Theo Johnson-Freyd

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Contents

• Teaching
  • Past Classes
• Other Stuff
  • Class Notes
  • Talks I Have Given
  • Current Projects
  • Non-math and other links

Teaching

Past Classes

• Summer 2009: Math 1B
• Spring 2009: Math 1A
• Fall 2008: Math 32
• Summer 2008: Math 1B
• Spring 2008: Math 53
• Fall 2007: Math 1B

Other Stuff

Class Notes

I type notes in most of my classes — I'm one of those "Live TeX"-ers — and post them online. You can find the notes here. Be warned: these notes are almost entirely unedited transcripts of the classes, except that sometimes I miss what people say or mishear them. The notes are filled with jokes, questions from the audience, and my own commentary. In particular, my primary reason for taking notes is to help myself engage with the material then and there; my secondary reason is to have a record of the class, and to provide that record to other people.

Warning: Since the notes provided below are class notes, and were not prepared by the instructor, they are probably about as accurate as any class notes, which is to say they may be replete with errors. Of course, anything good about the notes, and in particular all the mathematical material, is due to the professor of the class. Anything bad about them, and in particular every inaccuracy, is mine. Use them with care.

I don't know if anyone will find this useful, but I have also included tarballs of the TeX sources for these notes. Well, actually, each tarball is of my entire folder for the class. As such, these tend to be huge and filled with detritus: outdated PDFs, auxiliary files, partly completed problem sets, etc. You are welcome to download them, but I make no promises that the files will load on your computer: that will depend on whether your TeX installation exactly matches mine.

I was inspired to start typing lecture notes after watching Anton Geraschenko do it. Read his advice on Live-TeXing here, and check out his collection of class notes here.

Talks I Have Given

The following talks are largely expository.

Title and file	Date, venue	Abstract, references
Divergent Series	18 October 2007. Many Cheerful Facts.	Abstract: Mathematicians through the ages have varied from terrified of divergent sums to only mildly scared of them: Euler, most famously, made great use of divergent series, whereas Abel called them "the invention of the devil". In this talk, I will survey the most important methods of summing divergent series, and make general vague remarks about them. I will quote many results, but will studiously avoid proving anything. The material is almost entirely from G.H. Hardy, Divergent Series, 1949.
Enriching Yoneda	11 December 2007. Talk given at QFT Mini Conference, a student conference concluding a semester filled with three quantum-field-theory classes.	The goal of the talk was to formulate and prove the Yoneda embedding theorem for categories enriched over a closed monoidal category. The material for this talk is almost entirely from G.M. Kelly, Basic Concepts of Enriched Category Theory, Cambridge University Press, 2005.
Combinatorial Calculus: From Taylor Series to Feynman Diagrams.	July 7-12, 2008. Canada/USA Mathcamp	A one-week advanced-calculus class. The first few days I typed lecture notes including what I intended to say: these are available here. Most of the notes are definitions and exercises. These I put together into (almost) daily handouts. Handouts of exercises, including all the definitions and results from class, are available here from every day.
On Atoms, Mountains, and Rain	31 March 2009. Many Cheerful Facts.	Abstract: This talk won't include very many facts, but it will include many almost facts, aka "lies". A few lies we will tell: rocks are made of rock atoms, liquid water is a perfect cubic crystal lattice, and 1 = 2. Using these and similar "facts", we will derive from first principles the radius of an atom, the height of a mountain, and the volume of a raindrop. Doing so honestly, even if we knew all the fundamental equations of the universe, would be impossible; lying makes everything work out nicely. The material is almost entirely from to P. Goldreich, S. Mahajan, and S. Phinney, Order-of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies, 1999. Available at http://www.inference.phy.cam.ac.uk/sanjoy/oom/.
What the Hell is a Feynman Diagram?	29 September 2009. Ph.d. seminar, Institut for Matematiske Fag, Aarhus Universitet.	From the introduction: The goal of the talk is to introduce the notion of ``Feynman Diagram'' in a reasonably rigorous way, and to state some theorems proving that it is a good notion. I will organize the talk more-or-less via a ``mathematician's history of mathematics,'' which is to say a false history, one that gives the impression that all ideas inevitably lead up to what we now know is the true and complete story. [...] Thus, I will begin by describing why you might invent Feynman Diagrams. I'll then tell you about what the mathematicians have said about them. Time permitting, I'll finish with some speculation of my own. In fact, I said about half of what I had intended to say, and none of the interesting bits. Linked on the left are my prepared remarks.

Current Projects

• The Composition Law for Feynman Diagrams I: discrete-time quantum mechanics and II: how to glue in general. Papers written over winter break, in early January 2008. These papers are the beginning of a project suggested by Nicolai Reshetikhin. Ultimately, the goal is to show that Feynman-style integration by Feynman-diagram expansion satisfies all the natural algebraic identities expected for normal integration, and in particular that it satiesfies something like Fubini's theorem. These papers provide a proof of these identities for nondegenerate bosonic theories in 0- or 1-dimensional spacetimes. In dimensions 2 and higher, I need to learn enough renormalization theory to explain the interaction there; also interesting is BV formalism for how to Feynman-integrate guage theories. Update: I am in the final stages of writing up a much better discussion in the case of Quantum Mechanics (0+1-dimensional spacetime), and so these notes are close to outdated (they were always a little naive).
• I completed my Qualifying Exam on June 11. You may read my syllabus if you like.
• Largely as a study aid, I have rewritten my Lie Groups notes (old version (pdf)) into something more presentable. The current draft, complete but still only a draft, is available here (pdf), and TeX source is available here (tex). I would highly appreciate feedback.
• I also have some notes on Quantum Groups. They are rather disjointed, and probably won't be helpful to anyone but myself. Included are:
  • Poisson Lie linear algebra in the graphical language. This is a two-fold exercise: to practice drawing pictures in TikZ, and to work out all the definitions from the first part of Math 261B: Quantum Groups (pdf). In case you want to see how I drew all those pretty pictures, the TeX source is available here.
  • Some rather schizophrenic notes on quantization here. They're not great, and need some edits; moreover, there's nothing there that's not better explained in Chari and Pressley, A Guide to Quantum Groups, 1994.
  • A possibly-useful collection of notes on Hopf algebras.
  • The last chapter is unfinished. I am trying to understand the extent to which one can construct a universal quantization of a Lie bialgebra.

Non-math and other links

I used to post math and non-math essays on my weblog, The Orange Juice Files. Perhaps I will take it back up again sometime in the future. You can always put it in your RSS reader.

I am an avid cook. Some recipes and discussions are available on my food blog at Local Seasoning.