- "Integrable systems."
- Here is a survey article by Jacques Hurtubise on Hitchin system: "The geometry of generalized Hitchin systems." Harnad, J. (ed.) et al., Integrable systems: from classical to quantum. Proceedings of the 38th session of the Seminaire de mathematiques superieures, Montreal, Canada, July 26-August 6, 1999. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 26, 55-76 (2000).
- Beauville, A. "Jacobiennes des courbes spectrales et systemes hamiltoniens completement integrables", Acta Math. 164, 1990, 211-235
- Some of us are going to try to read some chapters from the book "Integrable systems: twistors, loop groups, and Riemann surfaces," by Hitchin, Segal, and Ward, over the course of this year.
- One place to start (for the smooth category) is the book by Ana Cannas da Silva and Alan Weinstein, "Lectures on Geometric Models for Noncommutative Algebra." (AMS)
- A recommended readable introduction is in Eckhard Meinrenken's paper "The basic gerbe over a compact simple Lie group." (Available on the arXiv.)
- Christoph Sorger's lecture notes, titled "Lectures on moduli of principal G-bundles over algebraic curves curves," can be found at this website.
- Moerdijk has some survey articles also, of which I think this is an example (Henrique, any others?): Moerdijk, Ieke. "Orbifolds as groupoids: an introduction." Orbifolds in mathematics and physics (Madison, WI, 2001), 205--222, Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002.
- Dave Metzler also has some recent work on orbifolds and stacks.
- Analysis on infinite-dimensional manifolds.
- Here is an article where the smooth structure on Diff(M) is explained: Hamilton, R. The inverse function Theorem of Nash and Moser, Bull Am Math Soc, 7, 1982, 65-222.
If you have things to add, please email Megumi Harada at