Introduction to Symplectic Topology

Dusa McDuff, Professor of Mathematics, Columbia University,Dietmar Salamon, Professor of Mathematics, ETH Zurich

Dusa McDuff was born in London, UK, in 1945. She studied Mathematics at the University of Edinburgh (B. Sc. (Hon) in 1967), at Cambridge University (Ph. D. in 1971, supervised by G.A. Reid), and also at Moscow University (1968-69 with I.M.Gelfand). After a postdoc in Cambridge, she lectured at the Universities of York and Warwick, before taking up a position in SUNY, Stony Brook, USA in 1978. She moved to Barnard College in 2008.

Dietmar Salamon was born in Bremen, West Germany, in 1953. Studied Mathematics at the Universities of Hannover and Bremen from 1971 to 1978. PhD in Mathematics at the University of Bremen in 1982 under the supervision of Didi Hinrichsen. Postdoc positions at UW Madison and ETH Z urich from 1983 to 1986. Lecturer, Reader, and Professor at the University of Warwick from 1986 to 1998. Professor at ETH Zurich since 1998.

FOUNDATIONS
1. From classical to modern
2. Linear symplectic geometry
3. Symplectic manifolds
4. Almost complex structures
SYMPLECTIC MANIFOLDS
5. Symplectic group actions
6. Symplectic Fibrations
7. Constructing Symplectic Manifolds
SYMPLECTOMORPHISMS
8. Area-preserving dieomorphisms
9. Generating functions
10. The group of symplectomorphisms
SYMPLECTIC INVARIANTS
11. The Arnold conjecture
12. Symplectic capacities
13. Questions of existence and uniqueness
14. Open problems
A. Smooth Maps