The following draft textbook has been accepted for publication by World Scientific:
R. Borcherds, M. Haiman, T. Johnson-Freyd, N. Reshetikhin, and V. Serganova. Berkeley Lectures on Lie Groups and Quantum Groups. PDF.
I occasionally "Live-TeX" notes from classes and lectures. As with any notes, mine are replete with omissions and errors, undoubtedly; typing does allow me to catch questions from the audience and jokes from the professors, so these are included as well. Needless to say, anything good about the notes, and in particular presentation of 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. Also, please e-mail me with corrections: typos are trivial to fix, and mathematical errors should not be allowed to propagate. I was inspired to start typing lecture notes after watching Anton Geraschenko do it, and appreciate his advice.
- Philippe Di Francesco. Chern-Simons Research Lectures: Discrete Integrable Systems and Cluster Algebras, 10-12 April 2012. Prepared slides: Day 1 (8 MB), Day 2 (16 MB), Day 3 (13 MB). Unedited notes from the first two days.
- Denis Bernard. Chern-Simons Research Lectures: Stochastic Schramm-Loewner Evolution (SLE) from Statistical Conformal Field Theory (CFT): An Introduction for (and by) Amateurs, 19-23 March 2012. Prepared notes: arXiv:math-ph/0602049v1. Mildly edited notes.
- David Kazhdan. Chern-Simons Research Lectures: The classical master equation in the finite-dimensional case, 9-13 Jan 2012. Mildly edited notes.
- Jorg Teschner. Chern-Simons Research Lectures: Quantization of Hitchin's Moduli Spaces and Liouville Theory, 17-21 Oct 2011. Unedited notes.
- Fedor Smirnov. Chern-Simons Research Lectures: Correlation functions in integrable Quantum Field Theory, 28 Sept - 4 Oct 2011. Unedited notes. Slides.
- MSRI, Symplectic Geometry, Noncommutative Geometry and Physics, May 10, 2010 to May 14, 2010. (All slides and transcripts (tar.gz).)
- V. Serganova. Math 261B: Quantum Groups. Spring 2010. (Unedited: PDF, TAR.GZ.)
- N. Reshetikhin. Math 261B: Quantum Groups. Spring 2009. (Unedited: PDF (size exceeds 800 KB), TAR.GZ (size exceeds 9 MB).)
- M. Haiman. Math 261A: Lie Groups. Fall 2008. (Edited: PDF, TeX. Unedited: PDF (size exceeds 1 MB), TAR.GZ (size exceeds 6 MB).)
- M. Rieffel. Math 208: C* Algebras. Spring 2008. (Unedited: PDF (about 600 KB), TAR.GZ (about 4 MB).)
Please note that the TAR.GZ files include TeX sources and plenty of other detritus: 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.
An article in the Newsletter of the London Math Society about a conference we ran:
An approach to less climate-impactful conferences. With David Ayala, Lukas Brantner, André Henriques, and Aaron Mazel-Gee. Newsletter of the LMS, Issue 480, January 2019. pp32-33. (PDF.)
Here are two idiosyncratic notes surveying various mathematics:
Exact triangles as modules over an A∞-category. 2015. (PDF.)
Poisson Lie linear algebra in the graphical language. 2009. (PDF. TeX source.)
As many graduate students discover when taking their language exams, you don't need any training in French in order to read Mathematical French. (It helps that Mathematical English is more French-inflected than is Colloquial English.) As evidence, I have translated into English Deligne's article Catégories Tensorielles (French original).
One of my more satisfying activities is that I am a reviewer for MathReviews and zbMath. Of my reviews, two appeared in the September 2012 print addition: MR2742432 (2012i:55005): Stolz and Teichner, Supersymmetric field theories and generalized cohomology, 2011 and MR2752518 (2012i:81001): Baez and Lauda, A prehistory of n-categorical physics, 2011.