I am happily in graduate school at UC Berkeley, studying quantum field theory. My quals are in less than a week, so I am reading and reviewing. This term I discovered that my favorite way to study is to write copious amounts. If you like to read, I invite you to check out the following:
- Lie Groups and Lie Algebras (pdf). These are edited lecture notes from a one-semester class last fall. They should be fairly complete and accurate, but please let me know about any errors: typos are easy to fix, and mathematical errors should be corrected for morality sake.
- Poisson Lie linear algebra in the graphical language (pdf). This article outlines all the definitions from the theory of Lie bialgebras, but does it using only Penrose's ``birdtrack'' notation, championed by among others Cvitanovic.
- Some notes on Quantum Groups (pdf). These are not particularly edited, and are rather ideosyncratic, and include the graphical language article as a chapter.
I hope to say a few words here about some of this material. In particular, I'm thinking of writing about the following: the Weyl character formula; symplectic leaves of Poisson manifolds; what is quantization. Whether I actually write such entries is still up in the air, of course. Currently, I primarily post content directly to my website, but that doesn't have an RSS feature. If there are still people who watch this space, leave a comment, and I'll get into the habit of writing a blog entry any time I post something new to my website.
