Dissertation Haiku

March 10, 2011


Undercooked noodle:
Chance to land near Cantor set?
Log n over n.

This is not my thesis.

March 4, 2011


(It has Keyboard Cat.)

Thesis, 2nd complete draft.

Some more corrections here. I need to double-check a few more things, but hopefully I won’t have to change much more. Some frivolous pictures were added as well.

EDIT: I linked to this page somewhat widely, so I’ll just link all future updates here as I go along:

3rd complete draft.

4th complete draft.

Published version. Fixed a couple technical parts dealing with Poisson kernels, and also broke some college formatting requirements for stylistic reasons.

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.

I signed the letters and everything. Starting date, for now, is July 1.

Now for the thought of the day:

I’ve been thinking, lately, that the key to writing impenetrable pseudomathematical sentences may lie in adding some vocabulary from music threory:

Locally anisotropic modulations on augmented Mixolydian modules: a multifunctorial approach to cobordism invariants of C# algebras

Recently, a lot of interest has grown in the method of chromatic bifurcations in the study of coholomorphic functor algebras on Phrygian manifold functor spaces. In this paper, we study a discrete analog of the dualization of the classical problem, where a suitable analog of a globally half-diminished Tchaikovsky measure does not seem to be available; in particular, we prove that there are no non-trivial spaces of vector-valued Debussy measures that are invariant under third inversions. While this complicates the analysis, some partial analogs of the classical results are still available, albeit in a suspended Baroque space. The upshot of our multifunctorial approach is that converses are easy to come by, thus demonstrating – surprisingly – the transposition-invariance of time signatures, as conjectured by Wagner for dualized Phrygian spaces and disproved by Copland. Taken together with the II-V-I Lemma, this shows that the product of two coprime Mandelbrot polynomials does not have any perfect fourths as factors.

I think I’m on to something.

NSF grant

January 17, 2011

I just got the email that I won the NSF postdoctoral fellowship to work with Izabella Laba at UBC next academic year, where we’ll be working on Buffon’s needle, ergodic theory, differentiation theorems, and left wing politics, presumably. This should be good.