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.
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.
Today is the first day of the eighth week of the semester.
The middle of the semester was officially last Friday.
Some people may read that and deduce that it’s all downhill from here. Any time I hear that phrase to describe midterm, I’m always a bit blown away. Really, it makes me wonder: Is this what downhill feels like?
Apparently, I’m the speaker at Wednesday’s Complex Analysis seminar. Abstract and other info can be found here.
Our next topology exam is scheduled for next Friday. I’m also anticipating an exam in Galois theory around the same time.
I’m on a short deadline for picking a presentation topic for my Riemannian Geometry presentation.
So, I said all that to say: (a) I still exist. (b) Life is hectic. (c) I’m not sure when I’ll get around to posting more of Hatcher 2.1, but I’ll probably be moving on to Hatcher 2.2 here in about…30 seconds. Also, (d) I really need some down-time. And a haircut. And a drink.
For now, I’m going to come study some Riemannian Geometry: I have to (very soon) pick a topic for a presentation in that class, and so it’s getting more and more necessary that make sure I know what’s going on now. Maybe I’ll surprise myself and know a lot.
I’m about to have to get ready to meet some friends, but just FYI: I’ve added a couple new Hatcher solutions from section 2.1. I’ve got several more written down, but this surely isn’t a speedy venture. Just FYI.
I have another TAing duty starting up in about 20 minutes, but I decided to spend the rest of my time putting something here.
(I spent the time before this doing differential geometry computations on the blackboard)
Things are going. I made it through exam week(s) volume 1 without too much pain (other than the preparation therefor), and though I’m still waiting to hear back on how I performed on my homology exam, I think I managed to do pretty well overall. That’s a plus.
I also managed to finish the rough draft of my poster for FSU’s math fun day! That’s also a plus.
Now, I’ve begun looking to the (near) future. Indeed, I have some presentations coming up and I’m in the process of learning material and picking topics, etc. etc., to try not to put that stuff off until the last minute. Overall, I’m pretty excited: At the end of this semester, I’ll have grown quite a bit as a mathematician and will have done some of the “most meaningful work” of my career in the direction of being a professional mathematizer.
I like it.
I plan on spending some time this weekend putting Hatcher solutions up, as well as trying to finish catching up in do Carmo so I can be prepared for my Riemannian Geometry presentation.
Things right now are pretty not-terrible, though, despite my ceasing to exist here every now and again.
I hope to have some big things to roll out soon. Keep me honest, interwebz!
Edit: In all this talk about my career, I forgot the most exciting news to happen in recent weeks! On September 23rd, my son turned the big zero-one! Yep, that means my wife and I managed to raise an amazingly awesome bag of awesomeness for an entire year without killing or seriously maiming him! We’re both as excited as that last sentence seems to convey we would be!
This is a short little thing I’m throwing up here just to say a couple things:
It’s been busy around this place.
It’s been busy around my life.
I owe you guys some stuff.
Re: The Last Item: I’ve got some moderating to do here. I’ve gotten a few comments on my Hatcher solutions pointing out that I’m really embarrassingly bad at topology. Rest assured: I’ve received your comments, I know how terrible I am, and I’ll be working to rectify the situation as soon as time permits.
Maybe I’ll have a follow-up to this later this evening.
"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