- Course Description -
This seminar will be a first course in symplectic geometry and topology. We will definitely cover Part I of McDuff-Salamon (Chapters 1-4). We will also hopefully cover portions of Part II (Chapters 5-7) and discuss additional topics. Here is an outline of the first 4 chapters.
- Ch. 1: Hamiltonian mechanics, Lagrangian mechanics, general overview
- Ch. 2: linear symplectic geometry, affine non-squeezing, symplectic vector bundles
- Ch. 3: symplectic manifolds, homotopy method, Darboux theorem, submanifolds, almost complex geometry
- Ch. 4: almost complex structures, Kahler manifolds