UM Student Analysis Seminar: Spring/Summer 2010

Spring/Summer 2010 Reading Groups:
(1) Poincare Conjecture
(2) Harmonic Analysis

The Poincare Conjecture/Geometric PDE

To get on or off the email list, go to directory.umich.edu, search for "poincare-reading-group," bind to your umich uniqname, and join the group, or email Rafe. Everything here is tentative/flexible, and will be adjusted as the spring goes on.

Logistics: Mondays (2pm) and Wednesdays (now back to 2pm, as of 6/28, earlier starting now at 3pm as of May 26, Wednesdays only), (as of 6/28), 2866 (formerly 3096) East Hall. (We can reschedule this as needed, based on participants' schedules.)

Text: Terry Tao's lecture notes for a course he taught. We'll be following the nicer-formatted version in his book Poincare's Legacies (volume 2), a free copy of which is available here [warning: large file] on his website. In the free draft online, the lecture notes are chapter 3; in the printed version of the book, the notes are in chapter 2. (Other than the chapter number and the pagination, the draft and the actual version of the book seem to be basically the same, with the same numbering for lectures, equations, theorems, etc., so either is fine. The book is available for $30 on Amazon or from AMS.) (These are based on the original lecture notes that are on his blog, which have different numbering and less nice formatting. These blog entries are convenient to look at, though, since they have links to wikipedia entries for many undefined terms, which are merely italicized in the text.)

Background: Tao writes that he's written the notes so that, in theory, it is self-contained, although knowing at least one of Riemannian geometry, PDE, and/or topology would be helpful. I think everyone involved is somewhat familiar with at least one of these, and most of us aren't very familiar with all three, so hopefully the combination of our backgrounds will make this a good learning experience for everyone.

Format: It probably makes sense to be flexible with our format, seeing what works best. I suggest that we start by meeting twice a week, aiming to cover about one section of Tao per meeting. (Each of his lectures seem to correspond to one hour-long class. We can aim to cover it all in an hour or so, but schedule the room for two hours to leave some wiggle room if it takes longer. If things seem to go significantly over an hour, we could take a break.) There are twenty lectures, so at this rate we'd be able to cover most of it before people leave. One person will present each lecture, but it will be informal and collaborative, and it's okay if the lecturer doesn't know everything.

Note: Feel free to email the speaker of the section ahead of time if there are things that you found confusing about the section that you'd like talked about. Speaker email addresses (add @umich.edu) are listed.

Date SpeakerTitle
Monday, May 10Rafe Kinsey (rkinsey@)Lecture 1: Riemannian Manifolds and Curvature
Wednesday, May 12Joe Roberts (joeprob@)Lecture 2: Flows on Riemannian Manifolds
Monday, May 17Nic Ford (nicf@)Lecture 3: The Ricci Flow Approach to the Poincare Conjecture
Wednesday, May 19Allen Wu (yilunwu@) [Part 1]
Rafe Kinsey (rkinsey@) [Part 2]		Lecture 4: The Maximum Principle, and the Pinching Phenomenon
(may carry over a bit to Monday)
Monday, May 24 (2pm)Brian Mann (brmann@)Lecture 5: Extinction of second homotopy
Wednesday, May 26
(3 pm NEW TIME for Wednesdays)		Jordan Watkins (jpwatkin@)Lecture 6: Extinction of third homotopy I
Friday, May 28, 3pm
Special Day, 3096EH		Joe Roberts (joeprob@) Lecture 7: Extinction of third homotopy II
Monday, May 31; Wednesday, June 2N/ANo meetings this week
Monday, June 7 (2pm)Rafe Kinsey (rkinsey@)Lecture 8: Rescaling of Ricci flows and $\kappa$-non-collapsing
Wednesday, June 9 (3pm)Joe Roberts (joeprob@)Lecture 9: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy
Monday, June 14 (2pm)Jordan Watkins (jpwatkin@)Lecture 10: Comparison geometry, the high-dimensional limit, and the Perelman reduced volume
Wednesday, June 16 (3pm)Rafe Kinsey (rkinsey@)Lecture 11: Variation of L-Geodesics, and monotonicity of Perelman reduced volume
(And last section of Lecture 10, presented by Jordan)
Monday, June 21 (2pm)Brian Mann (brmann@)Lecture 12: $\kappa$-non collapsing via Perelman Reduced Volume
Wednesday, June 23 (3pm)Joe Roberts (joeprob@)Lecture 13: High curvature regions of Ricci flow and $\kappa$-solutions
Monday, June 28 (2pm) 2866 EHRafe Kinsey (rkinsey@)Lecture 14: Li-Yau-Hamilton Harnack inequalities and $\kappa$-solutions
Wednesday, June 30 (2pm) 2866 EHJordan Watkins (jpwatkin@)Lecture 15: Stationary points of Perelman's entropy or reduced volume are gradient shrinking solitons
Wednesday, July 7 (12pm), room 2866Joe Roberts (joeprob@) Lecture 16: Geometric limits of Ricci flows, and asymptotic gradient shrinking solitons
(This is as far as we got.)

