I went back to Sunnyvale for a few days, but I returned to Santa Barbara this morning. Thanksgiving always feels so short — there is so much with which to reacquaint myself, but I only have a few days to do so. Nonetheless, it was nice to get far away from Santa Barbara, and I returned much more relaxed as a result of having solved four of my five ring theory problems.

This week is going to be busy. In addition to four assignments, I have to give a talk to the functional analysis seminar on Wednesday, book a flight home (which is much harder than it sounds given that I need a seat for my cello), and be perfectly calm before sunrise on Saturday.

I also need to get UCSB to change the calendar for 2006-2007. I think I can do it, but I need to work very quickly if I want to have any chance at all.

Incidentally, the abc conjecture is amazing. The interesting thing is that its interesting consequences are all extremely easy, unlike those of the Riemann Hypothesis. It deserves more of my study when I finish with more pressing tasks.

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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.

Can’t you find someone who’s driving to the Bay Area? That’s what most people at UCSC do (in the other direction, of course).

Well, perhaps. I tried that for Thanksgiving, but the people I asked kept stalling, and a week before we had to get out of here I decided I had had enough and booked a flight. I doubt anything would be different this time around.

abc conjecture?

Define the radical of n to be the product of the distinct prime factors of n (so for example the radical of 108 is 6), and write rad(n). Then for any epsilon>0, there exists some K (depending on epsilon) so that if a+b=c and gcd(a,b)=1, then c<k*(rad(abc))^(1+epsilon).

So here’s an easy exercise (and it is actually easy). Prove that Fermat’s Last Theorem is true for sufficiently high exponents given the abc conjecture.