# Main Page

Note: As of 2012, an upgrade to MediaWiki has broken my LaTeX hack. When I get the chance, I will change over everything into a PDF so that it becomes readable. Test edit

## 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 you take decent notes, please let me borrow your loose sheets so I can scan them. Thanks! -Ben

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 Main author Status Scans Description
1 09-03 Notes Christian Done Ben Overview of moduli spaces,review of G-bundles and connections
2 09-08 Notes Bhairav Done Ben Sobolev spaces and gauge theoretic analysis
3 09-10 Notes Tatyana Draft Ben $\mathcal{A}/\mathcal{G}$ is a metric space, local structure of a quotient
4 09-15 Notes Unclaimed Unstarted Ben Stabilizers and holonomy, outline of slice theorem
5 09-17 Notes James Started Ben Proof of slice theorem, except injectivity
6 09-24 Notes Lu Done Ben Injectivity, and remarks on the Yang-Mills equation
7 09-29 Notes Alex Done Ben Classifying space for $\mathcal{G}$
8 10-01 Notes Andy Done Ben $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$
9 10-06 Notes Steven Done Ben $\mathcal{G}$-equivariant cohomology of $\mathcal{A}$ over $\Sigma$
10 10-08 Notes Nikhil Done Ben Stabilizers and the rank 2 case
11 10-15 Notes Ben Draft Details on $N(2,1)$
12 10-20 Notes Alex Done Ben Calculation of the Morse index of YMF
13 10-22 Notes Christian Started Ben Morse Theory
14 10-27 Notes Bhairav Done Ben Morse-Bott Theory
15 10-29 Notes David Draft Ben Poincare polynomial of $N(2,1)$
16 11-03 Notes Nikhil Unstarted Ben $N(2,1)$ as a Symplectic quotient
17 11-05 Notes Lu Done Ben Uhlenbeck's gauge-fixing lemma
18 11-12 Notes Unclaimed Unstarted Ben Uhlenbeck's lemma (cont'd)
19 11-17 Notes Unclaimed Unstarted Ben Uhlenbeck's lemma ($L^n$ estimates)
20 11-19 Notes Unclaimed Unstarted Ben Uhlenbeck's lemma ($L^n$ estimates cont'd)
21 11-24 Notes Steven Draft
22 11-26 Notes Unclaimed Unstarted
23 12-01 Notes Unclaimed Unstarted
24 12-03 Notes Unclaimed Unstarted
25 12-08 Notes Andy Started 4-d Yang-Mills
26 12-10 Notes Tim Done Construction of Instantons

### 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 commands are supported. You can make commutative diagrams via \xymatrix. This Wiki should recognize most things between \begin{document} and \end{document}. 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.