I have neglected this journal for over two months, so it’s probably about time to post something. I have surprisingly little to say for myself; I managed to survive my first quarter of graduate school somehow. I wish I could say I did better than mere survival, but I feel that anything else would be a lie. I don’t foresee next quarter as being much better. Spring quarter, however, could potentially be quite pleasant. Too bad I’ll still be living in the same dreadful apartment then.

At least I managed to do some actual mathematics yesterday, or at least start doing some. Ravi asked me if it is possible to generalize Conway’s construction of nim fields (fields of order 2^2^n sitting inside \mathbb{N} with an unusual additive and multiplicative structure). I haven’t checked that everything works properly, but I think I have a construction for fields of order p^q^n (p must be prime of course, and I think q probably needs to be prime as well, although I’m not certain about that). There is a game described in Winning Ways 3 with the right sort of additive structure. The multiplicative structure is harder to understand in terms of games (although it does show up occasionally).

My general feeling is that this year is something of a setback in my mathematical career. As an undergraduate, I did what I wanted, took classes that I thought would be interesting and challenging, and got what I wanted out of them. This year, I take classes that someone else thinks I ought to take so that I end up knowing things that someone else thinks I should know. I understand that it’s important for graduate students to know these things, but it would be nice if there were a bit more flexibility in it. Perhaps they could allow us to take one class of our own choosing and spread the required classes over two years. We might lose some of the community that we have (since most of us are in all the same classes), but at least it would be less painful that way.

Fortunately, I’m taking a week off early next quarter to do arithmetic dynamics. I need to reread part of Silverman’s book so that I don’t demonstrate that I am a complete moron at the workshop.

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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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