I’ve made it to Los Altos: I’m going to be staying with my dad, but during the next couple weeks visiting Berkeley to go to a conference, and to meet up with my advisor.

I ended up talking Route 22 on VTA, and then walking a few miles to go here, in the dark, using GPS to guide me. I was amazed that this method worked!

I guess I should warn you that I am about to reveal plot details of Dan Brown’s books.

I read Digital Fortress by Dan Brown, which was an unfortunate use of time. That book, for starters, is isomorphic to the Da Vinci Code; they are both about a female cryptologist, who gets involved with a university professor, who is himself dragged into a global conspiracy. Humorously, at one point, they use a 5-letter password (which just happens to the female cryptologist’s name, just like in the Da Vinci Code). And like every Dan Brown book, this book also happens to begin with someone dying, who, as the holder of a secret, tries to reveal his secret before he dies.

The more unfortunate thing was the portrayal of mathematics and computer science in Digital Fortress. Terrifying, really.

I watched Neon Genesis Evangelion this summer again, and I’m watching El Hazard now. I am extremely tempted to purchase Mysterious Cities of Gold DVD’s—does anyone else remember how awesome that was?

My cat Tasha is beautiful, and I will miss her while I am in Berkeley.

I am extraordinarily excited by the possibility that Sufjan Stevens might, in his epic quest to author a musical tribute for all 50 states, choose Minnesota next. Perhaps I am swayed by the fact that I am listening to Sufjan Stevens’ The Avalanche, and realizing again that I rather love him.

And I spend quite a bit of time brushing my teeth everyday, but I rather rarely discuss toothbrushing technique, or, for instance, how I learned to brush my teeth.

My Forget Me Not plug-in for Safari was reviewed on MacWorld!

• MacWorld
• Apple Matters
• MacUser

It’s great to read the comments and find out what users wish were different: a lot of people don’t just want to Unclose Window but also Unclose Tab.

For me, I really would have liked to have Unclose Window be underneath the Edit menu, but because the undo hierarchy is linked to the window (i.e., when you switch windows, the possible things you can undo changes) it isn’t possible to undo the very destruction of the window itself.

The whole idea of “undoing” something is very amusing, especially the modern sense; the old sense of “undoing” something by destroying it is quite dissimilar from the idea of restoring to a previous state.

In August, two of my friends from college have died: Daniel Bartlett and Michelle Knapp. I’m not sure what else I can say; I remember them so clearly…

From Recent Advances in the Langlands Program, quoted in This Week’s Finds:

First of all, it should be remarked that according to the Tannakian phylosophy, one can reconstruct a group from the category of its finite-dimensional representations, equipped with the structure of the tensor product.

I suppose one should think of this as the categorification of Pontrjagin duality?

For a long while, I had wondered how this goes; this Introduction to Tannaka Duality and Quantum Groups will probably answer my questions.

Here is a question that I haven’t been able to find very much about:

What are the finite subgroups of the rotation groups ?

For examples, I can take a Coxeter group, and choose elements corresponding to rotations (e.g., the subgroup generated by products of generators), but that’s not going to produce very many examples.

I’ve been thinking for a while that I ought to start a research blog–something just to keep myself organized about the things I am thinking about, my thoughts on the papers I’ve read, my ideas, my questions. I figure I might as well make it public, though I seriously doubt anyone is going to read this.

Anyway, hence this blog. We’ll see how it works.

Here’s a very easy theorem.

Theorem. All closed orientable 3-manifolds are parallelizable. All closed orientable 3-manifolds are the boundary of a 4-manifold.

Proof. Let be an orientable -manifold. Recall that the Wu class is the unique cohomology class such that , and Wu’s theorem says that . The up-shot is that Stiefel-Whitney classes are homotopy invariants, even though they are defined using the tangent bundle.

Since is orientable, we have . Since , the Steenrod squares and kill everything, so and . By Wu’s theorem, , and . In other words, all the Stiefel-Whitney classes vanish.

Orientability matters; after all, being orientable is the same thing as vanishing. For example, is not parallelizable, since .