These notes and comments are where I give my views, explain intuitions, and generally give my biased view of things geometric and analytic as well as things data oriented.

Of course, like anyone who has been exposed to the joys and perils of email, websites, etc. If you want my most candid views of things that are controversial, see me in person.

Comments: by date

4-9-2007

Note: today's lecture was an overview. One student commented about not following all the geometry and being a little uncertain about n-vectors and n-forms. We will revisit all the technical details more carefully and will define everything and give at least careful intuitive explanations of defined things and theorems.

5-3-2007

In the notes for Monday, 4-30-2007, that I put up today I didn't have anything about the mean curvature interpretation of the first variation of the area. I mentioned this briefly in class and will go over this again briefly at the beginning of class next Monday. I will also add equations to these comments once the latex rendering module gets added to this website -- this is supposed to happen pretty soon.

Notes: various -- things I generate, things I find, etc

4-11-2007-1

The first four lectures given by Urs Lang at a Spring school in Switzerland in 2005 are useful to have. Here is a link to the pdf: Urs Langs Lectures. The last lecture concerns recent developments that are less relevant to what we will be talking about. Another useful -- though brief -- set of notes from the same Spring School are those by Giovanni Alberti. A link to those notes is here: Alberti 2005 Les Diablerets Notes. Albteri also wrote a short article for the Encyclopedia of Mathematical Physics about GMT. You can download those notes from here.

4-17-2007-1

The notes from the lecture yesterday can be found here: notes-4-16-2007.pdf. I actually wrote over twice the number of pages of notes that I gave the lecture from, so at least this time the notes contain most of what I said.

4-27-2007-1

The notes from Monday (4-23-2007) can finally be downloaded from here: notes-4-23-2007.pdf.

5-1-2007-1

I mentioned the nice notes by Camillo De Lellis on Preiss' theorem. He also proves Marstrand's Theorem along the way. Here are those notes. (Jonas Azzam is talking about Marstrand's theorem in the Analysis seminars at 3 on Tuesdays, rm 6221 in Math Sciences.)

5-1-2007-2

I expect to get the notes from Monday posted here sometime tomorrow.

5-3-2007-1

The notes from Monday (4-30-2007) are now available here: notes-4-30-2007.pdf.

5-10-2007-1

The notes from Monday (5-7-2007) are now available here: notes-5-7-2007.pdf.

5-16-2007-1

The notes from Monday (5-14-2007) are now available here: notes-5-14-2007.pdf.

6-7-2007-1

The notes from 5-21-2007 are now available here: notes-5-21-2007.pdf.

6-14-2007-1

I was recently told about the existence of a soon to be published book on GMT by Krantz and Parks. There is a preprint version of the book available here. I haven't had the time to look at it carefully, but it seems to be quite informative. In particular I would not let the less than superb figures influence you negatively since it seems at first glance to be both easily readable and fairly complete. And of course, the figures are easy to improve.

6-16-2007-1

The notes from 6-4-2007 are now available here: notes-6-4-2007.pdf. I did not write out the proof of both directions of the last theorem (E rectifiable iff there is an app tangent plane a.e.) as I thought I would. I may add notes later since there is a slip in the proof as it appears in Simon's book. Well, that finishes off the UCLA-LANL course. It was fun. Keep in touch!

Cheers,

Kevin