Resources for the holomorphic curves course at MSRI

  • Background for holomorphic curve analysis: List of good things to know, most of which can be found in Appendix A,B from McDuff-Salamon J-holomorphic Curves and Symplectic Topology and Lecture notes on Fredholm theory by Tom Mrowka (from OpenCourseWare: Geometry of Manifolds)

  • Lecture notes:
    lecture 1 (Introduction and Gromov nonsqueezing),
    lecture 2 (basic properties of holomorphic curves),
    lecture 3 (Fredholm theory),
    lecture 4 (Transversality - was actually meant as #5 but got switched so the bubbling exercise could be discussed before lecture 5),
    lecture 5 (Gromov compactness)

  • Exercises: set 1, set 2, set 3

  • Further references:
    Uncertainty principle, non-sqeezing theorem and the symplectic rigidity by Yong-Geun Oh