Course notes

2012-03-18T20:38:56Z

129.67.186.126: added talk titles

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.
#It feels good for some reason.
#If you're curious about how to typeset something you've seen in these notes, you can download the source and have a look.
#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.
#If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
#The source is much faster to download an compile if you're on a slow connection.

Since I've learned about it, I've started using [http://en.wikipedia.org/wiki/Subversion_(software) 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 [http://stacky.net/old-webpage/svnguide.html svn crash course] just for you.

{| class="wikitable"
|-
|My notes
|What?
|Who?
|When?
|Additional Resources
|-
|[http://stacky.net/files/written/GIT/GIT.pdf pdf][svn://sheafy.net/courses/git_fa2009 svn][http://stacky.net/files/written/GIT/GITSource.tgz tgz]
|Geometric Invariant Theory
|[http://math.berkeley.edu/~serganov/ Vera Serganova]
|Fall 2009
|
|-
|[http://stacky.net/files/written/Halg/Halg.pdf pdf][svn://sheafy.net/courses/halg_sp2008 svn][http://stacky.net/files/written/Halg/HalgSource.tgz tgz]
|Homological Algebra
|[http://math.berkeley.edu/~teichner Peter Teichner]
|Spring 2008
|
|-
|[http://stacky.net/files/written/defthy07/defthy07.pdf pdf][svn://sheafy.net/defthy_su07 svn][http://stacky.net/files/written/defthy07/DefThySource.tgz tgz]
|[http://www.msri.org/people/members/defthy07/ Deformation Theory Workshop, MSRI]
|[http://www.math.princeton.edu/~lieblich/ Max Lieblich] 
[http://math.berkeley.edu/%7Emolsson Martin Olsson] 
[http://math.berkeley.edu/~osserman/ Brian Osserman] 
[http://math.stanford.edu/~vakil/ Ravi Vakil]
|Summer 2007
|Other peoples' notes can be found [http://www.msri.org/people/members/defthy07/lectures.html here] and [http://math.stanford.edu/~vakil/defthy/ here].
|-
|[http://stacky.net/files/written/Stacks/Stacks.pdf pdf][svn://sheafy.net/courses/stacks_sp2007 svn][http://stacky.net/files/written/Stacks/FullStackSource.tgz tgz]
|Math 274, [http://math.berkeley.edu/%7Emolsson/274.html Stacks]
|[http://math.berkeley.edu/%7Emolsson Martin Olsson]
|Spring 2007
|
|-
|[http://stacky.net/files/written/AlgTopology/AlgebraicTopologyNotes.pdf pdf][http://stacky.net/files/written/AlgTopology/AlgebraicTopologyNotes.tex tex]
|Math 215A, Algebraic Topology
|[http://math.berkeley.edu/%7Eteichner/ Peter Teichner]
|Fall 2006
|
|-
|[http://stacky.net/files/written/CommRings/CommRing.pdf pdf][http://stacky.net/files/written/CommRings/CommutativeRingsSource.tgz tgz]
|Math 274, [http://stacky.net/files/written/CommRings/index.html Commutative Rings]
|[http://math.berkeley.edu/%7Elam/ Tsit Yuen Lam]
|Fall 2006
|
|-
|[http://stacky.net/files/written/LieGroups/LieGroups.pdf pdf][http://stacky.net/files/written/LieGroups/LieGroupsSource.tgz tgz]
|Math 261A, Lie Groups and Lie Algebras
|[http://math.berkeley.edu/%7Ereshetik/ Nicolai Reshetikhin] [http://math.berkeley.edu/%7Eserganov/ Vera Serganova] [http://math.berkeley.edu/%7Ereb/ Richard Borcherds]
|Spring 2006
|
|-
|[http://stacky.net/files/written/SymplecticGeometry/SymplecticGeomNotes.pdf pdf][http://stacky.net/files/written/SymplecticGeometry/SymplecticGeometrySource.tgz tgz]
|Math 242, Symplectic Geometry
|[http://math.berkeley.edu/%7Ealanw/ Alan Wienstein]
|Fall 2005
|
|-
|
|Math 252, [http://math.berkeley.edu/%7Eserganov/math252/index.html Representation Theory]
|[http://math.berkeley.edu/%7Eserganov/ Vera Serganova]
|Fall 2005
|[http://math.berkeley.edu/%7Eserganov/ Vera Serganova]'s [http://math.berkeley.edu/%7Eserganov/math252/index.html Representation Theorey notes] 

[http://www.maths.leeds.ac.uk/%7Epmtwc/ William Crawley-Boevey]'s lectures on [http://www.maths.leeds.ac.uk/%7Epmtwc/quivlecs.pdf representations of quivers]
|-
|[http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometryNotes.pdf pdf] [http://stacky.net/files/written/AlgebraicGeometry/AlgebraicGeometryNotes.tgz tgz]
|Math 256B, Algebraic Geometry
|[http://math.berkeley.edu/~vojta/ Paul Vojta]
|Spring 2005
|[http://math.berkeley.edu/%7Evojta/ Paul Vojta's] [http://stacky.net/files/written/VojtaSolutions/ handouts and solutions] 

