The role of the Legendre duality in symplectic homology.
- Rio de Janeiro: IMPA, 2012.
- video online
The aim of this meeting is to give an account of recent developments in Symplectic Topology focusing on applications in different areas. Particular emphasis will be given to the use of pseudo-holomorphic curves in the construction of global invariants related to the dynamics of Hamiltonian flows. These methods were introduced by Gromov in his seminal work and had a major impact with Floer's invention of his homology theory. Recently, these techniques were incorporated in a bigger framework introduced by Eliashberg, Givental and Hofer called Symplectic Field Theory. Exciting questions and connections with other areas of mathematics have emerged since then, making it an extremely active research branch.