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Ryuma ORITA
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Topics in Differential Topology

For master’s students; Semester 1, Thu. Period 3 (irregular) · Graduate School of Science and Technology, Niigata University

Syllabus

Note

Held irregularly on Thu. Period 3; the first session is on 4/10.

Schedule (as of 2025-07-10)

  1. Manifolds, tangent spaces, and differentials (4/10)
  2. Vector fields and differential forms (4/24)
  3. Pullbacks, wedge products, and exterior derivatives (5/8)
  4. Definition of symplectic manifolds (5/15)
  5. Examples of symplectic manifolds (5/29)
  6. Cotangent bundles (6/12)
  7. Lie derivatives, interior products, and Cartan’s formula (7/10)
  8. Hamiltonian dynamics 1 (8/6)
  9. Hamiltonian dynamics 2 (8/6)
  10. Hamiltonian dynamics 3 (8/7)
  11. Hamiltonian dynamics 4 (8/7)