Saturday, July 6, 2013

Berkeley REU and Commutative Algebra

I haven't been able to post for about the last month, unfortunately, primarily because I'm at Berkeley for a geometry/topology/rep. theory REU. The weather's great here, but I mostly sit in a room and do math all day, so I don't get to appreciate it much. My project is primarily concerned with wonderful compactifications of homogeneous spaces via representation theory, which is pretty neat (if abstract), but quite a bit of hard work, seeing as I know nothing about representation theory or wonderful compactifications... we have a blog up here on which we will sporadically post math.

I have a wonderful (pun intended) roommate -- you can find his blog here -- and in our free time we pretty much just do more math. Speaking of more math, I recently bought Reid's book on Commutative Algebra, and am now trying to work through it. In addition, I've resolved to learn a non-zero amount of algebraic topology, probably out of Hatcher, so I can take Khovanov's course next semester. To this end, especially since I probably won't be posting anything of much substance here for the next month or so, I will try to post some of my notes on algebra/algebraic topology. By notes I mean mostly: a) proofs that I want to work through to understand better and b) exercises.

I'll end this post here -- my next post will likely be some notes on modules and exact sequences, stuff that I probably should have learned a long time ago.