Math 758 — Spring 2001 Topics in Symplectic Topology

The theory of J-holomorphic curves is a central tool in symplectic topology, and the first part of this course will focus on this theory. (Depending on the student overlap with the current seminar on this topic, this will be either a summary or a more detailed presentation.) The theory will be applied to "non-squeezing" results and to the study of symplectomorphism groups (e.g., the Flux Conjectures).

The course will be run as a participatory seminar, with the instructor giving the beginning lectures (and perhaps some later). It will be based mostly on readings from the literature, drawing on works of: Gromov, McDuff and Salamon, McDuff and Traynor, McDuff and Polterovich, and (time permitting) Gottlieb and Oprea.