Teaching



Symplectic Geometry

One-semester graduate course taught in Spring Semester 2020 at the East China Normal University and Fall Semester 2021 at Saint Petersburg State University.

Lecture notes


I. Foundations

  1. Hamiltonian Functions
  2. The Structure of Symplectic Manifolds
  3. Group Actions and Hamiltonian Manifolds
  4. Reduction
  5. Reduction by Stages


II. Geometry of the Moment Map

  1. Morse Theory
  2. The Moment Polytope
  3. Delzant's Theorem
  4. Connections and Curvature
  5. The Duistermaat–Heckman Theorem
  6. The Exact Stationary Phase Approximation


III. Geometric Quantization

  1. Prequantization
  2. Complex Manifolds
  3. Kähler Quantization