Question

Hi Folks!

Sorry I've been out of touch. You know, I've been trying to integrate myself (was area man, now volume man, plus constant). Anyway, I haven't had enough coffee, and I seem to proving contradictions in mathematics. Can anyone verify or debunk the following seemingly obvious statement? I have hopelessly confused myself.

Let C be the 1/3 Cantor set. Let s=log2/log3. Then Hausdorff s-measure(C)=1=Hausdorff s-content(C).

Right? Philosophy: For the Cantor set, the obvious cover is the most efficient. Of coursing proving this is a pain - see notes from Juha's course last semester.

Am I crazy?

lectures 17 through 19 ..

.. ready for download at the usual place.

a word of caution: the last few lectures are somewhat technical in nature, so keep your eyes open wider for errors.

now we're up to sixteen.

.. lectures, that is. Lectures 14, 15, and 16 from last week and today are up for download at the usual place. Be warned:

1. In case the resolution looks a little strange, the original paper notes were on blue paper (it was the only 3-hole punch paper I could find without paying for it) and I saved these notes as greyscale JPEG graphics and then PDF files.
   
   
2. I oscillated with what the 'k' means in the definition of a CAT(k) space .. that is, if it is a nonpositive or a nonnegative parameter. The meaning, I hope, should be understood.
   
   
3. The latest lecture may be error prone. Mario himself refers to it as "the hardest theorem in elementary mathematics," and I might agree with him. It's a tricky manipulation of symbols, and now I know how my Calculus II students from yesteryear must have felt! q:

Wow

Check out this beautiful survey article for ICM by Mario.

you know the drill.

Lectures 11 through 13 can be downloaded here in PDF format. I felt the urge to kill the snotty nosed-brat who was hogging the library scanner, but now I'm calm and he gets to live.

Anyways, enjoy .. and for the record, the disparate dry humor in Lecture 13 is M. Bonk's, and not mine. I'm hardly that clever.

this week's SAnS title/abstract

hi Kevin, and all other interested parties;

I've submitted an abstract for UM Student Analysis Seminar this week, and the format will be a little different from previous times and traditional seminars.

This is a call for open problems: they don't need to be high-powered and result in a publication, but an opening to stimulate thought. The goal is to raise interest in varying subfields in analysis, and possibly lead to collaborations amongst us students.

So, anyone know a good problem? q:

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Tues, 7 Feb 2006 (5-6 pm)
Title: Open Problem Session
Speaker: none
Abstract: Interested parties will bring unsolved problems (related to mathematical analysis; possibly research level) and we will spend the hour discussing them, and hopefully make progress in solving them.

When choosing problems, we would prefer that the background not be too lengthy; problems of a general background (e.g. complex analysis, measure theory) are encouraged.