Symplectic Geometry and Holomorphic Curves

Course Descriptions and Lecturers:

Undergraduate and Beginning Graduate Lectures Overall Schedule

Lecturer:

Ingrid Daubechies, Princeton University

Title: An Introduction to Fourier Analysis and Wavelets, with some applications

Description: Infinite dimensional spaces, Fourier series, applications of Fourier series, Haar wavelets, smoother wavelets and their algorithms, sub-division and its role in computer graphics,
applications.

Teaching Assistants:

Cliona Golden, Princeton University
Cynthia Rudin, Princeton University

Advanced Graduate Lectures

Lecturers:

Eleny Ionel, University of Wisconsin
Dusa McDuff, IAS and SUNY Stony Brook

Title: Gromov--Witten invariants in symplectic geometry

Description: The first four lectures will be given by Eleny Ionel. Prof. Ionel will start by discussing the moduli space of J-holomorphic curves and the Gromov-Witten invariants, then present some of their properties and applications. Dusa McDuff will continue lecturing in the second week. Prof. McDuff will concentrate on discussing one application in detail, so that students can get the flavor of the needed analysis. The afternoon sessions will discuss examples, further applications and details of some proofs.

Teaching Assistants:

Olguta Buse, SUNY Stony Brook

Women-in-Science Seminar: Karen Uhlenbeck

Special Lectures: Yakov Eliashberg & Others

In Addition:

• research seminars
• course and seminar presentations by participants at every level
• working problem sessions

All participants are encouraged to interact with the local research community and work with scholars at higher and lower levels. Dinners and social activities are organized by the participants themselves. Lecturers and mentors serve on a volunteer basis and usually gain from their involvement in the program.