Riemannian Geometry is a little rusty. If you are very brave, you could take this seminar and Differential Geometry II concurrently.