Foundations of Ricci flow

Taught Course Centre (TCC) of Bath, Bristol, Imperial, Oxford, Warwick

Spring 2024

Peter Topping

In the spring of 2024 I will be delivering a graduate course in person (at Warwick) and online (via MS Teams) to students at Bath, Bristol, Imperial, and Oxford and Warwick.

Mailing list: Although I will be posting information to the Team directly, I also intend to maintain a mailing list. If you would like to join or leave then let me know.

Warwick location: The upgrade to our video-conferencing room has rendered it unusable, so we will start by lecturing on an ipad via the Team.

Time: Thursdays 11am -- 1pm. We will start on 25 January, one week behind the typical schedule. The last lecture is planned for 14 March, again one week behind the typical schedule.

Registration: To register for the course and get the online Teams link, please visit the main TCC web page.

Target audience: Graduate students who have just learned the basics of Riemannian geometry. No prior knowledge of Ricci flow will be assumed. It would be natural, but is not critical, to know some PDE theory.

Lecture notes: I will be updating my Ricci flow lecture notes that can be found HERE.

Credit: If you plan to take the course for credit then please let me know as soon as possible and I will consider how to arrange this. Maybe a presentation or a small project.

Content: Ricci flow is a particularly elegant example of a geometric flow. It evolves a Riemannian manifold under a type of heat equation to improve it in one or more senses. Amongst geometric flows it has an unrivalled track record of solving problems in other areas, particularly in pure differential geometry. In this course we will get an overview of some of the key ideas of the subject by piecing together a modern proof of Hamilton's original result classifying all closed 3-manifolds of positive Ricci curvature. Further details will be added in due course.