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The Outer Automorphism of S_6
I wanted to follow up on a brief comment Scott made in his last post about the outer automorphism of . An outer automorphism is (non-canonically) the same as finding two inequivalent actions of on...
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SF&PA: How complicated are groups?
One more warmup post before I get to actual Subfactors. If you were asked to rank finite groups in order of how complicated they were, what measurement would you use? There are three candidates that...
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SF&PA: An example
Alright, let’s try to build a bi-oidal category with a good theory of duals. The dumbest possible way to do this is to start with a good monoidal category and put in meaningless labels by hand to make...
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Two fun problems
One of the points of this blog is for us to share the little problems we’d be discussing at tea if we were all still in Berkeley. Here are two that came up in the last couple weeks. As we all know,...
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Generalized moonshine I: Genus zero functions
This is a plug for my first arXiv preprint, 0812.3440. It didn’t really exist as an independent entity until about a month ago, when I got a little frustrated writing a larger paper and decided to...
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Spanning polynomials with powers
So, here a cute little algebraic question that I came across thinking about a finite groups question Noah asked me (he or I might blog about that later): Choose your favorite set of m linear...
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Farey fractions, Ford circles, and SL_2.
The topic of this post came up during a conversation with some physicists about the fractional quantum Hall effect (which is quite fascinating, but I don’t feel particularly qualified to discuss). I...
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What makes the Monster Lie Algebra special?
This is a post I’d been meaning to write for several years, but I was finally prompted to action after talking to some confused physicists. The Monster Lie Algebra, as a Lie algebra, has very little...
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