Teaching



Functions of a Complex Variable

One-semester course currently being taught at George Mason University.

Lecture notes (in progress)



Analytic Geometry and Calculus III

Five-week summer course taught at George Mason University, 2024.

Lecture notes



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