So I’ve made it through the first two weeks of classes at Stanford. I find most them to be a lot less carefully worked out than the classes at Santa Barbara. In particular, we rarely bother to define terms or state the theorems we’re going to need in the algebra class. That’s fine for me since I already know this material, as do most (all?) of the other graduate students. But it’s probably more difficult for undergraduates who haven’t taken these courses before.

Actually all the first-year courses are boring since I took all these classes already. It seems they might be less mandatory than I previously suspected, so I’m thinking about not taking algebraic topology next quarter since there is a really interesting class on class field theory and central simple algebras at the same time, which will surely be of more use to a number theorist than a bunch of topology I already mostly know. There is also a course on ergodic theory and combinatorics next quarter, and I don’t think I can ignore it.

Algebraic geometry is much more interesting, even though I have already seen the stuff we’ve done so far (categories and sheaves) before. It was really helpful to do a lot of problems about categories/diagram chasing, and I think it will be similarly helpful to solve problems about sheaves. I’m also going to be doing a reading class on arithmetic geometry (probably using either Lorenzini or Hindry and Silverman).

Then there’s the local Langlands seminar. Brian Conrad (who is coming to Stanford next year and will probably be my advisor) is running a seminar at Michigan, and he is having us run a parallel seminar here, presumably so that he can continue where he left off when he gets here. So far we’ve just talked about some background on local fields and Galois representations and stated the local Langlands correspondence for GL_2 in terms that we have yet to define.

I’m also a course assistant for a basic calculus class. My first few office hours were very quiet, but today there was a veritable mob! I wonder if I can figure out a way not to have to repeat telling different people how to do the same problems. It seems like a difficult problem since some people come at the beginning of my office hours, and then others come at the end with the same questions. Anyway, I think they understand what I tell them. If not, they pretend they do. But maybe I said that about combinatorial game theory too (and indeed, some of them definitely did understand what I said; some didn’t).

Also, I was accepted to an AIM workshop on the uniform boundedness conjecture in arithmetic dynamics, so it would be helpful to review/learn some key results in arithmetic dynamics before January. I assume that this one will be more comprehensible than the one on the Tate conjecture (the statement of which I still do not understand), but I will still presumably be the least advanced participant in the workshop, so I should make an effort not to embarrass myself.

Listening to operas in English is extremely fun, especially given these childish and silly translations. Stanford’s Naxos subscription very kindly provides us with a good selection of operas in English translation. I must not let this prevent me from getting work done.

Assuming that collaboration is encouraged in your class and it won’t cause overcrowding, encourage people to hang around and work on the problems during office hours, and then when people have the same questions, recommend them to people who you have already helped / are working on the same question? (This is, I believe, the way it works for calculus at Harvard, although there multiple sections of the same class hold office hours together).

I am quite possibly applying to Stanford and even more possibly want to do algebraic number theory, so I’ll be interested to hear how things are going there… (how mandatory are these first-year classes supposed to be?)

(and Naxos subscriptions are nice ğŸ™‚

That’s a good idea. I’ll see if I can make it work this afternoon (if lots of people show up).

You’re supposed to take the first-year classes unless you know the material well enough to pass the qualifying exams. But if you don’t, you can still choose not to take it (although that may be a bit risky, especially since they are changing the qualifying exam to be more closely aligned to the course material, starting this Spring). If you can pass the qualifying exams on entrance, then you definitely don’t have to take the first-year courses in algebra and real analysis. You can also convince people that you don’t need to take the other sequence (generally complex analysis, algebraic and differential topology, maybe a bit of differential geometry) if you are really familiar with that material.

I might be able to provide more useful information about Stanford and possibly even algebraic number theory at Stanford once I’ve been here a bit longer.

i’ve decided i might become a geometrist! (geometricist?)

Geometer.