Tuesday, December 21, 2004

Goals before the New Year ..

This is the end /
My only friend, the end
Of our elaborate plans, the end
Of everything that stands, the end
No safety or surprise, the end
~ "The End" by the Doors

Everything's winding down.

After a week's stay in Ann Arbor my collaborator and I parted ways for the holidays; he left this morning to see family in Wisconsin. I'll be doing the same tomorrow, but instead to New York. For the second time today it occurs to me that I haven't been on Long Island for over a year.. I'm not certain how I feel about that.

The paper is officially done; it's just a matter of waiting for copies to be printed out, and then I can mail the article to the journal editor. After that, it's out of our hands: done, and done.

Someone told me today that the Winter Holidays for UM are only eight days long, and after he says this we both shudder. That's too short a time, I think to myself. There's so much to do in so little time. Too often I promised myself that as soon as classes were done, I could think about topics of research and all the reading that I meant to do, if only to enrich my understanding of this term's coursework or the odd topic that looks interesting.

Eight days? I can't do it all in that time.

As a result, I've done my best to select a few goals:
  • to rewrite my Quasiconformal Mapping notes. I don't know this topic nearly as well as I should, or more aptly, as well as an analysis student at University of Michigan should.

    As yet, QC Maps seems to me only a pretty theory, but there must be a reason why the UM analysts are so interested in these objects. What is the motivation, and how are QC mappings used in "applications" to further other theories?

  • To work on extremal problems on CC spaces. This is some remaining work from last week's conversations; at the very least, this gives me a good excuse to learn the Calculus of Variations, and how potential theory comes into play in an actual setting.
Let's hope that times works out.

1 comment:

Kevin said...

I think one thing that motivated alot of people to study QC maps was the fact that they arise naturally in the study of hyperbolic manifolds. For example, the fact that a QC map is differentiable a.e. is an important part of the proof of the Mostow Rigidity Theorem.