[http://modular.ucsd.edu/ William Stein's] [http://modular.ucsd.edu/AG.html notes and solutions] 

[http://math.berkeley.edu/%7Ereb/ Richard Borcherds's] selected [http://math.berkeley.edu/%7Ereb/courses/alggeom/ solutions] 

[http://math.arizona.edu/~cais/ Bryden Cais's] [http://math.arizona.edu/~cais/CourseNotes/AlgGeom04/ notes] and [http://math.arizona.edu/~cais/CourseNotes/AlgGeom04/Hartshorne_Solutions.pdf solutions] 

[http://mathsci.kaist.ac.kr/~jinhyun/ Jinhyun Park's] [http://mathsci.kaist.ac.kr/~jinhyun/sol2/hart.html solutions] 

[http://math.berkeley.edu/%7Emhaiman/index.html Mark Haiman]'s [http://math.berkeley.edu/%7Emhaiman/math256/index.html Math 256AB page]
|}

I gave a couple of talks on toric varieties in a student seminar. If [http://stacky.net/files/written/toric.pdf my notes] make sense to you, you're welcome to use them.

My notes ([http://stacky.net/files/written/AnalysisPrelim/AnalysisPrelim.pdf pdf], [http://stacky.net/files/written/AnalysisPrelim/AnalysisPrelim.tgz tgz]), made from [http://math.rice.edu/~av15/ Tony's] notes, of Yonathan's prelim workshop on analysis.

One of my favorite facts about right adjoint functors is that they [http://stacky.net/files/written/AdjointsCommuteLimits.pdf commute with limits].

[http://stacky.net/files/written/sestina.pdf 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 [http://math.berkeley.edu/~slofstra/mcf/ MCF]. My reference was [http://math.berkeley.edu/~gbergman/ George Bergman]'s preprint, [http://stacky.net/files/written/DiagramChasingBergman.pdf On diagram-chasing in double complexes].

==More moved notes==

[http://docs.google.com/View?docid=dsrd28g_14rgs6ptht Aspects of Moduli]:
{|class="wikitable"
|-
|Tom Bridgeland
| Stability in triangulated categories
| [http://stacky.net/files/written/AspectsModuli/TB.pdf pdf]
|-
|Kai Behrend
| Foundations of Donaldson-Thomas theory
| [http://stacky.net/files/written/AspectsModuli/KB.pdf pdf]
|-
|Alessio Corti
| Foundations of Donaldson-Thomas theory
| [http://stacky.net/files/written/AspectsModuli/AC.pdf pdf]
|-
|Valery Alexeev
| Moduli of higher-dimensional varieties
| [http://stacky.net/files/written/AspectsModuli/VA.pdf pdf]
|-
|Martin Olsson
| Logarithmic structures with a view towards moduli
| [http://stacky.net/files/written/AspectsModuli/MO.pdf pdf]
|-
|All in one (chronologically)
| [http://stacky.net/files/written/AspectsModuli/AspectsModuli.pdf pdf] [http://stacky.net/files/written/AspectsModuli/AspectsModuliSource.tgz tgz]
|}

Quantum Field Theory, my notes from
{|class="wikitable"
|-
|[http://math.berkeley.edu/~reshetik/ Nicolai Reshetikhin]'s [http://math.berkeley.edu/~reshetik/topics/CFT-TQFT.pdf course]
|[http://stacky.net/files/written/QFT/NR.pdf pub] [http://stacky.net/files/written/QFT/private/NR.pdf pri]
|-
|[http://math.berkeley.edu/~teichner Peter Teichner's] course
|[http://stacky.net/files/written/QFT/PT.pdf pdf]
|-
|[http://math.berkeley.edu/~reb/ Richard Borcherd's] course
|[http://stacky.net/files/written/QFT/RB.pdf pdf]
|-
|All in one (chronologically)
| [http://stacky.net/files/written/QFT/QFT.pdf pub] [http://stacky.net/files/written/QFT/private/QFT.pdf pri] [http://stacky.net/files/written/QFT/QFTSource.tgz tgz] [http://stacky.net/files/written/QFT/ 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 [http://sites.google.com/site/chrisschommerpriesmath/ 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 (<code>tar</code>-ed and <code>gzip</code>-ped) file, which has all the tex source in it. You'll find that the main file (<code>QFT.tex</code>) is quite boring. The actual lecture notes are in the other files and the top matter (like macro definitions) is in <code>QFTPreamble.tex</code>. As far as I know, the command <code>\input{abcdefg}</code> gives exactly the same result as pasting in the contents of the file <code>abcdefg.tex</code> (note that <code>abcdefg.tex</code> 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.

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Course notes