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18.979: Moduli Spaces
The Fall 2008 graduate geometry seminar is being taught by Prof. Mrowka. This Wiki is maintained by Ben.
References
The main references so far have been
- The Yang-Mills Equations on Riemann Surfaces (Atiyah, Bott),
- Instantons and Four-Manifolds (Freed, Uhlenbeck).
The Plan
Each student registered for a grade is to type up lecture notes for two or so lectures, and also correct mistakes, and ask/answer questions on this Wiki.
Lectures
If anyone is willing to donate their handwritten notes (on loose sheets of paper), I'd be happy to scan them in as a supplement my sloppy notes.
To stake a claim to a lecture, simply write up a draft of that lecture. (All changes will be attributed to your Wiki account.) No permission is required, but the more advanced students should leave the earlier/simpler lectures for the less advanced students.
| Wiki | Status | Scans | Description |
|---|---|---|---|
| 09-03 Notes | Unclaimed | Ben | Overview of moduli spaces |
| 09-08 Notes | Unclaimed | Ben | Sobolev spaces and gauge theoretic analysis |
| 09-10 Notes | Unclaimed | Ben | $\mathcal{A}/\mathcal{G}$ is a metric space, local structure of a quotient |
| 09-15 Notes | Unclaimed | Ben | Stabilizers and holonomy, outline of slice theorem |
| 09-17 Notes | Unclaimed | Ben | Proof of slice theorem, except injectivity |
| 09-24 Notes | Unclaimed | Ben | Injectivity, and remarks on the Yang-Mills equation |
| 09-29 Notes | Alex | Ben | Classifying space for $\mathcal{G}$ |
| 10-01 Notes | Andy | Ben | $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ |
| 10-06 Notes | Steven | Ben | $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ over $\Sigma$ |
| 10-08 Notes | Unclaimed | Ben | Stabilizers and the rank 2 case |
| 10-15 Notes | Draft | Details on $N(2,1)$ | |
| 10-20 Notes | Alex | Calculation of the Morse index of YMF | |
| 10-22 Notes | Unclaimed | ||
| 10-27 Notes | Unclaimed | ||
| 10-29 Notes | Unclaimed | ||
| 11-03 Notes | Unclaimed | ||
| 11-05 Notes | Unclaimed | ||
| 11-12 Notes | Unclaimed | ||
| 11-17 Notes | Unclaimed | ||
| 11-19 Notes | Unclaimed | ||
| 11-24 Notes | Unclaimed | ||
| 11-26 Notes | Unclaimed | ||
| 12-01 Notes | Unclaimed | ||
| 12-03 Notes | Unclaimed | ||
| 12-08 Notes | Unclaimed | ||
| 12-10 Notes | Unclaimed |
Supplementary notes
Editing the Wiki
This Wiki is editable by anyone. Just create an account, sign in, and an "edit" tab will appear at the top.
I use a hacked version of the Wikipedia LaTeX rendering engine. Most LaTeX "math mode" commands are supported, meaning anything you would enclose in $'s. You can make commutative diagrams via \xymatrix. What doesn't work are non-"math mode" commands like \begin{eqnarray*}. For example pages illustrating most features, see 10-06 Notes or 10-15 Notes.
Tips:
- If you don't already know LaTeX, try LyX. (Version 1.6.0 works well.) It will help you typeset your formulas, help you learn LaTeX, and export your work as a LaTeX document. With some minor modifications, you'll be able to paste that LaTeX into this Wiki.
- Be sure to save your work often! The "Save page" button is your friend. Otherwise, something might navigate you away from the Wiki, causing you to lose your work.
- Edit aggressively. All changes are reversible, so it's impossible to "screw things up."
- Hit the "Show preview" button to see what you're doing.
If you have trouble, feel free to let me know. If you need to use a package, a macro, or some command which isn't supported, I can easily hardcode it for you.
