Instructor: S. Wang

Description: Symplectic geometry provides essential tools for Mechanics, Mathematical Physics, Topology, to name a few. The course will cover the basic materials such as the following: symplectic vector spaces, symplectic manifolds; Darboux's theorem, coadjoint orbits; Hamiltonian functions, moment maps, Poisson bracket; contact manifolds; quantization. Time permitting, we'll also present the recent work of Taubes on Seiberg-Witten theory in symplectic 4-dimensional manifolds.

Intended textbook: An Introduction to symplectic geometry by R. Berndt (Vol 26, Graduate Studies in Math. AMS, 2001)

Prerequisite is minimum: Some knowledge on manifolds, vector fields, differential forms from Math 8250/403 is sufficient. Knowledge on vector bundles, connections, Lie groups from Math 8650/456 is useful but not required.