It's been a while.

Wow! I haven't written in quite a while, have I?


The picture above is a sign on NY Route 206 that I pass almost every time I travel between Saugerties and Ithaca. Triangle is a very small village. If you drive a little fast, you can hold your breath all the way through it. I took a picture of it for my friend James, who has passed it himself many times, and has remarked what a funny picture it would make.


I've been spending a very relaxing winter break in Saugerties. It's good to see my family, and to spend enough time at home so that it feels like home again. It's also been great to see all of the animals on the great Goldberg Farm. I've posted some wonderful pictures here. My little Sofi-cat has really enjoyed being in Saugerties too. She loves visiting her cousins, and she gets to sit on a screen porch and watch birds and squirrels. It's like camp. I always feel a little bad about bringing her back to my stuffy little apartment in Ithaca.


I've even been doing some math, too! Some of it has been my own research, but a lot of it has been some more general textbook reading. Early on, I read through most of Humphreys text on Lie algbras. I realized that part of each of my meetings with my advisor often ends up being him reminding me about some Lie algebra theory that I should remember. (Even when I do remember it, it's still worth having him explain it, because he is a very, very good lecturer.) I still won't remember all of it, but each time I relearn the stuff a little more of it sticks.


The book I've been spending most of my time reading is Sharpe's text on differential geometry. I've started reading some of it many times before, but tended to get bogged down in all the structure and terminology. This time, I started from the very beginning and read through every chapter, which has been A-MAZ-ING. I highly recommend it, and I highly recommend going through it start to finish, (or at least start to wherever-you-stop-reading). The development of the Lie group-Lie algebra theory by focusing on the Maurer-Cartan form is especially interesting. And I am now ALL ABOUT principal bundles. They are AWESOME. Bundles ROCK.


I've been doing other reading also. One of the things I've been reading is Neil Gaiman's blog. He's my favorite human being that I don't actually know. His work is awe-inspiring. He is an amazing storyteller. I first read his work in the Sandman comic book, and since then have read all of his novels and many of his short stories. Read his stuff.


I'm going to have to stop for now, because one of the things I've done during this break is experiment, not always on purpose, with my sleep schedule. For instance, just last night I went to sleep at 3:30 AM and woke up at 5:30 AM. I took a nap earlier this evening, but I don't think I'm going to be able to make it much longer. I'll write more later.