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*