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MAT 562: Symplectic Geometry and Topology
Stony Brook Fall 2026 |
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All readings listed in the table below are from Foundations of Symplectic Geometry (to be posted here), except as noted. MS refers to McDuff&Salamon's Introduction to Symplectic Topology, 3rd Ed. Warner refers to his Foundations of Differentiable Manifolds and Lie Groups.
| Date | Topic | Read | Problem Set |
| 08/24, M | no lecture | MS Intro & Chapters 1,2 | ps1 |
| 08/26, W | Examples of symplectic manifolds | Sections 1.1/4/5, 2.1-4, B.1/2 MS Section 3.1 Warner pp69,70 | |
| 08/31, M | Hamiltonian flows |
| Moser's principle | |||
| Symplectic tubular neighborhood theorem | |||
| Lagrangian tubular neighborhood theorem | |||
| Almost complex structures | |||
| Complex structures and nondegenerate 2-forms | |||
| Pseudoholomorphic maps | |||
| Kahler manifolds | |||
| Torus actions | |||
| Moment maps | |||
| Convexity Theorem | |||
| Properties of moment polytopes | |||
| Kahler case | |||
| Symplectic quotients | |||
| Delzant theorem: surjectivity | |||
| Hamiltonian symplectic cut | |||
| Delzant theorem: injectivity | |||
| Symplectic cut |