MATH 285G : Perelman’s proof of the Poincaré conjecture

  • Course description: The course will cover as much of Perelman’s proof as possible.  Specific topics include: Existence theory for Ricci flow, finite time blowup in the simply connected case, Bishop-Cheeger-Gromov comparison theory, Perelman entropy, reduced length and reduced volume and applications to non-collapsing, Perelman compactness theorem, structure and asymptotics of ancient κ-non-collapsing solutions, analysis of horns and necks, surgery.


·        The first class will be on Wednesday, April 2 (I will be in Washington, DC on Monday March 31).

·        There will be no class on Monday, April 7 (I will be in Toronto).

·        There will be no class on Monday, May 5 (I will be in Washington DC again).

·        The last class will be on Friday, June 6 (I will be in Ohio for the following week).

·        Instructor: Terence Tao,, x64844, MS 6183

·        Lecture: MWF 4-4:50, MS5137

·        Quiz section: None

·        Office Hours: M 2-3

·        Textbook: I will use a number of sources, including Morgan-Tian’sRicci flow and the Poincaré conjecture”, Chow-Knopf’s “Ricci flow: an introduction”, Kleiner-Lott’s “Notes on Perelman’s papers”, and various papers, including of course Perelman’s.   I will post lecture notes on my blog site.

·        Prerequisite: The Math 234 class (Ricci flow) from last winter is highly recommended.  I will put some basic foundational material on PDE and Riemannian geometry in my lecture notes, but if you are not familiar already with Ricci flow, I would expect that one would need a significant amount of self-study in these topics in order to keep up with the course. 

·        Grading: Grading is based on attendance.

·        Reading Assignment: Lecture notes will be provided on my blog site.  Students are encouraged to comment on these posts.

·        Homework: There is no homework for this course.

Online resources:

·        The original papers of Perelman:

1.      The entropy formula for the Ricci flow and its geometric applications

2.      Ricci flow with surgery on three-manifolds

3.      Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

·        Bruce Kleiner’s Ricci flow page.

·        Kleiner-Lott’s “Notes on Perelman’s papers”.

·        Morgan-Tian’s book “Ricci flow and the Poincaré conjecture”.

·        Cao-Zhu’s “Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture”.

·        My own exposition of Perelman’s proof.

·        The blog for this course.