h-principle and its applications to contact and symplectic geometry.

Organized by

• Introduction to h-principle
  • The language of jets and Thom transversality theorem
  • Holonomic approximation theorem and its applications
  • The notion of h-principle.
  • Gromov's h-principle for open manifolds and its few classical applications
• Introduction to symplectic and contact topology
  • Notion of symplectic and contact structures
  • Darboux, Weinstein neighborhood theorems
  • Moser and Gray stability results
  • Lagrangian and Legendrian manifolds and their basic properties:
    • Lagrangian and Legendrian neighborhood theorems
    • Relation between Lagrangian and Legendrian submanifolds
  • Hamiltonian and Liouville vector fields:
    • Defintions and some examples
  • Lagrangian intersection problems
  • Formulations of Arnold conjectures with motivations
• Applications of h-princple to symplectic and contact geometry