algebraic topology is off the chain!

Off the chain complex, that is! :p My TA sabbatical is this quarter, so I'm taking classes instead of teaching. And furthermore, since my income isn't tied to research, I decided I'm not going to feel guilty if I spend nearly all my time learning neat shit and don't get much research done. This could change if the theory professors do a good enough job at talking some sense into me, but my intention is to stand my ground as much as possible. Especially since I doubt I'll have time to learn this stuff once I'm a postdoc and paid full time to do research.

So this quarter I'm taking General Relativity, Algebraic Topology, and String Theory. I intend to do all of the homework for GR and String Theory, and at least a good bit of the Algebraic Toplogy work depending on how much I care about the proofs they give us (so far they look incredibly fun, but I'm thinking by the end it might get esoteric enough that it's not worth my time). I also went to the first Differential Geometry class on Wednesday, but it was fairly boring/simple stuff and it looks like it will be pretty much a repeat of the (rather advanced) undergrad Differential Geometry class I took at Georgia Tech--it's even out of the same book. Nevertheless, I'll probably go to some of those lectures toward the end of the quarter. Actually, maybe I will go to more of them--there were a bunch of things that went over my head when I took it as an undergrad, even though I somehow miraculously ended up with an A. I just hope the pace picks up soon.

By far, I am the most excited about Algebraic Toplogy. Yeah, I should be psyched about string theory because it's actual physics as opposed to just math (heh... no matter what Peter Woit tells you) but it looks like the way this course is being taught is going to be very useful and relevant to physics. And I just really like his style of teaching. And the topic is even cooler than I'd imagined. Not to mention, I get to use mighty words like p-skeleton, surgery, sheaf cohomology, cobordism, homotopy, category fibered in groupoids, etc. (and stop feeling dumb when math people talk over my head).

It looks like the layout of the class will be particularly relevant to physics, and the professor tends to be very good about explaining the meaning of things before he gives you the boring rigorous mathy definition for stuff. Not to mention, it's his area of specialty so he's very excited about it himself.

Course Description (from http://count.ucsc.edu/~tamanoi/math211.html):

In addition to basic materials of algebraic topology (category theory, homology groups, cohomology groups, Poincare duality for manifolds, and homotopy groups), in this quarter we plan to include materials on the following topics as long as time permits. My aim is to expose students to various powerful mathematical ideas and methods without much technicalities which non-topology students may not have a chance to get exposed to during their career.

(i) (co)homology of fibre bundles, Lie groups, loop spaces, and Hopf algebras,

(ii) various cohomology theories such as de Rham cohomology and sheaf cohomology, and the relations among them,

(iii) spectral sequence (Serre, Eilenberg-Moore, etc)

(iv) rational homolopy theory

Good mathematical ideas have universal nature, and they can be applied to other areas of mathematics, often with success.

Fiber bundles, lie groups, loop space, and Hopf algebras are all particularly important in physics, so it's great for me that he's going to spend time on them. Hopf Algebras are tied into non-commutative geometry and "quantum groups" (something I didn't even know about, way back when limbsoup asked me about them and I was like "uh, I have no idea"). And non-commutative geometry is very relevant to Matrix Theory, which I've been really wanting to get back to at some point. Oh, and the other really nice thing is we're using Allen Hatcher's book which is downloadable online for free (albeit 550 pages).

All in all, I think I'm going to have boatloads of fun this quarter. Also, I recently registered to attend the Singularity Summit at Stanford on May 13th, which is going to rock. Nick Bostrom, Douglas Hofstadter, Ray Kurzweil, Eric Drexler, Eliezer Yudkowski, Max More, and many more speakers (check Wikipedia for more info on any of these people)... pretty much all the people who've coined the most terms on my livejournal interests list! Best part is, it's completely free (last thing they had like this was around $150 to get in).

oh, and I almost forgot...

I mentioned this in a friends-only post, but yes... the post I made on April 1st was indeed an April fools joke. Hope you enjoyed it, because I did! I just uploaded a bunch of pictures that show my actual tattoo (not Kid Rock's tattoo--and yes, as amberphlame pointed out, I'm not cut anywhere near as well as Kid Rock himself). See pics below to see the original picture and how it was photoshopped (with Gimp).

Since I'm going to get the rest of it done tomorrow (the color added) I'll just post a link to the Gallery I uploaded them to for now for those who are interested in the halfway-done version:

real tattoo pics, plus original and doctored images--click a couple times for larger images

So in a couple days I should have the color version up.

My favorite reaction I got from the fake tattoo (which was pretty much what I was going for) was from my dear friend Mike:

"You had Barb and I for a few minutes, our mouths agape with disbelief. It
was an impressive photoshop job. Even once I realized what day it was, I
thought you had done some sort of wash-off temporary tattoo.

I've never really understood your thing with Kid Rock in the first place,
and it was almost believable (if horrific) that this had just gotten way out
of hand. Barb asked if you had given up physics for trucking."

Yes, I am a fan of Kid Rock, and yes I did go through a brief phase (circa 1999) where he was my favorite artist, and yes I've listened to his Devil Without a Cause album literally hundreds of times and have many of the lyrics memorized. But no... I certainly would never get a tattoo that says "American Badass" nor do I think that song is anything but recycled crap (the Metallica version was okay, but the Kid Rock version just plain sucks.) My username was kidrock on gehennom mostly because I was drunk at a party and when Jon Beckham suggested it (based on all the newsgroup sigs of mine where I used hilarious/witty lines from Kid Rock songs) as he was setting up my account, I was like "yes, of course! that's the best username ever!" Since then it's kind of grown into a running joke with me, culminating in this April Fools prank.