9/1 Course logistics. Some questions about symplectic dynamics. Some ideas in the proof of two or infinity.
9/3 Symplectic manifolds. Submanifolds of symplectic manifolds.
9/8 Moser's trick. Some results about existence and uniqueness of symplectic structures. Darboux's Theorem; first steps in the proof.
9/10 Proof of Darboux's Theorem.
9/15 The canonical 1-form on a cotangent bundle. Standard neighborhoods of Lagrangian, contact and symplectic submanifolds. The Weinstein and Arnold conjectures.
9/20 Floer theory ideas for proving the Weinstein and Arnold conjectures.
9/22 - 10 /6 Definition and background for ECH. Sketch of proofs of foundational results. Reference: https://arxiv.org/pdf/1303.5789, Chapter 3
10/8 Some questions about 3D Reeb flows. Different proofs of the 3D Weinstein conjecture. ECH spectral invariants.