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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 (work in progress, comments/corrections are encouraged), except as noted; please read the background material contained in Chapter 1 and Appendicies A,B as needed. MS refers to McDuff&Salamon's Introduction to Symplectic Topology, 3rd Ed. Warner refers to his Foundations of Differentiable Manifolds and Lie Groups. EG Notes refers to this.
| Date | Topic | Read | Problem Set |
| 08/24, M | no lecture | MS Intro & Chapters 1,2 EG Notes Sections 1,4 |
ps1 solutions |
| 08/26, W | Examples of symplectic manifolds | Sections 1.1/5 | |
| 08/31, M | Connections and flows of vector fields | Sections 2.1/2, B.1/2, MS pp94-98 Warner pp36-41,69-72 | |
| 09/02, W | Hamiltonian flows | Section 1.4, MS pp99-107 | |
| 09/09 | Moser's trick | Section 2.6; MS Section 3.2 Warner pp220-3 |
ps2 |
| 09/14 | Tubular neighborhood theorems | Section 2.3; MS Section 3.4 | |
| 09/16 | Almost complex structures | Section 1.3 |
| 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 |