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|[[09-03 Notes]]
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  || [[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]]  
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| 2
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  || [[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]]  
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  || [[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]]  
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  || [[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
 
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|-
|[[09-17 Notes]]  
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| 5
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  || [[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]]  
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| 6
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  || [[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]]  
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| 7
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  || [[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]]  
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| 8
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  || [[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]]  
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| 9
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  || [[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 $\Sigma$
 
|-
 
|-
|[[10-08 Notes]]  
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| 10
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  || [[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]]  
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| 11
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  || [[10-15 Notes]]  
 
   || Draft
 
   || Draft
 
   ||
 
   ||
 
   || Details on $N(2,1)$  
 
   || Details on $N(2,1)$  
 
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|[[10-20 Notes]]  
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  || [[10-20 Notes]]  
 
   || Alex
 
   || Alex
 
   ||  
 
   ||  
 
   || Calculation of the Morse index of YMF
 
   || Calculation of the Morse index of YMF
 
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|[[10-22 Notes]]  
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  || [[10-22 Notes]]  
 
   || Unclaimed
 
   || Unclaimed
 
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   ||  
 
   || Morse Theory
 
   || Morse Theory
 
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   || Unclaimed
 
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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 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.