So I have seven lectures left in combinatorial game theory, and we’re probably 1.5-2 lectures away from being done with everything I want to cover in volume 1 (which is really pretty close to everything). I certainly hadn’t expected we’d move so quickly. Looking back at my proposed outline I made over winter break now just makes me laugh. I really underestimated…something. The students in the class? Myself? Some other factor? So I plan to spend a lecture on chess, and Dylan is going to give a lecture on go, but then there are still >=3 lectures left. So I’m thinking about talking about the material on infinite and loopy games from volume 2. (The other option would be to talk about misère games from papers by Aaron Siegel and Thane Plambeck, but it’s a bit more technical than I really want to get, especially for people who might not be particularly comfortable with group theory, much less the weird theory of commutative semigroups.)
So I think I can do the material on impartial loopy and infinite games without any trouble, but I’d like to get to the partizan games as well. And there isn’t much point in talking about those if students don’t understand ordinals. So I have to put together some material on ordinals. That’s fine with me, but I’m a bit lost for motivation. I looked through some “fun math” books I got when I was in high school/early college, and they all talk about cardinals, but none of them talk about ordinals. I tried writing up some notes on ordinals this morning, but they were clearly completely useless. Can anyone give me some inspiration for stuff to say about ordinals? Any books that treat them in a very elementary manner? Thanks!
I have all sorts of cool projects to do this quarter, but somehow they aren’t as inspirational to me as they ought to be. I gave a talk on homogeneous distributions in one of my classes a few weeks ago, and I’m supposed to give another talk on the Poisson summation formula and distributions and its number-theoretic applications soon (this is what happens when you’re a number theorist in a class of analysts…), but I don’t know how distributions come up in number theory, other than a paragraph on Herbrand distributions that I didn’t understand very well from Weil’s Basic Number Theory (which should never have been named that!).
Then I have a paper to write on quantum algorithms in algebraic number theory. I think this will be fun once I can get used to reading computer science papers. Reading computer science papers is a bit annoying because computer scientists are so concerned with efficiency. Of course, that’s most of the point of their subject, but it isn’t of mine, so it feels a bit weird.
And I was “accepted” (it feels funny to say I was accepted when I didn’t have to do anything to justify my competence, but they said they have plenty of room, so perhaps that’s why) to the algebra summer program. I’m excited about that!