I was a bit envious at first that Conway was giving a talk at Berkeley yesterday, but we had a famous mathematician giving a talk here as well: Sir Michael Atiyah. He was talking about quaternions and what happens when you try to do analysis with them. At first he was going slowly enough that I could understand what he said, but my knowledge became insufficient when he started getting into subtleties of sheaf cohomology. (I deserve to be punished for not knowing enough about sheaf cohomology given that we spent some time on the subject in complex analysis last year.) But Atiyah managed to convince me somehow that I almost understood what was going on until I really started to think about it more. So even though I didn’t really understand it, I really enjoyed the talk.
I really don’t know what to take next quarter. I talked to my advisor yesterday, and he told me that I should get some of my requirements out of the way because a few years ago a student saved them for the end, and when he gave a good answer to a question on an exam or paper or something, the grader thought he had cheated(!) because he wasn’t used to people giving good answers, and the student had his graduation delayed as a result. So maybe I’ll do that. I have to decide between continuing differential geometry and continuing probability theory next quarter since they conflict. Probability theory is certainly a lot easier, but that isn’t a good reason to continue one over the other.
The problems for the noncommutative rings class are very hard this time. It took me all morning and afternoon on Sunday to solve a single problem, but since then things have gone a little better.
And here’s a problem that I don’t know how to solve. Find a group that is isomorphic to a direct product of three copies of itself but not of two. I can’t imagine it should be that hard though.