Harmonic Analysis

We will be working through parts (most of chs. 1-6) of Katznelson's book, An Introduction to Harmonic Analysis. (Note: there are several slightly different editions of the book, more or less the same, but some with extra sections. We'll address this as it comes up.) Email Rafe for more info and to get on the mailing list. Meetings will be Wednesdays and Fridays, at 1:00 (Michigan time = 1:10 real time), in 3096 EH.

We'll have someone lead the group each day, but it won't be a lecture. The idea is for everyone to have read the sections ahead of time and thought about the exercises; we'll go over subtleties of the proofs, theorems, examples, and then talk about exercises in a collaborative manner.

Note: Feel free to email the leader of the day ahead of time if there are things that you found confusing about the sections that you'd like more time on. The leader's email addresses (add @umich.edu) are listed.

Date LeaderSections
Friday, May 14 (2pm)Rafe Kinsey (rkinsey@)logistics, 1.1
Wednesday, May 19 (1pm)Austin Shapiro (auspex@)1.2, 1.3
Friday, May 21 (1pm)Tom Ngo (hieu@)1.4, 1.5
Wednesday, May 26 (1pm) Zhiqiang Li (lizq@)1.6, 1.7
Friday, May 28 (1pm)Jared Whitehead (jaredwh@) 1.8, 1.9 (not in older editions)
Wednesday, June 2
(1:10pm from now on = 1:00 Michigan Time)		Rafe Kinsey (rkinsey@) 2.1, 2.2, 2.3 (last section optional)
Friday, June 4Rafe Kinsey (rkinsey@)3.1 (and look at exercises II.1.3, II.2.1, II.3.1 from last time)
Wednesday, June 9Tom Ngo (hieu@) 3.2, 3.3
Friday, June 11Alex Mueller (amuell@)4.1, 4.2, 4.3 (not in old editions)
Wednesday, June 16Austin Shapiro (auspex@)6.1, 6.2 (we skipped chapter 5)
Friday, June 18Austin Shapiro (auspex@)continuation of last time, particularly 6.1 exercises, and all of 6.2 with exercises
Wednesday, June 23Zhiqiang Li (lizq@)6.3, 6.4
Friday, June 25Jared Whitehead (jaredwh@)6.5, 6.6

This finishes the formal meetings of the group for the summer. Those who are still around and want to meet informally to discuss aspects of harmonic analysis (e.g. from Stein's books or Tao's lecture notes) can use the group email list to arrange this. (Email Rafe to get on the email list.)

Go back to the student analysis seminar homepage.

Email rkinsey (at) umich (dot) edu with comments, questions, and corrections.
Last modified: Tue Jul 20 14:51:46 EDT 2010
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