UM PDE Reading Group: Fall 2010

We will be talking about various advanced topics in PDE, hopefully including Sobolev Inequalities and Embeddings, Energy Methods, Strichartz Estimates, Morawetz Estimates, and more. For more information, contact Jen Beichman (jbeich@); for matters pertaining to the webpage, email Rafe Kinsey (rkinsey@). To get on or off the email list, go to directory.umich.edu, search for "pde-reading-group," bind to your umich uniqname, and join the group, or email Jen or Rafe.

Logistics: Mondays 4pm-5pm (3866 EH) and Thursdays 5pm-6pm (officially we're in 4437 EH, on psych side, but we will probably try to take an open classroom on the math side with chalkboards, most like 4096 or 4088, if you can't find us call one of us), starting October 25.

For Winter: We will be continuing the reading group, although times might change (we're thinking of Mondays at 4 and Wednesday at 3).

Date	Speaker	Topic
Monday, Oct 25	Joe Roberts (joeprob@)	Sobolev Inequalities and Embeddings I. Mostly Evans ch 5, sections 2-5 (and first part of section 6 time permitting). (We're using the first edition, the second edition might have slightly different numbering. Either is fine.)
Thursday, Oct 28	Rafe Kinsey (rkinsey@)	Sobolev Inequalities and Embeddings II. Evans 5.6-5.9
Monday, Nov 1	Jen Beichman (jbeich@)	Time decay from energy estimates and motivation for Strichartz estimates
Thursday, Nov 4	Rafe Kinsey (rkinsey@)	Intro to Harmonic Analysis, Marcinkiewicz Interpolation References: Tao, Lecture Notes 1 and 2; Stein-Weiss, ch. 5
Monday, Nov 8	Jen Beichman (jbeich@)	Oscillatory integral operators
Thursday, Nov 11	Jeff Calder (jcalder@)	Calderon-Zygmund Operators
Monday, November 15	Jeff Calder (jcalder@)	Littlewood-Paley Theory
Thursday, November 19	Joe Roberts (joeprob@)	Sogge, 3.1
Monday, November 22	Joe Roberts (joeprob@)	Sogge, 3.1, cont'd
Thursday, November 25	n/a	No meeting (Thanksigiving)
Monday, November 29	Joe Roberts (joeprob@)	Sogge, 3.1, cont'd
Thursday, December 2	Jen Beichman	Abstract setting for Strichartz estimates, the non-endpoint versions of the estimates in full generality, some set-up for the endpoint case, maybe including Lemma 1.4 (none of the corollaries). pp 122-126, 129-130 of Sogge (2nd edition)
Monday,December 6	Rafe Kinsey	Sogge, pp 130-136 (through end of 4.1): technical lemmas and the proof of the endpoint homogeneous estimates. 12/6
Thursday,December 9	Purvi Gupta (prvgupta@)	Sogge, pp 136-139, 139-141 (beginning of 4.2): Christ Kiselev Lemma, inhomogeneous estimates.
Monday, December 13	Benson Muite	Applications of estimates

References

Various of us have copies of the books listed, as might the library (ask around before recalling from the library, since there's a good chance that it's one of us that has the copy).

A course at Johns Hopkins covering similar topics to us, with links to lots of papers.
Evans, Partial Differential Equations
Sogge, Lectures on Nonlinear Wave Equations, 2nd ed
Stein, Harmonic Analysis (1993)
Stein and Weiss, Fourier Analysis (1971)
Stein, Singular Integral Operators
Tao, Lecture Notes on Harmonic Analysis, 247A (see also 247B notes)

Go back to the PDE reading group homepage.

Go back to the student analysis seminar homepage.

Email rkinsey (at) umich (dot) edu with comments, questions, and corrections on the webpage.
Last modified: Mon Dec 20 14:39:48 EST 2010

Back to the UM Seminars page.