So this is my last quarter as an undergraduate. I feel that I am now completely ready to move on with my life and begin graduate school in the fall (at Stanford). Stanford has outstanding offers for two senior faculty positions in algebraic number theory for next year; I really hope that at least one of them is forthcoming, or else I may find myself looking for another thesis topic. They already have two analytic number theorists, so that would be a reasonable place to start; other possible areas are algebraic K-theory, ergodic theory, and algebraic geometry.

I expect this quarter to be much more manageable than the last in terms of courseload. I have only four course, but then I’m also teaching one. I think I should allow myself a lot of time for preparing lectures so that I don’t do (too many) really stupid things while speaking. So far preparation time hasn’t been too significant, but that’s because I spent a lot of time last quarter thinking about what I’d talk about at the beginning. I think my first two lectures went pretty well. I found myself having slight difficulties coming up with the best possible wordings for the rules for the games we will be concerning ourselves with (mostly Nim, Hackenbush, and Domineering). But the people taking the class at least pretend to enjoy it (and I hope that they aren’t just pretending!), so I imagine it’s going pretty well. We’ve more or less finished chapter one of Winning Ways, but I’m not exactly following the book, and I didn’t talk about some other (non-Hackenbush) games at all.

Now for the classes I’m not teaching… Quantum computing. I don’t know anything about quantum mechanics, so presumably I’ll pick something up along the way. So far not much has been new to me; we spent the last lecture discussing Turing machine computations, but I did that sort of stuff all last quarter, so it was just review. The next class is “Hilbert space formalism” and other stuff, so that will probably also be mostly review except the stuff on quantum information. But the lecture this coming Wednesday is on stuff I know nothing about, so that should be exciting.

Number theory and cryptography. All the number theory he has talked about so far is extremely basic stuff that I knew in high school. But some of the cryptographic stuff I hadn’t seen before. (What? Number theory has applications to the real world? How dare they!) So at least I’m getting something out of it.

Elliptic curves. This was going really well for me last quarter; I was understanding just about everything we did, but then a two-week break sort of messed up my memory. But I think I’m back on track now after a bit of review. We’re doing elliptic curves over local fields, which are fine, but I’m really excited about elliptic curves over global fields, which will be the next topic. It would be extremely interesting to see a proof of the Mordell-Weil Theorem, for instance.

Distributions, Fourier transforms, and Paley-Wiener theory. This class is tough. I’m a bit rusty on this sort of analysis to begin with, and Mihai’s lectures are notoriously speedy in general. Unfortunately, the textbook for the class (Lars Hörmander’s The Analysis of Linear Partial Differential Operators, I) is out of print, so we have to rely on photocopies, which have the annoying tendency of making me not want to read them. I must overcome this bad habit. So this class is going to be difficult if I really want to stay on top of things, which I think I do.

I ran into Ibarra (my professor from my computation and complexity course last quarter and the automata theory course the quarter before) in the hall of the compsci department last week. I think he was disappointed in my performance in his class last quarter. He said that my final was “good, but it wasn’t the top.” I told him I accepted Stanford’s offer, and that pleased him. I don’t think he thought it was even worthwhile to look at other places after Stanford accepted me, and given some of the people on the computer science faculty (and particularly theory people) at Stanford (for example, Knuth (emeritus) and Ullman), that might be reasonable, but of course I’m not in the computer science department.

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About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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4 Responses to

  1. Anonymous says:

    The Hörmander book
    Are you sure Hörmander is out of print? There was a reprint as late as 2003 so the book should be possible to find.

    • Simon says:

      Re: The Hörmander book
      Various places claim to be able to get it, but I’m not sure if I really believe them. Springer claims to ship it in 2-3 business days, so I tried ordering a copy from there, but this is the fourth, and I haven’t heard a word from them; furthermore, the professor said he asked them for it last quarter and still has yet to receive it (but he has a copy of the book in Russian, which is fine for him, but not so fine for the rest of us). Amazon says they can get it in 4-6 weeks, which is not so helpful for me, and anyway I’m not sure I believe them. Last time they told me that, they decided a month later that they were never going to be able to get it.

  2. Anonymous says:

    Hi:)
    Hi 🙂 I was also in Ibarra’s class last quater(grad level). Which one is you? Too bad I missed the chance to take your combinatorial game theory class 🙂 Hope we can be friends.
    Best wishes for you in Stanford 🙂
    ^Shhh^
    Email: newshhh_at_sina_dot_com

    • Simon says:

      Re: Hi:)
      I’m Simon. I don’t know if that helps to narrow it down at all, but I’m not quite sure how else to describe myself.

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