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.
Fortunately, my topology advisor Dr. Fenley is amazing in lots of ways, not the least of which is patience; he’s helpfully answered even the most idiotic of questions, he’s dealt with me floundering amidst an ocean of reading, and he’s even stepped in to help me delegate things in a way that’s more conducive to success.
All things considered, I can’t really complain.
Currently, I have a reading list of things to read on my this is urgent to the future of your topology studies list encompassing things like basic 3-manifold theory (Hempel, e.g.) and hyperbolic geometry (Casson and Bleiler, say), and more advanced notions like -covered foliations (Fenley’s work, or Calegari’s) and other monumental works (Gabai, and Gabai, and Gabai…). There’s a lot of ground to make up, which seems even more daunting because it’s happening at the same time I’m trying to dredge through things that are far beyond my level of understanding.
Math are hard.
My other work is still shaping up and so my reading there currently encompasses tons of ideas, not the least of which are hypercomplex geometry, Clifford analysis, Yang-Mills theory, gauge theory, etc. Apparently, there’s a lot of variation in the direction we may end up going, and there are lots and lots of things to learn about the directions before we decide. On this front, I’m equally happy with the advisement I’m receiving; this particular advisor is well-known for his approachability and his good-natured demeanor, and I’m finding that he’s almost as excited to learn about new things as I am. That’s always fun.
When I’m not reading (and feeling behind in said reading), I’m usually teaching (precalculus) or preparing to teach. Occasionally, I also go to class/seminar, and on a rare occasion, I manage to see my wife (to whom I’ve now been married for eight years! Happy anniversary, Bee!) and son (who’s 16.5 months old currently and who will probably be going off to college soon).
Anyone who says that grad school doesn’t impose on one’s ability to juggle responsibilities is probably lying. Just FYI.
I’m hoping to spend some time this summer jet setting around the U.S. </exaggeration>, going to conferences and the like. I’ve spent a good bit of time this week putting faculty members in uncomfortable positions, asking for recommendations and being a general nuisance along those lines, hoping to procure funding from anyone who wants to share. From what I can tell, though, this summer has some serious rockstar events in the field of Mathematics. I’m beyond excited, though the odds at these things coming together may not be especially high.
My goal for this space in the coming weeks is to start coming here, typing up things I’m reading (for my sake more than anyone’s) and hoping to get experts in these fields to comment and participate. As such, the odds at Hatcher solutions materializing is slim, and the odds at me progressing in differential geometry purely for its sake is even slimmer.
Everything has a direction now.