Singer’s talk on index theory on Friday was quite interesting, but I was really tired and almost fell asleep in the beginning. After that I worked on Haar measure for half an hour or so and then headed off to Hillel. My grandparents came down for the weekend and arrived at Hillel shortly after 6. For the first time this quarter (I think), I stayed for dinner. Dinner at Hillel is very chaotic, and it’s also a very social event, which doesn’t make shy people such as myself particularly comfortable.
On Saturday, I went to Ryavec’s office at around 8:30 to get a photocopy of a section of a book that deals with Haar measure. I didn’t find those pages especially useful though since the proof is different from the one I am presenting. At around 9:15, I went over to Hillel again since I told my grandparents that I would be there before 9:45. I arrived at 9:32 and was surprised to see that many people were already there. There was apparently a pre-service thing starting at 9:30 (I would presume) that I didn’t know about, but I went anyway. The rest of the weekend was filled with events that will probably be dull to read about. (I just realized that some events are much more interesting than they sound in writing.) Hence I’ll move on to something that may interest my audience. It also might not. I’ll just have to guess.
This morning, I wrote up one of the things that had been annoying me about Haar measure (i.e. I don’t understand it properly). I hope that I got it right. There are two more of those left. I should get them done today so that I can get my homework for Wednesday done at a reasonable hour tomorrow. Differential geometry is getting more interesting finally. We were talking about spherical geometry today. He asked about the analogies between a line in a plane and a great circle on a sphere, so I said that if we discount parallel lines (or add a point at infinity at which all parallel lines meet), then any two lines meet a point, and any two great circles meet at a pair of antipodal points, etc. He made it clear that that wasn’t the answer he wanted, so I tried again and said that a line splits the plane into two regions. He didn’t like that either. He wanted us to say that they are both the shortest distance between two points. That was too obvious.
We finished doing sum of five squares in HLCM. Apparently cubes are really hard, and there are still many unsolved questions such as the minimum number needed to get an asymptotic formula.