## 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.

**Announcements:**

·
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, tao@math.ucla.edu, 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’s “Ricci 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.