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
Observation I. Every article in this field is remarkably long.
I’ve currently got articles whose lengths are 60, 58, 50, 39, 59, 56, 58, 76, and 50 pages long in my “reading queue”. Of the others, there are none that are shorter than 25 pages with the exception of Gabai’s second article (18 pages, though sandwiched between a 60 page original and a 58 page triquel).
One would think that longer automatically implies “more detailed” (i.e., less terse, less difficult to read, etc.), but this isn’t necessarily the case; in particular, Gabai’s articles are ridiculously complex and brilliant and amazing, and even legitimate 3-manifold topologists specializing in foliation theory confess that it takes forever (literally not literally) to make it through even one of them.
My prediction is that when my son’s in college, the average math Ph.D. will take 10 years. Give or take.
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!
Welp, I haven’t been around these parts in a bit. That’s not to say I haven’t been working, though; I’ve just been working through things that don’t necessarily make good reading…
Okay, so maybe that’s not entirely true. I have, however, been spending a lot of time on just a couple projects for my advisors and so there hasn’t been an abundance of topics to post about here. I think I’m getting to a point, though, where I can start posting some things here and maybe use that to reconcile the fact that I can’t understand most things I read, etc. We’ll see.
So yea…the semester’s over. It turned out not to be a terrible one for me in the end despite being pretty terrible throughout. The upshot: I managed a 4.0 that semester and ended up with advisors. That’s a victory for sure.
I’ll do my best to come back around these parts in the next day or two and post something of substance. I’d like to try to do some sort of expositing on geometric topology things (foliations, laminations, universal circles) and maybe some Clifford things too; I’d also like to attempt to reconcile my previous goal of learning how to do things from Hatcher.
So, I’ve been doing a piss-poor job of keeping this part of the internet pruned and tended to, etc. I’ve decided to stop in and give this thing a good once-over with how the semester’s been going now that the semester is (finally) nearing its end.
My teaching assignment this semester was awful. I’ve been unimpressed mostly throughout.
I gave two seminar talks at FSU’s complex analysis seminar: Complex Structures on Manifolds and Constructing Complex Manifolds Using Lie Groups. The first went pretty okay; the second was very spur of moment and came when I was in the middle of battling the flu and was unsurprisingly less-good.
I’ve had two bouts of exams so far this semester and have managed to escape both with A averages.
I recently concluded the two mandatory class-related presentations I had for the semester: I talked about Frobenius’ Theorem on the integrability of -plane distributions for my Riemannian Geometry class, and about Hyperkähler manifolds for my class on Complex Manifolds. Like above, the first of these was pretty okay and the second was kinda “meh”.
I picked doctoral advisors.
That last point is one I’m particularly happy about.
As I tend to do, I managed to pick a path that’s not the standard among students (from what I can tell) in that I picked two advisors who work in two totally unrelated fields. Be that as it may, however, I’ll officially be under the tutelage of Drs. Sergio Fenley and Craig Nolder who – respectively – study geometric topology and hypercomplex analysis/geometry. For Dr. Fenley, I’m going to be studying various aspects of foliation theory; for Dr. Nolder, I think I’m going to be studying various aspects of lots of different things.
To say I’m excited would be an understatement.
Currently, then, I’m in the process of balancing end-of-semester duties and candidacy prep duties, which means I basically haul giant stacks of books around with me 24/7 and try to read any time my eyes/brain aren’t needed for something else. It’s exhausting and nerve-wracking and brain-intensive and amazing and surreal. I literally can’t express how excited I am.
When classes start back on Monday, there will be one week of non-finals classes followed by one week of finals; over the course of those two weeks, I’ll have lots of TAing to do and lots of exams to take. When those weeks are over, though, I’ll be enveloping myself in reading roughly 20 hours a day.
I think that’s about all I’ve got presently. I’ve been on the look-out for various fellowship/scholarship opportunities, as well as various summer programs and internships, etc. I’ll try to post progress on those fronts (and others, too) here as I remember. Between all that, I think it’s safe to say that my updating of Hatcher solutions is on the (very very far) back burner for a bit, but if I’m able, I plan to spend time going through, correcting the screw-ups that exist (believe me, there are many) and trying to get generally better-familiarized with the techniques necessary to master that material.
"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