I just flew into Vancouver…

February 23, 2011

…and boy, is my brain tired.

The first complete draft of my thesis is available now. You can thank my laptop battery for holding out the whole time, going through Houston and everything. Hopefully the last two chapters look a bit facelifted. A couple references are missing, but whatever. I’m hungry.


What it takes

February 17, 2011


Thesis – third partial draft.

The organization has changed a little; the gasket upper bound and the general upper bound now have separate chapters, 4 and 5. I did edits on 4 already, but I’ve hardly touched 5 beyond just pasting it in; however, I included chapter 5 as is so the references to theorems will appear the way they should.

The last chapter contains the deepest problems and harshest technical difficulties, but it can probably still be made clearer in places. Now is probably the time for that…

Here’s theĀ  thesis including chapter 3. I’ve started working on chapter 4, but it’s very long and I’m not ready to show it to anyone yet.

Chapter 3 probably isn’t the most friendly or necessary segment, overall. It can probably be skipped unless you’re especially interested in that particular problem or know of some application. It is a weak general result that was found way back when Alexander Volberg and I were trying to figure out the best form we could find of what later became the main theorem of Chapter 2. It’s unlikely that Chapter 3 would have been written had we had those insights sooner. Chapter 3 can be pushed farther probably, but it’s gotten to the point where connections to other problems would have to be necessary first before I’d go back to working on that problem.

So my thesis is coming along. I hope it gets easier, but at the moment, it’s slow going.

Here’s the first partial draft for you to peruse.

Chapter 1 is brand new, but it’s entirely expository. All of my published research so far is about the same problem, so I went ahead and unified the notation and spent a great deal of time laying out background. Chapter 1 of my thesis is the most thorough and expository paper I have written so far about the broad strokes and main ideas of my research. Mathematicians (pretty much anyone who knows Holder’s inequality, say) wanting to know what’s going on with my research in medium-broad strokes without slogging through an actual research paper will hopefully find this part to be a light read.

Chapters 2-4 will be in ascending order of difficulty. Chapter 2 is a bit long, but it’s mostly due to choices in favor of more exposition. I might slowly wean the reader off of this as I go along. Chapter 3 will repeat 2 to a large extent, and chapter 4 will have so much technical bulk to it that I’ll have to choose points of exposition sparingly.

Please let me know if anything looks wrong or badly formatted. As far as formatting goes, there are some TeX tricks I haven’t looked up yet but need to to fix some things, so if you see anything that needs to be made prettier, assume that I don’t know the code.