The last time I posted something meaningful here (not counting the 2014 year-in-review and the most recent claim of attempting necromancy), it was June 2014 and I was about to embark on a summer of traveling. Around that same time, my son was 21 months old, I was working part-time at Wolfram, and I was a pre-doctoral candidate whose academic situation had gone (apparently without being blogged about) from two doctoral advisors with two separate projects to a single advisor plus a second non-advisor faculty colleague.
Typing that out makes me realize how much has changed.
For those of you keeping score, it’s now August 2015, and 13 months after the last update, lots and lots of things have changed. For example, my son is now one month away from being three years old. There’s also a lot of professional stuff, too. Let’s go somewhat chronologically.
I passed my advanced topics exam (ATE) and became a doctoral candidate. My work was on Gabai’s colossal (first) work on Reebless foliations in 3-manifolds, and while I definitely learned more significant math than I’ve ever learned, I feel like there’s so much in that paper than I’m years away from understanding.
I flew up to Baltimore to interview for an NSA gig. I didn’t get chosen.
I went to the 40th annual spring lecture series at the University of Arkansas and had a complete blast. I ended up slipping on ice, busting my ankle up pretty badly, and having some travel woes near the end but when all was said and done, I met some cool people (Benson Farb, Allen Hatcher) and saw some really great talks. Oh, and great coffee!
I went to Rhode Island College and gave an invited lecture on limit sets and computer visualization. It was an honor and I couldn’t have hoped for a better first invited lecture experience.
I finished a pretty uneventful spring semester at FSU. Lots of work. Lots and lots of work.
Once summer (2015) rolled around, I got accepted to some pretty great things:
I was fortunate enough to be awarded a pair of scholarships from the FSU math department.
And now, here we are! It’s officially September 1 (1:07am now): That means Fall semester has started at FSU (which means I’m now a fourth year doctoral student; eek) and things are back in full swing. It never gets familiar, really, no matter how many times it happens. C’est la vie, I guess.
I’ve got a bunch of stuff going on, professionally:
I’m still trying to make progress on my dissertation research (3-manifolds and, eventually, foliations).
I’m studying Dirac operators / spin manifolds / hypercomplex structures / supermanifolds / miscellaneous things that seem to get more and more into the realm of theoretical physics as we progress. This is with my non-advisor faculty colleague.
I’m trying to get a small research project going with an undergraduate at FSU on topological quantum computing (maybe Microsoft will take interest?).
Non-professionally, things have also happened. I got pretty serious into working out for a bit; later, I lost track due to travels, though I’ve since made some pretty considerable body transformations due to a healthier diet. I’ve also tuned back my Wolfram hours to give me more time to do student things; I’ve upgraded my workstations (desktop and mobile); I’ve made the switch from Windows to Linux (full-time rather than as a hobby)…
…that may actually be about it!
So there! Now we’re caught up! That means that I can pick up next time with an actual update / piece of newness / whatever. And who knows – maybe there will even be some math thrown in here! gasp
So, to summarize the direction of my most recent mathematical endeavors: I woke up and decided that part of my aspiration was to become a geometric topologist, and I did that despite the fact that topology is (far and away) my worst subject.
That sounds precisely as terrible as it probably is.
Spending a lot of time on the precalc class I’m teaching this semester, too.
A routine is finally starting to shape up, which means things are getting back to normal; I’m hoping blogging becomes a part of that again. Hoping.
Right now, I’m learning about surface automorphisms in hyperbolic space and working on collecting a library of data about the current status of classifications of manifolds with hypercomplex structures. I’m downloading articles constantly, reading seemingly nonstop, and always feeling behind.
I couldn’t be happier.
Here’s hoping that the new year is being as kind to all you folks!
I just wanted to drop in and update here. I haven’t been posting much in the last day or two, but not because I haven’t been workin’ it!
Here’s what’s been going on.
Wednesday, I stayed home and had a Clifford Analysis day. I read a solid three or four pages of my professor’s paper before calling it a day.
Because I felt like I hadn’t done enough on the Clifford front, I went to my office Thursday armed with new writing supplies and spent a solid few hours verifying the claims made in the aforementioned three or four pages I’d read. That was a good feeling.
Friday was (differential) geometry day, and I started the day working some “trivial” problems from Spivak’s little book. In the middle of the day, I had a phone interview with Pearson for a potential part-time job; that interview went well and I’m moving on to the second stage of the employment process. I spent some more time in Spivak’s little book before spending the remainder of my evening working problems from Volume One of Spivak’s magnum opus. Those problems are also “elementary” but they’re a bit harder. The challenge was good.
Today is supposed to be algebra day. Because we only recently were in a position to remedy some previously-existing financial woes, however, we spent most of the day split between running errands and spending time out and about with our son. I did take both Eisenbud/Harris and Perrin with me, along with my trusted G2 and Composition Book; very little progress was made, however.
