Today my dad, Abbe, and a character new to you readers called David, and I are going to a Civil War reenactment later today in Groton to celebrate the town’s three-hundred fiftieth anniversary. I’m not entirely sure just what the Civil War has to do with the year 1655 — shouldn’t we be killing King Philip or something? Then again, I suppose there’d be one of those political demonstrations, and nothing kills a town celebration faster. — but I’m pretty excited. Bring on the fife and drum corps!
It is only fitting that I introduce David properly before I get much further. [Those who are especially anxious can jump down to the bottle where I discuss math.] David comes to us from Russia via Maryland. His father and mine used to work together a number of years ago. David and I first spoke on the phone when he was sixteen, which must’ve made me about thirteen. He wanted to be a video game programmer. So he went to school to learn computer science. He moved up here, and my dad helped him with his programming assignments from time to time. For a little while, David even lived with us, during school holidays and that sort of thing. I can’t remember the last time I spoke with him. But I do remember it consisted of a very perfunctory “No, I’m not graduating this year. I’ll be done in the fall…Yes, still math…Probaby go to grad school, not sure. You?” But before grad school, I need to get my thesis done. And I’m no closer than I was two weeks ago. This is a problem, considering my encroaching Thursday presentation. I told Aaron I’d talk vaguely about “spinor structures and Lorentz manifolds.” There is a theorem of Geroch that says a spinor structure exists on any Lorentz manifold. This seems like it might be appropriate. I say it seems because it’s not really. The original proof relies on some pretty strong topological machinery. Even to define a spinor structure takes us into the world of principal bundles. And the other kids in the tutorial are freshmen and sophomores. There is a more, er, elementary proof that is heavily steeped in Clifford algebra. So the elementarity of it is really a matter of opinion.
I do have to write an appendix on principal bundles, so I could conceivably do that instead and mention spinors at the end. Write now I’m rewriting Lecture 2 since that horrible hour of bundles I subjected Amit to. Something good might come of this, I believe. Right now the next three lectures in my head go something like this:
Lecture 2 Spinors without the Bundles
Lecture 3 Bundles without the Spinors
Lecture 4 Putting It Together: Spinor Structures
As soon as I write these things [hopefully today], I’ll post them and send out an email. Let me know if you want to be added. I love adding people.
[A new draft of Lecture 2 is up. But it’s woefully incomplete.]