Klaus Kroencke

Lecture course  Ricci flow, Summer term 2019

The course takes place Tuesday 14:00-15:50 in H2 with a five minute break in between. The lecture starts in the second week of April. No lecture on April 2 and June 4!

For the course, basic knowledge of Differential and Riemannian Geometry is preassumed. More precisely, you should be familiar with the following concepts: Riemannian manifolds, Levi-Civita connection, geodesics, and curvature quantities. Basic knowledge in Partial Differential Equations is very helpful, but not inevitable.

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, wich tends to flow a given function to even nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics.
In this lecture course, we discuss the following topics: Einstein metrics and Ricci solitons, Ricci flow on surfaces and 3-manifolds, entropies

For the preparation of the course, I use the following books: