For master’s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University
Textbooks
- Ana Cannas da Silva, “Lectures on Symplectic Geometry”, Springer
Course contents
- Symplectic vector spaces
- Symplectic manifolds; cotangent bundles
- The tautological 1-form and the canonical 2-form
- Lagrangian submanifolds of cotangent bundles
- Conormal bundles; constructing symplectomorphisms
- The method of generating functions; applications to geodesic flow
- Periodic points; billiards; recurrence
- Isotopies and time-dependent vector fields; Lie derivatives
- Interior products; Cartan’s formula; Hamiltonian diffeomorphisms
- The Moser trick
- Moser stability; Moser isotopies; Darboux’s theorem
- Weinstein’s Lagrangian neighborhood theorem
- Weinstein’s tubular neighborhood theorem; the tangent space of the symplectomorphism group
- The Arnol’d conjecture; non-displaceability; partial symplectic quasi-states
- Heavy and superheavy sets
- Motion of a spinning top and superheavy sets