So far this semester, I’ve had a bunch of exams (A’s on all of them), given two seminar talks (one “eh,” one worse than that), and I’ve made progress towards my advisor / candidacy situation. I still have more exams (blah), two more presentations (double blah), and some fellowship things to get done.
I’d like to say that in the midst of all this, I’ll stop by more, say more things, post more solutions, etc., but at the rate it’s going, I’ll likely not be back here until December something-er-other.
I hope this finds everyone well and that the holidays treat you and yours particularly special.
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 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!
So, I’ve officially survived the first week of my (second) second year as a Ph.D. student. It’s hard to imagine sometimes that I’ve been a grad student for over three years.
I’m such an old man.
It’s been even less easy than I’d anticipated, too, which is nicht spaß; sadly, too, this is the first week where teaching responsibilities are actually a thing (we get week 1 off from such things), so now it’s difficult and time-consuming. Jajajajaja.
Rather than making this entry all about Yours Truly, I figured I’d pit stop in and use some of my (*gasp*) unoccupied time write up a little spiel I saw for the first time in my Riemannian geometry class last week.
In topology, there’s an idea called invariance of dimension which can be stated in many different contexts, situations, etc. This can be modified in the case of manifolds with differential structures, and because the idea of the proof seemed a bit cool, I decided to throw it up here for you guys. Throughout, the notation denotes a manifold of dimension with an associated differential structure.
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!
"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