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| − | |[[09-03 Notes]] | + | | 1 |
| + | || [[09-03 Notes]] | ||
|| Unclaimed | || Unclaimed | ||
|| [../scans/09-03_Ben.pdf Ben] | || [../scans/09-03_Ben.pdf Ben] | ||
|| Overview of moduli spaces | || Overview of moduli spaces | ||
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| − | |[[09-08 Notes]] | + | | 2 |
| + | || [[09-08 Notes]] | ||
|| Unclaimed | || Unclaimed | ||
|| [../scans/09-08_Ben.pdf Ben] | || [../scans/09-08_Ben.pdf Ben] | ||
|| Sobolev spaces and gauge theoretic analysis | || Sobolev spaces and gauge theoretic analysis | ||
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| − | |[[09-10 Notes]] | + | | 3 |
| + | || [[09-10 Notes]] | ||
|| Unclaimed | || Unclaimed | ||
|| [../scans/09-10_Ben.pdf Ben] | || [../scans/09-10_Ben.pdf Ben] | ||
|| $\mathcal{A}/\mathcal{G}$ is a metric space, local structure of a quotient | || $\mathcal{A}/\mathcal{G}$ is a metric space, local structure of a quotient | ||
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| − | |[[09-15 Notes]] | + | | 4 |
| + | || [[09-15 Notes]] | ||
|| Unclaimed | || Unclaimed | ||
|| [../scans/09-15_Ben.pdf Ben] | || [../scans/09-15_Ben.pdf Ben] | ||
|| Stabilizers and holonomy, outline of slice theorem | || Stabilizers and holonomy, outline of slice theorem | ||
|- | |- | ||
| − | |[[09-17 Notes]] | + | | 5 |
| + | || [[09-17 Notes]] | ||
|| Started | || Started | ||
|| [../scans/09-17_Ben.pdf Ben] | || [../scans/09-17_Ben.pdf Ben] | ||
|| Proof of slice theorem, except injectivity | || Proof of slice theorem, except injectivity | ||
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| − | |[[09-24 Notes]] | + | | 6 |
| + | || [[09-24 Notes]] | ||
|| Lu | || Lu | ||
|| [../scans/09-24_Ben.pdf Ben] | || [../scans/09-24_Ben.pdf Ben] | ||
|| Injectivity, and remarks on the Yang-Mills equation | || Injectivity, and remarks on the Yang-Mills equation | ||
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| − | |[[09-29 Notes]] | + | | 7 |
| + | || [[09-29 Notes]] | ||
|| Alex | || Alex | ||
|| [../scans/09-29_Ben.pdf Ben] | || [../scans/09-29_Ben.pdf Ben] | ||
|| Classifying space for $\mathcal{G}$ | || Classifying space for $\mathcal{G}$ | ||
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| − | |[[10-01 Notes]] | + | | 8 |
| + | || [[10-01 Notes]] | ||
|| Andy | || Andy | ||
|| [../scans/10-01_Ben.pdf Ben] | || [../scans/10-01_Ben.pdf Ben] | ||
|| $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ | || $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ | ||
|- | |- | ||
| − | |[[10-06 Notes]] | + | | 9 |
| + | || [[10-06 Notes]] | ||
|| Steven | || Steven | ||
|| [../scans/10-06_Ben.pdf Ben] | || [../scans/10-06_Ben.pdf Ben] | ||
|| $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ over $\Sigma$ | || $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ over $\Sigma$ | ||
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| − | |[[10-08 Notes]] | + | | 10 |
| + | || [[10-08 Notes]] | ||
|| Unclaimed | || Unclaimed | ||
|| [../scans/10-08_Ben.pdf Ben] | || [../scans/10-08_Ben.pdf Ben] | ||
|| Stabilizers and the rank 2 case | || Stabilizers and the rank 2 case | ||
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| − | |[[10-15 Notes]] | + | | 11 |
| + | || [[10-15 Notes]] | ||
|| Draft | || Draft | ||
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|| Details on $N(2,1)$ | || Details on $N(2,1)$ | ||
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| − | |[[10-20 Notes]] | + | | 12 |
| + | || [[10-20 Notes]] | ||
|| Alex | || Alex | ||
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|| Calculation of the Morse index of YMF | || Calculation of the Morse index of YMF | ||
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| − | |[[10-22 Notes]] | + | | 13 |
| + | || [[10-22 Notes]] | ||
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|| Morse Theory | || Morse Theory | ||
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Revision as of 10:28, 27 October 2008
Contents |
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 |
|---|---|---|---|---|
| 1 | 09-03 Notes | Unclaimed | Ben | Overview of moduli spaces |
| 2 | 09-08 Notes | Unclaimed | Ben | Sobolev spaces and gauge theoretic analysis |
| 3 | 09-10 Notes | Unclaimed | Ben | $\mathcal{A}/\mathcal{G}$ is a metric space, local structure of a quotient |
| 4 | 09-15 Notes | Unclaimed | Ben | Stabilizers and holonomy, outline of slice theorem |
| 5 | 09-17 Notes | Started | Ben | Proof of slice theorem, except injectivity |
| 6 | 09-24 Notes | Lu | Ben | Injectivity, and remarks on the Yang-Mills equation |
| 7 | 09-29 Notes | Alex | Ben | Classifying space for $\mathcal{G}$ |
| 8 | 10-01 Notes | Andy | Ben | $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ |
| 9 | 10-06 Notes | Steven | Ben | $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ over $\Sigma$ |
| 10 | 10-08 Notes | Unclaimed | Ben | Stabilizers and the rank 2 case |
| 11 | 10-15 Notes | Draft | Details on $N(2,1)$ | |
| 12 | 10-20 Notes | Alex | Calculation of the Morse index of YMF | |
| 13 | 10-22 Notes | Unclaimed | Morse Theory | |
| 14 | 10-27 Notes | Unclaimed | ||
| 15 | 10-29 Notes | Unclaimed | ||
| 16 | 11-03 Notes | Unclaimed | ||
| 17 | 11-05 Notes | Unclaimed | ||
| 18 | 11-12 Notes | Unclaimed | ||
| 19 | 11-17 Notes | Unclaimed | ||
| 20 | 11-19 Notes | Unclaimed | ||
| 21 | 11-24 Notes | Unclaimed | ||
| 22 | 11-26 Notes | Unclaimed | ||
| 23 | 12-01 Notes | Unclaimed | ||
| 24 | 12-03 Notes | Unclaimed | ||
| 25 | 12-08 Notes | Unclaimed | ||
| 26 | 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.
