Course notes

This page collects math notes I've taken, mostly course notes. I've also written some TeXnical notes and scripts.

I provide the source for most of my notes for a couple of reasons.

1. It feels good for some reason.
2. If you're curious about how to typeset something you've seen in these notes, you can download the source and have a look.
3. Somebody might download all my notes, correct the errors and unclear presentation, and then send them back to me. It's not likely, but it could happen.
4. If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
5. The source is much faster to download and compile if you're on a slow connection.

Since I've learned about it, I've started using Subversion (svn) for everything. If you actually make corrections in any of the notes, I recommend doing it through svn. If you don't yet know how to use svn, I wrote an svn crash course just for you.

My notes	What?	Who?	When?	Additional Resources
pdfsvntgz	Geometric Invariant Theory	Vera Serganova	Fall 2009
pdfsvntgz	Homological Algebra	Peter Teichner	Spring 2008
pdfsvntgz	Deformation Theory Workshop, MSRI	Max Lieblich Martin Olsson Brian Osserman Ravi Vakil	Summer 2007	Other peoples' notes can be found here and here.
pdfsvntgz	Math 274, Stacks	Martin Olsson	Spring 2007
pdftex	Math 215A, Algebraic Topology	Peter Teichner	Fall 2006
pdftgz	Math 274, Commutative Rings	Tsit Yuen Lam	Fall 2006
pdftgz	Math 261A, Lie Groups and Lie Algebras	Nicolai Reshetikhin Vera Serganova Richard Borcherds	Spring 2006
pdftgz	Math 242, Symplectic Geometry	Alan Wienstein	Fall 2005
	Math 252, Representation Theory	Vera Serganova	Fall 2005	Vera Serganova's Representation Theorey notes William Crawley-Boevey's lectures on representations of quivers
pdf tgz	Math 256B, Algebraic Geometry	Paul Vojta	Spring 2005	Paul Vojta's handouts and solutions William Stein's notes and solutions Richard Borcherds's selected solutions Bryden Cais's notes and solutions Jinhyun Park's solutions Mark Haiman's Math 256AB page

I gave a couple of talks on toric varieties in a student seminar. If my notes make sense to you, you're welcome to use them.

My notes (pdf, tgz), made from Tony's notes, of Yonathan's prelim workshop on analysis.

One of my favorite facts about right adjoint functors is that they commute with limits.

Sestina's and primes, an easy problem Richard Dore and I worked out our first year in grad school, which I wrote up for some reason.

I talked about the Salamander Lemma in MCF. My reference was George Bergman's preprint, On diagram-chasing in double complexes.

More moved notes

Aspects of Moduli:

Tom Bridgeland	Stability in triangulated categories	pdf
Kai Behrend	Foundations of Donaldson-Thomas theory	pdf
Alessio Corti	Foundations of Donaldson-Thomas theory	pdf
Valery Alexeev	Moduli of higher-dimensional varieties	pdf
Martin Olsson	Logarithmic structures with a view towards moduli	pdf
All in one (chronologically)	pdf tgz

Quantum Field Theory, my notes from

Nicolai Reshetikhin's course	pub pri
Peter Teichner's course	pdf
Richard Borcherd's course	pdf
All in one (chronologically)	pub pri tgz dir

The public version is missing the last two weeks of Reshetikhin's class, and the private version is not. If you want the username and password for the private version, ask me for it and I'll give it to you.

For more QFT stuff, see Chris Schommer-Pries' QFT site for Fall 2007. (doesn't exist any more?)

For those who just want to get some notes, just download the pdf file. For those who want to look at the souce, download the tgz (tar-ed and gzip-ped) file, which has all the tex source in it. You'll find that the main file (QFT.tex) is quite boring. The actual lecture notes are in the other files and the top matter (like macro definitions) is in QFTPreamble.tex. As far as I know, the command \input{abcdefg} gives exactly the same result as pasting in the contents of the file abcdefg.tex (note that abcdefg.tex should be in the same directory as the main file).

If you have notes that I'm missing or if you have a correct/clear explanation for something which is incorrect/unclear, let me know (either tell me what you'd like to modify, give me some notes to go on, or update the tex yourself and send me a copy). Real (mathematical) errors should be fixed because it would be immoral to let them propagate (er ... that is, sit there), and typographical errors hardly take any time to fix, so you shouldn't be shy about telling me about them.