I’m actually about to dip out for the evening here in a few minutes, but depending on how much energy I have tonight, I might buckle in and try to figure out some of this sheaf theory stuff. If I had a fourth Algebraic Geometry Observation published, it would be that transferring between theory and problems which apply said theory is very VERY difficult.
So it’s now creeping into the third (full) week of June. School got out for me during the first (full) week of May. Regardless of how woeful you may consider your abilities in mathematics, I’m sure you can deduce something very clear from these facts:
Summer is about half over.
Generally, that fact in and of itself wouldn’t be too terrible. I mean, big deal: Half the summer’s over, and I’ve been working throughout. How big of a failure can that really be?
In this case, it’s actually a pretty big one.
Despite my having read pretty much nonstop since summer began, I haven’t really made it very far into anything substantial. Compounded onto that is the fact that I’ve had to abandon a handful of reading projects after making what appeared to be pretty not-terrible progress into them because of various hindrances (usually, a lack of requisite background knowledge).
It’s been a pretty frustrating, pretty not successful summer, objectively.
Also, by and large, yesterday was a day consisting entirely of (differential) geometry / topology, so it’s really no surprise that – again – my dreams were all math related and tied to that general realm of theory. More precisely, I spent my entire sleep cycle pondering the Poincaré Conjecture (can we call it the Perelman Theorem yet?) and Ricci Flows. That’s certainly a night well spent.
Unsurprisingly, my day today will be largely similar. I downloaded a bunch of resources concerning the aforementioned topics (Poincaré-Perelman and Ricci Flows), as well as some (more) texts on Riemanninan Geometry (which I started perusing yesterday). Also in the works: A colleague of mine (who I’ll call DW2) and I have decided to work through Atiyah and MacDonald’s Introduction to Commutative Algebra, and I’m pretty sure if I don’t spend a significantly-larger amount of time on my professor’s Clifford paper, I’m going to have zero things about which to ever talk with him…
…then there’s the algebraic geometry stuff I’m working on in Eisenbud and Harris / Dummit and Foote, and the material from the seven or so other books I’m reading through concurrently right now….
Every day I’m huss-uh-lin’….
I have some things I want to write here later – expository things and what not – but for now, it’s just this check-in. Auf Wiedersehen!
As I type this, it’s 2:45am on a Wednesday. I haven’t been around these parts since Sunday night (actually, 3:30am Monday morning), so one would think I’d have accumulated a ginormous list of professional doings to post proudly about here.
I decided to spend as much time as possible today studying after a few days of being nonchalant with it. I went to bed early-ish last night, woke up early-ish this morning, and hit the books with very few breaks in between.
As it turns out, this recipe gave me ample opportunity to learn new things. Who woulda thunk?
I started with my professor’s paper on -conformal Cliffordian mappings. I made it through a couple more pages of that guy, verifying theorems and assertions as I went along. Then, right as I was on the precipice of real math, I realized how mentally taxing my morning had been and shifted direction a bit.
My new direction: Dummit and Foote. I started section 15.2 on Radicals and Affine Varieties. About 2/3 of the way through that section, I realized I really really need to learn some stuff about Gröbner Bases, so I decided to forego that and keep the ball rolling. I spent a few minutes flipping through Osborne’s book on Homological Algebra and upon realizing I’m far too underwhelming to tackle that guy, I shifted focus again to Kobayashi and Nomizu.
Of course, K&N has kind of worn out its welcome around here, and upon reading a page or two, I decided to break out a different Differential Stuff book instead. My target? Warner’s book Foundations of Differentiable Manifolds and Lie Groups. This book is a nice amalgam of Geometry and Topology, as evidenced by its somewhat nonstandard definition of tangent vectors. Maybe I’ll share some of that later.
Finally, I decided to shift my focus back towards Algebraic Geometry, whereby I broke out Eisenbud and Harris’s book The Geometry of Schemes and tried to stay afloat. Much to my own surprise, I was able to make it through fifteen-or-so pages without floundering completely and/or ripping all my hair out, so I’m hoping that maybe the information I’ve picked up in other places has done me some good. We’ll see for sure moving on.
Overall, I think I cranked out about 45-50 pages of reading today – and all (well, most) on material that’s completely new. It ain’t a Fields Medal, but it ain’t a flop either.
I woke up 16 hours ago and spent almost every minute of the day juggling algebra stuff: I spent a bunch of time alternating between -modules and the algebraic geometry preliminaries I needed to understand that. Then, around 6:30pm, my brain sort of…went to sleep.
I took a break for dinner and decided I couldn’t just waste my time before bed, so I decided to spend some time solving some of Dr. Hatcher’s problems. I posted a couple new solutions here and here.
Now, it’s almost 1am. Unsurprisingly, I feel like I’ve gotten a second wind, so maybe I’ll try to do some more reading, or some more sorting through professors’ research, or some more algebraic topology problems, or some more….
"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos