Course notes

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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.

In 2007, I talked about the Salamander Lemma in MCF, and later blogged about it on the Secret Blogging Seminar. My reference was George Bergman's preprint, On diagram-chasing in double complexes (which wasn't yet on the arxiv at the time).

More moved notes[edit]

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

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.