Introduction to Pseudo-holomorphic curves and Symplectic Topology
(a mini-course)

Time and Place

Tuesday and Thursday, 9:00-10:20, Henry 154.

Overview of the course

Pseudo-holomorphic curves were first introduced and applied by Gromov in his remarkable paper of 1985 which revolutionized the field of symplectic geometry. They are still one of the central tools in the field and are actively being developed in new directions.

This mini-course will be comprised of two components. The first will be a reasonably detailed discussion of the definition and main properties of pseudo-holomorphic curves with special emphasis on their compactness properties. In the second part of the course we will survey many of their applications to symplectic topology.

Prerequisites

Basic differential geometry and topology. We will use several standard results in symplectic geometry. These will be stated completely and all relevaant notions will be defined. For the proofs of these results you are referred to the references below.
We will also use some nonlinear functional analysis. For an excellent and brief introduction to some of this material see Chapters 15-20 of Tom Mrowka's lecture notes here.

Office Hours

Tuesday 1:00 to 3:00, or by appointment.

References

Background Material

  • Lectures on Symplectic Geometry, by A. Cannas da Silva.
  • Introduction to Symplectic Topology (Second Edition), by D. McDuff and D. Salamon.
  • Symplectic Invariants and Hamiltonian Dynamics, by H. Hofer and E. Zehnder.
  • The Geometry of the Group of Symplectic Diffeomorphisms, by L. Polterovich.

    Foundational Material on Pseudo-holomorphic Curves

  • Holomorphic curves in symplectic geometry, by M. Audin, J. Lafontaine (Editors).
  • J-holomorphic curves and symplectic topology, by D. McDuff and D. Salamon.

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    This page last modified by Ely Kerman
    Friday, 20-Jan-2005 13:12:53 EST
    Email corrections and comments to ekerman@math.uiuc.edu