Fist day of 2010

This post has been migrated from my old blog, the math-physics learning seminar.

It’s the first (academic) day of 2010. I figured that the best use of this blog is as a log–that is, to log and plan my work for the semester/year/life. If you want to accomplish goals, the fist thing to do is to write them down! So here we go, crude outline for the next semester:

1. Work through Milnor’s Morse theory book, cover to cover. This should be easy since I’m taking a class in morse theory anyway.

2. Work through Kirwan’s thesis cover to cover. I’ve already been through quite a bit of it, and the only things that caused me any trouble last summer have since been cleared up.

3. Work though Gulliemin and Sternberg’s Equivariant cohomology book. Again, quite a bit of the material I already know, so this should be doable.

4. Finish working through HKLR. Really the only remaining part is supersymmetric nonlinear sigma models.

5. The details of the ADHM construction, once and for all. I should know this already.

6. Hilbert schemes of points on a surface. Really, the hyperkahler metric for the scheme of points on \(\mathbb{C}^2\). Again, I should know this already.

We’ll see how these go–this is probably ambitious, and many of these will get extended into the summer.