Last year I participated in the MaBloWriMo project of blogging every day for a month about a topic. I think I learned a bit of differential geometry as a result, and it was fun. But this semester, I have not really blogged very much. It’s partially been business and partially laziness. Given all the homework write-ups for my classes, the urge to blog is just subdued.
So my announcement that I am going to do MaBloWriMo again probably sounds rather silly. Nonetheless, I would like to give it a shot. I will probably not be able to post every day, but I’ll see if I can get at least fifteen posts up next month.
The plan is as follows. I will talk about commutative algebra, specifically the homological theory. Here are some of the topics I’d like to touch on:
- Basic properties of depth and the analogy to codimension
- The Auslander-Buchsbaum formula relating depth and projective dimension
- Cohen-Macaulay rings and their basic properties
- Properties of regular local rings (in particular, factoriality and the characterization in terms of finite global dimension)
- Koszul homology and cohomology, and the application to the quasi-coherent cohomology of an affine scheme (as in EGA III)
- How this all figures in Serre duality
That I think should be enough for several posts! Unlike last time, I will assume prior acquaintance with commutative algebra for these posts, in particular at the level of dimension theory. We’ll see how well I keep my promises.
Climbing Mount Bourbaki 
October 29, 2010 at 4:43 am
Apparently NaBloWriMo is actually October. Looks like we missed the boat last year.
October 29, 2010 at 10:44 pm
Sounds very interesting. Good luck!
October 31, 2010 at 11:55 pm
On the genre of academic blogging…
http://con.sagepub.com/content/15/4/470
Banal Bohemia: Blogging from the Ivory Tower Hot-Desk
Melissa Gregg
Abstract
While academic blogging has emerged as a distinct genre in the past few years (Walker, 2006), a notable gap exists between those who blog from secure positions within the profession and PhD and junior faculty bloggers whose employment status is more marginal. This article draws on subcultural theory to discuss the unique features of these two latter types and the functions they serve for their authors. The analysis demonstrates that blogs are important sites of support for those who aspire to and currently work in academia at the same time as they are a powerful indictment of the job conditions experienced therein. The article therefore concludes by suggesting that the positive aspects of collegiality and solace taking place online for a new generation of scholars risk remaining disconnected from an effective labour politics — one that could change the very nature of the grievances blogs appear so well designed to express.
November 1, 2010 at 8:45 am
Hmmm. I’ve seen blogs that do fit this criterion, but I’m pretty sure most *math* blogs that I know of: they tend to be about math rather than employment conditions or career issues (which I’m still refusing to start worrying about—there’ll be plenty of time for that in the future).
November 1, 2010 at 5:34 pm
That’s certainly a wise thing to do. The chances of getting a professorship at a good university is extremely slim for most people, probably not for you, but some people find it’s too scary that they may never get a job after getting a PhD in mathematics, worry about it, and ultimately do nothing. It’s best to just keep those things out of your mind … Anyway, competition is high these days when it comes to graduate school. I’m sure you’ve heard of Daniel Kane, who is a mathematics graduate student at Harvard; it certainly isn’t easy getting in to grad. school when they are people like him applying … In any case, if you just do a great PhD at a reasonably strong mathematics department, that’ll give you the best chances of getting a job. Anyway, as you said, don’t worry about it.
November 1, 2010 at 8:36 pm
Yeah. It’s certainly something I have thought about in the past — namely, that I’m currently investing a good chunk of my life (e.g. time spent on coursework, outside reading, or even this blog) pursuing a course of study where there is a reasonably high chance that I’ll end up out of work, in which case something like seven or eight years of my life will have been “wasted.” My take on the situation is to accept the daunting odds, but to treat mathematics as something intrinsically worth doing (i.e., not just for career perspectives). So that if academia doesn’t work out and I end up having to get a “real” job, I’ll at least have participated for a few years in an extremely fascinating area of human study. I like to think that I’d still consider the “wasted” eight years worthwhile.
November 1, 2010 at 10:31 pm
That’s definitely the right attitude going about things. However, while it might be hard to get professorship at Harvard, MIT etc. (and this often takes many years even for the people who have got to this stage), there’s no reason for you to stick to the US. There’re plenty of other great universities outside the US, who would rank prospective job applicants from the US highly. You *should* get in *somewhere* good for your PhD, but the sad reality is that top grad. school admissions is like a lottery draw simply because too many people apply, many of whom are strong candidates. But I can’t see you not being accepted by somewhere in the top 20 at the very least (hopefully, you should get in the top 10).
After grad. school, the odds get scarier. The problem is that they didn’t use to be this way a few decades ago. At that time, very few people actually pursued mathematics, and often the “rich” people used to get the benefits. I would put my money on it, that at least 50% of the people who’ve got PhD’s from strong schools a few decades ago, could well have not been accepted if they were to apply now with the same credentials.
But I have to say that you’re attitude is perfect. When people start becoming good, they start setting higher goals from themselves, and soon these goals start to become impractical. And by the time they realize this, they simply forget that they were doing mathematics because they loved the subject in the first place. This is just carbon monoxide in some sense; it kills people silently.
The good news is that mathematicians are in high demand everywhere. So having a PhD in mathematics, even if it can’t get you a professorship in mathematics, will certainly put you in good stead for the rest of your career.
November 1, 2010 at 11:35 pm
Thanks for the advice! It’s interesting that graduate schools are so much more competitive than they used to be (apparently this is true for undergraduate admissions, but I’m also very sure that getting into school X as a graduate student is orders of magnitude harder than an undergraduate). At any rate, there are other math-related jobs that I could imagine myself doing (e.g. programming, industry work, or secondary school teaching) where a PhD would probably help. And the years I spend doing that will be fun in any case, so I have no qualms about the present path.
I’ll definitely apply outside the U.S. as well — that’s a good idea.
November 1, 2010 at 5:35 pm
(Sorry, I gave an incorrect email by mistake, but I’m the same David who usually posts here despite the green tag …)