Introduction to Pseudoholomorphic Curves
(a mini-course)

Time and Place

Tuesday and Thursday, 2:30-3:50, Altgeld 443.

Overview of the course

Pseudoholomorphic curves were first introduced and applied by Gromov in his remarkable paper of 1986. They have revolutionized the field of symplectic topology and have significantly impacted many other areas, including algebraic geometry and low-dimensional topology. Applications of these objects are still being actively developed in many new directions.

This mini-course will be comprised of three sections. The first will be an overview of the required results on Riemann surfaces, the domains of pseudoholomorphic curves. This will culminate in a discussion of the Deligne-Mumford compactness theorem. The second section 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 final section of the mini-course, we will survey some applications to symplectic topology.

Prerequisites

Basic differential geometry and topology.

Office Hours

Tuesday 12:00 to 2:00, or by appointment.

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