# Part III - Symplectic Geometry

## Lectured by A. R. Pires, Lent 2018

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# Contents

- V Full version
- 1 Symplectic manifolds
- 1.1 Symplectic linear algebra
- 1.2 Symplectic manifolds
- 1.3 Symplectomorphisms and Lagrangians
- 1.4 Periodic points of symplectomorphisms
- 1.5 Lagrangian submanifolds and fixed points
- 2 Complex structures
- 3 Hamiltonian vector fields
- 3.1 Hamiltonian vector fields
- 3.2 Integrable systems
- 3.3 Classical mechanics
- 3.4 Hamiltonian actions
- 3.5 Symplectic reduction
- 3.6 The convexity theorem
- 3.7 Toric manifolds
- 4 Symplectic embeddings