Math 378-02: Topics in Symplectic Geometry (Nov 8-Dec 8)
Instructor: L. Ng

In this minicourse, we'll hit some highlights of the vast subject of
symplectic geometry. We'll start with a basic introduction: symplectic
structures, almost complex structures, Kahler manifolds, Darboux's theorem,
Lagrangian submanifolds, Hamiltonian vector fields, contact structures.
Then, time permitting, we'll branch out to cover a selection of more
advanced topics to be chosen later (here class input is strongly
encouraged). These topics might include things like: group actions and
moment maps; J-holomorphic curves and Gromov compactness; Lagrangian
intersection Floer homology; contact homology; Heegaard Floer homology. Note
that these topics are each rather large in scope, and a fairly large amount
of detail will have to be omitted for any of these. Familiarity with basic
differential geometry and algebraic topology will be assumed.