I seem to have broken my MaBloWriMo streak. I hope you’ll believe me when I say it was impossible for me to get a post up yesterday. Unfortunately, the rest of this week looks just as hairy (for completely different reasons), so I’m going to have to take a break. Here’s where we’re headed once I have time again:
I’m going to skip a lot of background at some point and just introduce several equivalent definitions of the Schur functions. My hope is that stating some of the important results of the theory, even without proof, will be enough to get other people interested in symmetric function theory. I also get a lot of material to go back to and flesh out in subsequent posts, since I haven’t gone through most of the proofs of the basic results very thoroughly.
After that, I want to meander slowly through parts of basic algebraic number theory and algebraic geometry. My goal here is to thoroughly understand the classical analogy between rings of integers in number fields and nonsingular affine algebraic curves. Since several bloggers have covered much of this material in some form already, I’ll try to link to other posts I’m aware of, but I’ll have to repeat some things because I want to motivate every definition I need.
Since I don’t have anything else to say at the moment, let’s make this post an open thread and we’ll see if the Scott Aaronson style of blogging works for me. General comments, questions, suggestions, requests, etc. welcome!